The statistical evidence for the detrimental effect of exposure to low levels of lead on the cognitive capacities of children has been debated for several decades. In this paper I describe how two techniques from artificial intelligence and statistics help make the statistical evidence for the accepted epidemiological conclusion seem decisive. The first is a variable-selection routine in TETRAD III for finding causes, and the second a Bayesian estimation of the parameter reflecting the causal influence of Actual Lead (...) Exposure, a latent variable, on the measured IQ score of middle class suburban children. (shrink)
Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.
A fixed-parameter is an algorithm that provides an optimal solution to a combinatorial problem. This research-level text is an application-oriented introduction to the growing and highly topical area of the development and analysis of efficient fixed-parameter algorithms for hard problems. The book is divided into three parts: a broad introduction that provides the general philosophy and motivation; followed by coverage of algorithmic methods developed over the years in fixed-parameter algorithmics forming the core of the book; and a (...) discussion of the essential from parameterized hardness theory with a focus on W [1]-hardness, which parallels NP-hardness, then stating some relations to polynomial-time approximation algorithms, and finishing up with a list of selected case studies to show the wide range of applicability of the presented methodology. Aimed at graduate and research mathematicians, programmers, algorithm designers and computer scientists, the book introduces the basic techniques and results and provides a fresh view on this highly innovative field of algorithmic research. (shrink)
Parameters of a Bertalanffy type of temperature dependent growth model are fitted using data from a population of stone loach ( Barbatula barbatula ). Over two periods respectively in 1990 and 2010 length data of this population has been collected at a lowland stream in the central part of the Netherlands. The estimation of the maximum length of a fully grown individual is given special attention because it is in fact found as the result of an extrapolation over a (...) large interval of the entire lifetime. It is concluded that this parameter should not at forehand be set at one fixed value for the population at that location due to varying conditions over the years. (shrink)
Biologists studying short-lived organisms have become aware of the need to recognize an explicit temporal extend of a population over a considerable time. In this article we outline the concept and the realm of populations with explicit spatial and temporary boundaries. We call such populations “temporally bounded populations”. In the concept, time is of the same importance as space in terms of a dimension to which a population is restricted. Two parameters not available for populations that are only spatially defined (...) characterise temporally bounded populations: total population size, which is the total number of individuals present within the temporal borders, and total residence time, which is the sum of the residence times of all individuals. We briefly review methods to estimate these parameters. We illustrate the concept for the large blue butterfly (Maculinea nausithous) and outline insights into ecological and conservation-relevant processes that cannot be gained without the use of the concept. (shrink)
Model simplicity in curve fitting is the fewness of parameters estimated. I use a vector model of least squares estimation to show that degrees of freedom, the difference between the number of observed parameters fit by the model and the number of explanatory parameters estimated, are the number of potential dimensions in which data are free to differ from a model and indicate the disconfirmability of the model. Though often thought to control for parameterestimation, the AIC (...) and similar indices do not do so for all model applications, while goodness of fit indices like chi-square, which explicitly take into account degrees of freedom, do. Hypothesis testing with prespecified values for parameters is based on a metaphoric regulative subject/object schema taken from object perception and has as its goal the accumulation of objective knowledge. (shrink)
The statistical community has brought logical rigor and mathematical precision to the problem of using data to make inferences about a model’s parameter values. The TETRAD project, and related work in computer science and statistics, aims to apply those standards to the problem of using data and background knowledge to make inferences about a model’s specification. We begin by drawing the analogy between parameterestimation and model specification search. We then describe how the specification of a structural (...) equation model entails familiar constraints on the covariance matrix for all admissible values of its parameters; we survey results on the equivalence of structural equation models, and we discuss search strategies for model specification. We end by presenting several algorithms that are implemented in the TETRAD II program. (shrink)
nature of modern data collection and storage techniques, and the increases in the speed and storage capacities of computers. Statistics books from 30 years ago often presented examples with fewer than 10 variables, in domains where some background knowledge was plausible. In contrast, in new domains, such as climate research where satellite data now provide daily quantities of data unthinkable a few decades ago, fMRI brain imaging, and microarray measurements of gene expression, the number of variables can range into the (...) tens of thousands, and there is often limited background knowledge to reduce the space of alternative causal hypotheses. In such domains, non-automated causal discovery techniques appear to be hopeless, while the availability of faster computers with larger memories and disc space allow for the practical implementation of computationally intensive automated search algorithms over large search spaces. Contemporary science is not your grandfather’s science, or Karl Popper’s. Causal inference without experimental controls has long seemed as if it must somehow be capable of being cast as a kind of statistical inference involving estimators with some kind of convergence and accuracy properties under some kind of assumptions. Until recently, the statistical literature said not. While parameterestimation and experimental design for the effective use of data developed throughout the 20th century, as recently as 20 years ago the methodology of causal inference without experimental controls remained relatively primitive. Besides a cessation of hostilities from the majority of the statistical and philosophical communities (which has still only partially happened), several things were needed for theories of causal estimation to appear and to flower: well defined mathematical objects to represent causal relations; well defined connections between aspects of these objects and sample data; and a way to compute those connections. A sequence of studies beginning with Dempster’s work on the factorization of probability distributions [Dempster 1972] and culminating with Kiiveri and Speed’s [Kiiveri & Speed 1982] study of linear structural equation models, provided the first, in the form of directed acyclic graphs, and the second, in the form of the “local” Markov condition.. (shrink)
Inconsistency of attitudes and behavior is due to the probabilistic connection between responses or actions and the (not directly observable) dispositions on which they depend. Latent variable models provide criteria for recognizing when attitude and behavior depend on the same disposition. Statistical tests of such models and techniques of parameterestimation are described. The viewpoint proposed here and illustrated with empirical examples contrasts with the prevalent reliance on correlational models and methods.
