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)
The paper deals with the problem of the estimation of an unknown probability from a finite number of experiments. We propose a normative (axiomatic) solution that restricts the class of admissible estimators to a one-parameter family. Moreover this solution coincides with the one obtained from Bayes theory with a β prior. Thus our results can be interpreted as a justification for the use of Bayesian inference with a β prior.
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 -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)
Many studies have investigated the topic of change or drift in item parameter estimates in the context of item response theory (IRT). Content effects, such as instructional variation and curricular emphasis, as well as context effects, such as the wording, position, or exposure of an item have been found to impact item parameter estimates. The issue becomes more critical when items with estimates exhibiting differential behavior across test administrations are used as common for deriving equating transformations. This paper (...) reviews the types of effects on IRT item parameter estimates and focuses on the impact of misbehaving or aberrant common items on equating transformations. Implications relating to test validity and the judgmental nature of the decision to