This paper contrasts two information-theoretic approaches to statistical explanation: namely, (1) an analysis, which originated in my earlier research on problems of testing stochastic models of learning, based on an entropy-like measure of expected transmitted-information (and here referred to as the Expected-Information Model), and (2) the analysis, which was proposed by James Greeno (and which is closely related to Wesley Salmon's Statistical Relevance Model), based on the information-transmitted-by-a-system. The substantial differences between these analyses can be traced to the following basic (...) difference. On Greeno's view, the essence of explanation lies in the relevance relations expressed by the conditional probabilities that relate the explanans variables to the explanandum variables; on my view, in contrast, the essence of explanation lies in theories viewed as hypothetical structures which deductively entail conditional probability distributions linking the explanans variables and the explanandum variables. The explanatory power of a stochastic theory is identified with information (regarding the values of explanandum variables) which is "absorbed from" the explanans variables. While other information which is "absorbed from" the explanandum variables (through the process of parameterestimation, for example) reflects descriptive power of the theory. I prove that Greeno's measure of transmitted information is a limiting special case of the E-I model, but that the former, unlike the latter, makes no distinction between explanatory power and descriptive power. (shrink)
Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameterestimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.
Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameterestimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions (...) of matrix models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)
The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox (...) fail to account for the predictive utility of universal laws like All ravens are black. (shrink)
The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those (...) based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errors-in-variables model. (shrink)
Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing (...) the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. (shrink)
The hidden-variables model constructed by Karl Hess and Walter Philipp is claimed by its authors to exploit a "loophole" in Bell's theorem; according to Hess and Philipp, the parameters employed in their model extend beyond those considered by Bell. Furthermore, they claim that their model satisfies Einstein locality and is free of any "suspicion of spooky action at a distance." Both of these claims are false; the Hess-Philipp model achieves agreement with the quantum-mechanical predictions, not by circumventing Bell's theorem, but (...) via ParameterDependence. (shrink)
This work develops an epistemology of measurement, that is, an account of the conditions under which measurement and standardization methods produce knowledge as well as the nature, scope, and limits of this knowledge. I focus on three questions: (i) how is it possible to tell whether an instrument measures the quantity it is intended to? (ii) what do claims to measurement accuracy amount to, and how might such claims be justified? (iii) when is disagreement among instruments a sign of error, (...) and when does it imply that instruments measure different quantities? Based on a series of case studies conducted in collaboration with the US National Institute of Standards and Technology (NIST), I argue for a model-based approach to the epistemology of physical measurement. To measure a physical quantity, I argue, is to estimate the value of a parameter in an idealized model of a physical process. Such estimation involves inference from the final state (‘indication’) of a process to the value range of a parameter (‘outcome’) in light of theoretical and statistical assumptions. Contrary to contemporary philosophical views, measurement outcomes cannot be obtained by mapping the structure of indications. Instead, measurement outcomes as well as claims to accuracy, error and quantity individuation can only be adjudicated relative to a choice of idealized modelling assumptions. (shrink)
The question of whether time is its own best representation is explored. Though there is theoretical debate between proponents of internal models and embedded cognition proponents (e.g. Brooks R 1991 Artificial Intelligence 47 139–59) concerning whether the world is its own best model, proponents of internal models are often content to let time be its own best representation. This happens via the time update of the model that simply allows the model’s state to evolve along with the state of the (...) modeled domain. I argue that this is neither necessary nor advisable. I show that this is not necessary by describing how internal modeling approaches can be generalized to schemes that explicitly represent time by maintaining trajectory estimates rather than state estimates. Though there are a variety of ways this could be done, I illustrate the proposal with a scheme that combines filtering, smoothing and prediction to maintain an estimate of the modeled domain’s trajectory over time. I show that letting time be its own representation is not advisable by showing how trajectory estimation schemes can provide accounts of temporal illusions, such as apparent motion, that pose serious difficulties for any scheme that lets time be its own representation. (shrink)
It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by (...) a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables. (shrink)
In 'Subjunctive Conditionals: Two Parameters vs. Three' Pavel Tichy articulates and defends a three-parameter account of counterfactuals. In the paper, he responds to a well known objection against the validity of various forms of inference, in particular strengthening of the antecedent, contraposition, and hypothetical syllogism. In this paper, I argue that his response to the objection is inadequate. I then propose an alternative form of the three-parameter account of counterfactuals that avoids the objection in question.
Big History - an integral conception of the past since the Big Bang until today - is a novel subject of cross-disciplinary interest. The concept was construed in the 1980-1990s simultaneously in different countries, after relevant premises had matured in the sciences and humanities. Various versions and traditions of Big History are considered in the article. Particularly, most of the Western authors emphasize the idea of equilibrium, and thus reduce cosmic, biological, and social evolution to the mass-energy processes; the informational (...)parameter involving all mental and spiritual aspects are seen as epiphenomena of material structures' complication that do not play their own role in evolution. In Russian tradition ascending to A. Bogdanov, E. Bauer, I. Prigogine, and E. Jantsch, sustainable non-equilibrium patterns are used. This implies attention to the pan-material sources and evolution of mental capacities and spiritual culture (as basic anti-entropy instruments) and humans' growing intervention in the material processes on Earth and outside it. The non-equilibrium approach in the context of modern control and self-organization theories, alters the portrayal of the past, and still more dramatically, estimation of the civilization's potential perspectives. (shrink)
It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by (...) a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables. (shrink)
This paper separates conditional parameter estima- tion, which consistently raises test set accuracy on statistical NLP tasks, from conditional model struc- tures, such as the conditional Markov model used for maximum-entropy tagging, which tend to lower accuracy. Error analysis on part-of-speech tagging shows that the actual tagging errors made by the conditionally structured model derive not only from label bias, but also from other ways in which the independence assumptions of the conditional model structure are unsuited to linguistic sequences. (...) The paper presents new word-sense disambiguation and POS tagging experiments, and integrates apparently conflicting reports from other recent work. (shrink)
We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas.
Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about (...) half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. (shrink)
One of the most pressing issues in understanding abduction is whether it is an instinct or an inference. For many commentators find it paradoxical that new ideas are products of an instinct and products of an inference at the same time. Fortunately, Lorenzo Magnani’s recent discussion of animal abduction sheds light on both instinctual and inferential character of Peircean abduction. But, exactly for what reasons are Peirce and Magnani so convinced that animal abduction can provide us with a novel perspective? (...) Inspired by Peirce’s and Magnani’s discussions of animal abduction, I propose to compare Peirce’s and Magnani’s views of animal abduction with the estimative power of non-human animals and humans, which was one of the internal senses in medieval psychology. (shrink)
This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective stress–strain curve and thermal conductivity of the composite material, finite-element analysis (FEA), in conjunction with the embedded fibre method (EFM), is used. Variable nanotube geometry, alignment and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the (...) EFM. Next, incremental and iterative FEA approaches are used for the determination of the nonlinear properties of the nanocomposite. For the determination of the electrical properties, a spanning network identification algorithm is used. First, a realistic nanotube morphology is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in a representative volume element. Then, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's current law is used in conjunction with FEA to solve for the voltages and currents in the system and thus calculate the effective electrical conductivity of the nanocomposite. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone and determines the effective conductivity. Monte Carlo analysis of 500 random microstructures is performed to capture the stochastic nature of the fibre generation and to derive statistically reliable results. The models are validated by comparison with various experimental datasets reported in the recent literature. (shrink)
Quantitative genetics (QG) analyses variation in traits of humans, other animals, or plants in ways that take account of the genealogical relatedness of the individuals whose traits are observed. “Classical” QG, where the analysis of variation does not involve data on measurable genetic or environmental entities or factors, is reformulated in this article using models that are free of hypothetical, idealized versions of such factors, while still allowing for defined degrees of relatedness among kinds of individuals or “varieties.” The gene (...) - free formulation encompasses situations encountered in human QG as well as in agricultural QG. This formulation is used to describe three standard assumptions involved in classical QG and provide plausible alternatives. Several concerns about the partitioning of trait variation into components and its interpretation, most of which have a long history of debate, are discussed in light of the gene-free formulation and alternative assumptions. That discussion is at a theoretical level, not dependent on empirical data in any particular situation. Additional lines of work to put the gene-free formulation and alternative assumptions into practice and to assess their empirical consequences are noted, but lie beyond the scope of this article. The three standard QG assumptions examined are: (1) partitioning of trait variation into components requires models of hypothetical, idealized genes with simple Mendelian inheritance and direct contributions to the trait; (2) all other things being equal, similarity in traits for relatives is proportional to the fraction shared by the relatives of all the genes that vary in the population (e.g., fraternal or dizygotic twins share half of the variable genes that identical or monozygotic twins share); (3) in analyses of human data, genotype-environment interaction variance (in the classical QG sense) can be discounted. The concerns about the partitioning of trait variation discussed include: the distinction between traits and underlying measurable factors; the possible heterogeneity in factors underlying the development of a trait; the kinds of data needed to estimate key empirical parameters; and interpretations based on contributions of hypothetical genes; as well as, in human studies, the labeling of residual variance as a non-shared environmental effect; and the importance of estimating interaction variance. (shrink)
The literature on time perception is discussed. This is done with reference both to the ''cognitive-timer'' model for time estimation and to the subjective experience of apparent duration. Three assumptions underlying the model are scrutinized. I stress the strong interplay among attention, arousal, and time perception, which is at the base of the cognitive-timer model. It is suggested that a multiplicative function of two key components (the number of subjective time units and their size) should predict apparent duration. Implications (...) for other cognitive domains are drawn, and in particular an analogy is suggested between apparent duration and apparent movement. (shrink)
The proponents of strong lexicalism hold the view that “words” are formed in the lexicon and are opaque for the syntax ((Dowty 1979), (DiSciullo and Williams 1987), (Jackendoff 1990) and many others). Modular morphology, on the other hand, offers the possibility that at least some words are partially formed in the syntax ((Baker 1988), (Borer 1988), (Hale and Keyser 1994), (Chomsky 1995) and many others). In (Stechow 1995) and (Stechow 1996) it has been argued that facts observed with German wieder (...) “again” cannot be accounted for within the framework of strong lexicalism and therefore favour the second position. The authors of this paper want to check these claims by investigating the behaviour of the German adverb fast “ almost”, the other classical adverb to which the method of decomposition has been applied in the linguistic literature (cf. (McCawley 1971)). Most adverbs cannot look into lexical decomposition structures, but some can. In order to have a suitable name, let us call these D-adverbs. Again and almost are the prototypical representatives of this class. The method adopted is to investigate whether fast has access to different aspects of verbal meaning depending on its position. Following (Dowty 1979), resultative verbs and prepositions are decomposed into BECOME + XP, where XP is the result state. Agentive verbs contain an additional AGENT part. Other thematic relations connecting the subject and the event are HOLDER and cause. If the syntax tells us that an adverb like wieder or fast must have wide scope with respect to BECOME, then we expect other readings than in a configuration where fast can have narrow scope with respect to BECOME. In other words, the motivation for decomposition is syntactic and semantic. The idea is that certain function projections in the classical VP have a meaning and hence scopally interact with adverbs. (shrink)
The proponents of strong lexicalism hold the view that “words” are formed in the lexicon and are opaque for the syntax ((Dowty 1979), (DiSciullo and Williams 1987), (Jackendoff 1990) and many others). Modular morphology, on the other hand, offers the possibility that at least some words are partially formed in the syntax ((Baker 1988), (Borer 1988), (Hale and Keyser 1994), (Chomsky 1995) and many others). In (Stechow 1995) and (Stechow 1996) it has been argued that facts observed with German wieder (...) “again” cannot be accounted for within the framework of strong lexicalism and therefore favour the second position. The authors of this paper want to check these claims by investigating the behaviour of the German adverb fast “ almost”, the other classical adverb to which the method of decomposition has been applied in the linguistic literature (cf. (McCawley 1971)). Most adverbs cannot look into lexical decomposition structures, but some can. In order to have a suitable name, let us call these D-adverbs. Again and almost are the prototypical representatives of this class. The method adopted is to investigate whether fast has access to different aspects of verbal meaning depending on its position. Following (Dowty 1979), resultative verbs and prepositions are decomposed into BECOME + XP, where XP is the result state. Agentive verbs contain an additional AGENT part. Other thematic relations connecting the subject and the event are HOLDER and cause. If the syntax tells us that an adverb like wieder or fast must have wide scope with respect to BECOME, then we expect other readings than in a configuration where fast can have narrow scope with respect to BECOME. In other words, the motivation for decomposition is syntactic and semantic. The idea is that certain function projections in the classical VP have a meaning and hence scopally interact with adverbs. (shrink)
Scarce public resources requiretrade-offs between competing programs indifferent sectors, and the careful allocationof fixed resources within a single sector. Thispaper argues that a general quality of lifeinstrument encompassing health-related andnon-health-related components is suitable fordetermining the best trade-offs betweensectors. Further, this paper suggests thatsubjective well-being shows the propertiescrucial to a general quality of life measureand has additional advantages that makes itparticularly useful for the allocation ofpublic and health care resources. The paperargues that Western societies are in anunusually prosperous situation today whichallows (...) to concentrate efforts not only onreducing harm but also on improving positivestates of health. Further, subjectivewell-being can be evaluated from the patient'sperspective and incorporates a valuation oflife expectancy. Criteria required for anappropriate questionnaire that measuressubjective well-being are presented. (shrink)
The literature on speculative bubbles in foreign exchange rates is voluminous, with much of it failing to reject the presence of bubbles in many exchange markets.1 Serious testing of this issue began with the work of Meese (1986), Evans (1986), and Woo (1987). Each used a different approach, and each found evidence failing to reject the presence of bubbles in at least some exchange markets.
It is claimed that the English genitive marker 's' suprisingly mirrors- at least in some dialects of English - the three main different usage of the mono-morphemic reflexives such as 'se' in French. A solution to this paradox already noted by Jespersen (1918) is proposed drawing on Watkins paradox according to which the study of what looks like 'social' parameters might be relevant for linguistics.
I comment on the controversy between McCloskey and Ziliak and Hoover and Siegler on statistical versus economic significance, in the March 2008 issue of the Journal of Economic Methodology. I argue that while McCloskey and Ziliak are right in emphasizing ?real error?, i.e. non-sampling error that cannot be eliminated through specification testing, they fail to acknowledge those areas in economics, e.g. rational expectations macroeconomics and asset pricing, where researchers clearly distinguish between statistical and economic significance and where statistical testing plays (...) a relatively minor role in model evaluation. In these areas models are treated as inherently misspecified and, consequently, are evaluated empirically by other methods than statistical tests. I also criticize McCloskey and Ziliak for their strong focus on the size of parameter estimates while neglecting the important question of how to obtain reliable estimates, and I argue that significance tests are useful tools in those cases where a statistical model serves as input in the quantification of an economic model. Finally, I provide a specific example from economics ? asset return predictability ? where the distinction between statistical and economic significance is well appreciated, but which also shows how statistical tests have contributed to our substantive economic understanding. (shrink)
In this paper, a mathematical model of the respiratory mechanics is used to reproduce experimental signal waveforms acquired from three newborn lambs. As the main challenge is to determine specific lamb parameters, a sensitivity analysis has been realized to find the most influent parameters, which are identified using an evolutionary algorithm. Results show a close match between experimental and simulated pressure and flow waveforms obtained during spontaneous ventilation and pleural pressure variations acquired during the application of positive pressure, since root (...) mean square errors equal to 0.0119, 0.0052 and 0.0094. The identified parameters were discussed in light of previous knowledge of respiratory mechanics in the newborn. (shrink)
A great deal of discussion in recent philosophy of language has centered on the idea that there might be hidden contextual parameters in our sentences. But relatively little attention has been paid to what those parameters themselves are like, beyond the assumption that they behave more or less like variables do in logic. My goal in this paper is to show this has been a mistake. I shall argue there are at least two very different sorts of contextual parameters. One (...) is indeed basically like variables in logic, but the other is very different, and much more like overt referring expressions. This result is of interest in its own right, to those of us who are concerned to map out the details of the semantic and pragmatic workings of language. But it will have some wider morals as well. One of the important issues behind the debate over hidden parameters has been how we can posit hidden structure in language, and how far such structure can stray from the intuitive forms and contents speakers see in communication. I shall argue that one sort of hidden parameter is surprisingly close to the contents and forms speakers find intuitive, while another is more remote. I shall show that the.. (shrink)
A comparison of Neyman's theory of interval estimation with the corresponding subjective Bayesian theory of credible intervals shows that the Bayesian approach to the estimation of statistical parameters allows experimental procedures which, from the orthodox objective viewpoint, are clearly biased and clearly inadmissible. This demonstrated methodological difference focuses attention on the key difference in the two general theories, namely, that the orthodox theory is supposed to provide a known average frequency of successful estimates, whereas the Bayesian account provides (...) only a coherent ordering of degrees of belief and a subsequent maximization of subjective expected utilities. To rebut the charge of allowing biased procedures, the Bayesian must attack the foundations of orthodox, objectivist methods. Two apparently popular avenues of attack are briefly considered and found wanting. The first is that orthodox methods fail to apply to the single case. The second is that orthodox methods are subject to a typical Humean regress. The conclusion is that orthodox objectivist methods remain viable in the face of the subjective Bayesian alternative — at least with respect to the problem of statistical estimation. (shrink)
The role of ethics in technology development has been often questioned, especially in the early days of societal reflection of technology. However, the situation has changed dramatically. Ethical consideration now is generally declared to be indispensable in shaping technology in a socially acceptable and sustainable way. The expectations of ethics are large; often even a kind of “New Ethics” is postulated. In the present paper an over-estimation of the role of ethics for technology development is rejected. It is argued (...) that ethical reflection is, indeed, indispensable in certain problem areas and situation types; but there is, on the other hand, space for technology development free from the requirement for ethical reflection. The absence of a requirement for ethical reflection, however, always has to be considered relative to some “morale provisoire” (provisional morality) as an accepted normative framework within which technology development may occur without explicit ethical reflection. If this framework, however, is doubted or is shown to be insufficient the situation changes completely. Ethical reflection in this case becomes necessary, to consider this normative framework in order to offer modifications or supplements. (shrink)
We assess Cartwright's models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbach's screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.
One of the major problems in the implementation of the precautionary principle in environmental cases is the estimation of the weight of evidence. In this paper we propose a formal method that determines the weight of evidence based on the specific parameters of a given case. The proposed method is based on an artificial intelligence approach called fuzzy logic, which is commonly used as an interface between logic and human perception, and often applied to computer-based complex decision making. We (...) use one fuzzy expert system that provides a quantification of the estimated environmental damage, and a second fuzzy expert system that computes the weight of evidence in a given case. The proposed expert system can be easily defined and adjusted by regulators and environmental science and policy experts. (shrink)
Let p be a set. A function φ is uniformly σ 1 (p) in every admissible set if there is a σ 1 formula φ in the parameter p so that φ defines φ in every σ 1 -admissible set which includes p. A theorem of Van de Wiele states that if φ is a total function from sets to sets then φ is uniformly σ 1R in every admissible set if anly only if it is E-recursive. A function (...) is ES p -recursive if it can be generated from the schemes for E-recursion together with a selection scheme over the transitive closure of p. The selection scheme is exactly what is needed to insure that the ES p - recursively enumerable predicates are closed under existential quantification over the transitive closure of p. Two theorems are established: a) If the transitive closure of p is countable than a total function on sets is ES p -recursive if and only if it is uniformly σ 1 (p) in every admissible set. b) For any p, if φ is a function on the ordinal numbers then φ is ES p -recursive if and only if it is uniformly ∑ 1 (p) in every admissible set. (shrink)
A model is proposed for the population dynamics of an annual plant (Sesbania vesicaria) with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). A simple linear matrix model is deduced from the life cycle graph. The dominant eigenvalue of the projection matrix is estimated from demographic parameters derived from field studies. The estimated values for population growth rate () indicates that the study population should be experiencing a rapid exponential increase, but (...) this was not the case in our population.The addition of density dependent effects on seedling survivorship and adult fecundity, effects for which field studies provide evidence, considerably improves our model. Depending on the demographic parameters, the model leads to stable equilibrium, oscillations, or chaos. Study of the behaviour of this model in the parameter space shows that the existence of a seed bank allows higher among-year variation of adult fecundity, without leaving the region of demographic stability. Field data obtained over 3 years confirm this prediction. (shrink)
In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the (...) paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms. (shrink)
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.
In earlier work we have described how computer algebra may be used to derive composite rate laws for complete systems of equations, using the mathematical technique of Gröbner Bases (Bennett, Davenport and Sauro, 1988). Such composite rate laws may then be fitted to experimental data to yield estimates of kinetic parameters.Recently we have been investigating the practical application of this methodology to the estimation of kinetic parameters for the closed two enzyme system of aspartate aminotransferase (AAT) and malate dehydrogenase (...) (MDH) (Fisher 1990a; Fisher 1990b; Bennett and Fisher, 1990). (shrink)
Parameters in E-Z Reader models are estimated on the basis of a simple data set consisting of 30 means. Because of heavy aggregation, the data have a severe problem of multicolinearity and are unable to adequately constrain parameter values. This could give the model more power than the empirical data warrant. Future models should exploit the richness of eye movement data and avoid excessive aggregation.
Deterministic models in population dynamics often are really approximations to stochastic models, justified by an appeal to the law of large numbers. It is proposed to call such models pseudodeterministic. Four questions are discussed in this article: (1) What errors may be made by equating deterministically predicted values to expectations? (2) When, and in what sense, may numbers be assumed to be large? (3) How large are the variances, coefficients of variations, etc., as assigned to the variables in the stochastic (...) versions of the models? (4) What role may pseudodeterministic models play in empirical research, where problems of statistical reliability arise?As an example, a modified Nicholson-Bailey model of the interaction between insect parasitoids and their hosts is discussed; the modification consists of assigning a random (density-independent) mortality to the parasitoid population. A stochastic version of this model is discussed. The expectation of the final host density is compared with the value computed from the deterministic model. The latter value is systematically lower than the former. The magnitude of the difference depends on parameter values. The variability to be expected with the stochastic model is characterized by the coefficient of variation of the final host density; its dependence on parameter values and initial conditions is discussed. It is concluded that it is worthwhile in practical applications to estimate parasitoid mortality, and that the coefficient of variation in real situations may be far from negligible. (shrink)
Professor Franklin is correct to say that there are significant areas of agreement between his account of formal science (Franklin, 1994) and my critique of his account. We both agree that the domain-independence exhibited by the formal sciences is ontologically and epistemically interesting, and that the concept of ‘structure’ must be central in any analysis of domain-independence. We also agree that knowledge of the structural, relational properties of physical systems should count as empirical knowledge, and that it makes sense to (...) talk about an empirical ‘science’ of structure. Where we disagree is over the frequency of occasions where ‘practical certainty’ is actually attained: Franklin argues that practical certainty is not uncommon in the formal sciences, while I argue that there are barriers to practical certainty that Franklin fails to appreciate. In Franklin’s response, he briefly presents and offers criticisms of my two main arguments against his central thesis. Franklin asserts that the flaw in my first argument is that it does not appreciate that modern mathematical models exhibit structural stability, and thus that many of their predictions are robust under small variations in input or parameter values (and hence, insensitive to the inevitable gaps between estimates and actual values). Nevertheless, what I had in mind in using the term ‘realistic modelling situations’ were models of fairly complex natural systems, such as the dripping faucet, spruce budworm and ecosystem ecology examples. My objection is not that mathematical models of such systems cannot legitimately and accurately describe structural properties that are genuinely predicable of real-world systems, but simply that for.. (shrink)
We report two issues concerning diverging sets of Bayesian (conditional) probabilities-divergence of "posteriors"-that can result with increasing evidence. Consider a set P of probabilities typically, but not always, based on a set of Bayesian "priors." Fix E, an event of interest, and X, a random variable to be observed. With respect to P, when the set of conditional probabilities for E, given X, strictly contains the set of unconditional probabilities for E, for each possible outcome X = x, call this (...) phenomenon dilation of the set of probabilities (Seidenfeld and Wasserman 1993). Thus, dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962). (1) In a wide variety of models for Robust Bayesian inference the extent to which X dilates E is related to a model specific index of how far key elements of P are from a distribution that makes X and E independent. (2) At a fixed confidence level, (1-α), Classical interval estimates A n for, e.g., a Normal mean θ have length O(n -1/2 ) (for sample size n). Of course, the confidence level correctly reports the (prior) probability that θ ∈ A n ,P(A n )=1-α , independent of the prior for θ . However, as shown by Pericchi and Walley (1991), if an ε -contamination class is used for the prior on the parameter θ , there is asymptotic (posterior) dilation for the A n , given the data. If, however, the intervals A ′ n are chosen with length $O(\sqrt{\log (\text{n})/\text{n})}$ , then there is no asymptotic dilation. We discuss the asymptotic rates of dilation for ClassClassical and Bayesian interval estimates and relate these to Bayesian hypothesis testing. (shrink)
Simple chaotic systems are useful tools for testing methods for use in numerical weather simulations owing to their transparency and computational cheapness. The Lorenz system was used here; the full system was defined as ‘truth’, whereas a truncated version was used as a testbed for parametrization schemes. Several stochastic parametrization schemes were investigated, including additive and multiplicative noise. The forecasts were started from perfect initial conditions, eliminating initial condition uncertainty. The stochastically generated ensembles were compared with perturbed parameter ensembles (...) and deterministic schemes. The stochastic parametrizations showed an improvement in weather and climate forecasting skill over deterministic parametrizations. Including a temporal autocorrelation resulted in a significant improvement over white noise, challenging the standard idea that a parametrization should only represent sub-gridscale variability. The skill of the ensemble at representing model uncertainty was tested; the stochastic ensembles gave better estimates of model uncertainty than the perturbed parameter ensembles. The forecasting skill of the parametrizations was found to be linked to their ability to reproduce the climatology of the full model. This is important in a seamless prediction system, allowing the reliability of short-term forecasts to provide a quantitative constraint on the accuracy of climate predictions from the same system. (shrink)
The design of the bronchial tree has largely been proposed as a model of optimal design from a physical-functional perspective. However, the distributive function of the airway may be more related to a geometrical than a physical problem. The bronchial tree must distribute a three dimensional volume of inspired air on a two dimensional alveolar surface, included in a limited volume. It is thus valid to ask whether an optimal bronchial tree from a physical perspective is also optimum from a (...) geometrical point of view. In this paper we generate a simple geometric model for the branching pattern of the bronchial tree, deducing relationships that permit estimation of the departures from the geometrical optimum of each bifurcation. We also, for comparative purposes, estimate the departures from the physical optimum. From the geometrical assumptions: i) a symmetrical dichotomic fractal design, ii) with minimum volume and iii) maximum dispersion of the terminal points; and several simulations we suggest that the optimality is characterized by a bifurcation angle Θ ∼ 60° and a length reduction scale γ = (1/2)1/3 = 0.7937. We propose distances from the physical and geometrical optimality defined as Euclidean distances from the expected optima. We show how the advanced relationships and the distances can be used to estimate departures from the optimality in bronchographs of four species. We found lower physical and geometrical departures in the distal zone than those of the proximal zones, as well as lower physical than geometrical departures from optimality. (shrink)
A rational justification for therapeutic decisions can be developed using probability and decision theory. The set of treatments and their outcomes or consequences, which are states of health, have to be defined; and estimates made of the probabilities of outcomes, their utilities, and the costs of treatments. Most difficult is the estimation of utilities of states of health but this may be possible using a wagering technique. Until it is possible to establish some equivalence between utility and money, costs (...) may be introduced by measuring the efficiency of treatment by comparing expected utilities per unit cost. The whole method is examined practically in a plausible clinical setting. Emphasis is laid on the value of testing the completed model using a computer to get an intimate feel of the problem using different assumptions and different values for all the parameters. (shrink)
Abstract Instrumental variables estimation is widely applied in econometrics. To implement the method, it is necessary to specify a vector of instruments. In this paper, it is argued that there are compelling reasons to use the data for instrument selection, but that it is desirable to ensure the resulting estimator still behaves in the way predicted by standard textbook theory. These arguments lead one to propose three criteria for data based instrument selection. The remainder of the paper assesses the (...) extent to which these criteria are met by two algorithms for data based instrument selection. The first algorithm is the method of structurally ordered instrumental variables proposed in the context of economy-wide linear simultaneous equation models. The second algorithm is proposed in the context of the method of generalized instrumental variables, which is commonly used to estimate the parameters of Euler equation models. (shrink)
Leibniz’s De incerti aestimatione, which contains his solution to the division problem, has not received much attention, let alone much appreciation. This is surprising because it is in this work that the definition of probability in terms of equally possible cases appears for the first time. The division problem is used to establish and test probability theory; it can be stated as follows: if two players agree to play a game in which one has to win a certain number of (...) rounds in order to win the pool, but if they break the game off before either of them has won the required number of rounds, how should the pool be distributed? Our article has two aims: it provides the readers with the first published English translation of De incerti aestimatione, and it also gives them a brief commentary that explains Leibniz’s philosophical and mathematical concepts necessary in order to understand this work. The translation is as literal as possible throughout; it shows how Leibniz struggled at times to find a solution to the division problem and how he approached it from different angles. The commentary discusses Leibniz’s views on four key concepts: fairness, hope, authority and possibility. The commentary then outlines how Leibniz attempted to solve the problem of division. (shrink)
The distinction between explanation and prediction has received much attention in recent literature, but the equally important distinction between explanation and description (or between prediction and description) remains blurred. This latter distinction is particularly important in the social sciences, where probabilistic models (or theories) often play dual roles as explanatory and descriptive devices. The distinction between explanation (or prediction) and description is explicated in the present paper in terms of information theory. The explanatory (or predictive) power of a probabilistic model (...) is identified with information taken from (or transmitted by) the environment (e.g., the independent, experimentally manipulated variables), while the descriptive power of a model reflects additional information taken from (or transmitted by) the data. Although information is usually transmitted by the data in the process of estimating parameters, it turns out that the number of free parameters is not a reliable index of transmitted information. Thus, the common practice of treating parameters as degrees-of-freedom in testing probabilistic models is questionable. Finally, this information-theoretic analysis of explanation, prediction, and description suggests ways of resolving some recent controversies surrounding the pragmatic aspects of explanation and the so-called structural identity thesis. (shrink)
The Representational Theory of Measurement conceives measurement as establishing homomorphisms from empirical relational structures into numerical relation structures, called models. There are two different approaches to deal with the justification of a model: an axiomatic and an empirical approach. The axiomatic approach verifies whether a given relational structure satisfies certain axioms to secure homomorphic mapping. The empirical approach conceives models to function as measuring instruments by transferring observations of an economic system into quantitative facts about that system. These facts are (...) evaluated by their accuracy and precision. Precision is achieved by least squares methods and accuracy by calibration. For calibration standards are needed. Then two strategies can be distinguished. One aims at estimating the invariant (structural) equations of the system. The other strategy is to use known stable facts about the system to adjust the model parameters. For this strategy, the requirement of models as homomorphic mappings has been dropped. (shrink)
Nanotechnology: Considering the Complex Ethical, Legal, and Societal Issues with the Parameters of Human Performance Content Type Journal Article Pages 265-275 DOI 10.1007/s11569-008-0047-6 Authors Linda MacDonald Glenn, Albany Medical College/Center Alden March Bioethics Institute Albany NY 12208 USA Jeanann S. Boyce, Montgomery College Dept. of Computer Science and Business 7600 Takoma Avenue Takoma Park MD 20912 USA Journal NanoEthics Online ISSN 1871-4765 Print ISSN 1871-4757 Journal Volume Volume 2 Journal Issue Volume 2, Number 3.
Student cheating and reporting of that cheating represents one form of organizational wrong-doing and subsequent whistle-blowing, in the context of an academic organization. Previous research has been hampered by a lack of information concerning the validity of survey responses estimating the incidence of organizational wrongdoing and whistle-blowing. An innovative method, the Randomized Response Technique (RRT), was used here to assess the validity of reported incidences of wrongdoing and whistle-blowing. Surprisingly, our findings show that estimates of these incidences did not vary (...) significantly when RRT questionnaire results were compared to those obtained from standard surveys. In fact, a large number of business undergraduates admitted cheating while only a small percentage reported peers'' cheating when they observed it. These results should be sobering for managers and their implications are considered in some detail. (shrink)
In this empirical study, we present two new models that are corporate ethics based. The first model numerically quantifies the corporate value index (CV-Index) based on a set of predefined parameters and the second model estimates the market-to-book values of equity in relation to the CV-Index as well as other parameters. These models were applied to Canadian companies listed on the Toronto Stock Exchange (TSX). Through our analysis, we found statistically significant evidence that corporate values (CV-Index) positively correlated with firm (...) performance. The results are even more significant for firms with low market-to-book values. Our empirical findings suggest that corporate ethics is vital for management, employees, shareholders, stakeholders, and the community at large. In addition, we have tested and confirmed five hypotheses that are used to illustrate corporate ethics behavior and performance. (shrink)
Although widely recognized as one of sociology's true classics. Max Weber's The Protestant Ethic and the Spirit of Capitalism has largely failed to influence the development of sociological theory in the United States. Because it has been read almost exclusively as a study of the "role of ideas" in economic development, its diverse and multifaceted theoretical contributions generally have been neglected. This study explicitly calls attention to The Protestant Ethic as a theoretical treatise by examining this classic in reference to (...) four major debates in postwar sociological theory in the United States. Moreover, it demarcates an array of major parameters in American theorizing. The conclusion speculates upon the reasons for the strong opposition to The Protestant Ethic's theoretical lessons and argues that a style of theorizing unique to sociology in the United States has erected firm barriers against this classic text. (shrink)
Predictions about the health risks of low level radiation combine two sorts of measures. One estimates the amount and kinds of radiation released into the environment, and the other estimates the adverse health effects. A new field called health physics integrates and applies nuclear physics to cytology to supply both these estimates. It does so by first determining the kinds of effects different types of radiation produce in biological organisms, and second, by monitoring the extent of these effects produced by (...) given levels of exposure. This essay examines the interplay between evidential constraints and external, contextual interests and values in studying the biological hazards of radiation. By analyzing the debate over linear vs. quadratic dose response models, the essay focuses on problems of developing quantitative, rather than qualitative, estimates of the risks of increased cancer incidence in an exposed population. (shrink)
A general conceptual framework for large-scale neocortical dynamics based on data from many laboratories is applied to a variety of experimental designs, spatial scales, and brain states. Partly distinct, but interacting local processes (e.g., neural networks) arise from functional segregation. Global processes arise from functional integration and can facilitate (top down) synchronous activity in remote cell groups that function simultaneously at several different spatial scales. Simultaneous local processes may help drive (bottom up) macroscopic global dynamics observed with electroencephalography (EEG) or (...) magnetoencephalography (MEG). A local/global dynamic theory that is consistent with EEG data and the proposed conceptual framework is outlined. This theory is neutral about properties of neural networks embedded in macroscopic fields, but its global component makes several qualitative and semiquantitative predictions about EEG measures of traveling and standing wave phenomena. A more general “metatheory” suggests what large-scale quantitative theories of neocortical dynamics may be like when more accurate treatment of local and nonlinear effects is achieved. The theory describes the dynamics of excitatory and inhibitory synaptic action fields. EEG and MEG provide large-scale estimates of modulation of these synaptic fields around background levels. Brain states are determined by neuromodulatory control parameters. Purely local states are dominated by local feedback gains and rise and decay times of postsynaptic potentials. Dominant local frequencies vary with brain region. Other states are purely global, with moderate to high coherence over large distances. Multiple global mode frequencies arise from a combination of delays in corticocortical axons and neocortical boundary conditions. Global frequencies are identical in all cortical regions, but most states involve dynamic interactions between local networks and the global system. EEG frequencies may involve a “matching” of local resonant frequencies with one or more of the many, closely spaced global frequencies. Key Words: binding problem; cell assemblies; coherence; EEG; limit cycles; neocortical dynamics; pacemakers; phase locking; spatial scale; standing waves; synchronization. Footnotes1 The relationship between the synaptic action fields proposed in the target article and cell assemblies is clarified with Figure R1 (p. 416) of the Response. (This figure was not available to Commentators. (shrink)
A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing host density, (...) and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)
While the control of cell migration by biochemical and biophysical factors is largely documented, a precise quantification of cell migration parameters in different experimental contexts is still questionable. Indeed, these phenomenological parameters can be evaluated from data obtained either at the cell population level or at the individual cell level. However, the range within which both characterizations of cell migration are equivalent remains unclear. We analyse here to which extent both sources of data could be integrated within a unified description (...) of cell migration by considering the motility of the endothelial cell line EAhy926. Using time-lapse video-microscopy and associated analysis of digital image time series, we quantified EAhy926 random motility coefficient, migration speed and trajectory persistence time in two different migration assays: the in vitro wound healing assay, and the cell-populated agarose drop assay. In order to analyse the agreement between independent quantifications of cell motility based either on individual cell analysis or cell population dynamic analysis, a theoretical multi-agents cellular model was developed and discussed as a possible theoretical framework able to unify these multi-scale data. Model simulations especially reveal the potential bias induced by cell proliferation and cell-cell adhesion when cell migration parameters are estimated from the extensively used in vitro wound healing assay. (shrink)
The distinction itself is best explained as follows. At the empirical level (at the bottom), there are curves, or functions, or laws, such as PV = constant the Boyle’s example, or a = M/r 2 in Newton’s example. The first point is that such formulae are actually ambiguous as to the hypotheses they represent. They can be understood in two ways. In order to make this point clear, let me first introduce a terminological distinction between variables and parameters. Acceleration and (...) distance (a and r) are variables in Newton’s formula because they represent quantities that are more or less directly measured. The distinction between what is directly measured and what it is not is to be understood relative the context. All I mean is that values of acceleration and distance are determined independently of the hypothesis, or theory, under consideration. I do not mean that their determination involves no kind of inference at all. For instance, acceleration is the instantaneous change in velocity per unit time, and this is not something that is directly determined from raw data that records the position of the moon at consecutive points in time. It is consistent with that raw data that the motion of the moon is actually discontinuous, so that the moon has no acceleration. So, there are definitely theoretical assumptions make about the moon’s motion that are used to estimate the moon’s acceleration at a particular time. But these assumptions are not unique to Newton’s theory. The same assumptions are also made by the rival hypotheses under consideration. In fact, the existence of quantities such as instantaneous acceleration is only called into question by the far more recent theory of quantum mechanics. Likewise, in the case of Boyle’s law, there is no controversy in viewing the volume of the trapped air as being determined in a way that does not make use of the theory that Boyle is introducing. (shrink)
A standard view of probability and statistics centers on distributions and hypothesis testing. To solve a real problem, say in the spread of disease, one chooses a “model”, a distribution or process that is believed from tradition or intuition to be appropriate to the class of problems in question. One uses data to estimate the parameters of the model, and then delivers the resulting exactly specified model to the customer for use in prediction and classification. As a gateway to these (...) mysteries, the combinatorics of dice and coins are recommended; the energetic youth who invest heavily in the calculation of relative frequencies will be inclined to protect their investment through faith in the frequentist philosophy that probabilities are all really relative frequencies. Those with a taste for foundational questions are referred to measure theory, an excursion from which few return. That picture, standardised by Fisher and Neyman in the 1930s, has proved in many ways remarkably serviceable. It is especially reasonable where it is known that the data are generated by a physical process that conforms to the model. It is not so useful where the data is a large and little understood mess, as is typical in, for example, insurance data being investigated for fraud. Nor is it suitable where one has several speculations about possible models and wishes to compare them, or.. (shrink)
I discuss the behavior of the Akaike Information Criterion in the limit when the sample size grows. I show the falsity of the claim made recently by Stanley Mulaik in Philosophy of Science that AIC would not distinguish between saturated and other correct factor analytic models in this limit. I explain the meaning and demonstrate the validity of the familiar, more moderate criticism that AIC is not a consistent estimator of the number of parameters of the smallest correct model. I (...) also give a short explanation why this feature of AIC is compatible with the motives for using it. (shrink)
The Representational Theory of Measurement conceives measurement as establishing homomorphisms from empirical relational structures into numerical relation structures, called models. Models function as measuring instruments by transferring observations of an economic system into quantitative facts about that system. These facts are evaluated by their accuracy. Accuracy is achieved by calibration. For calibration standards are needed. Then two strategies can be distinguished. One aims at estimating the invariant (structural) equations of the system. The other is to use known stable facts about (...) the system to adjust the model parameters. For this latter strategy, the requirement of models as homomorphic mappings is not required anymore. (shrink)
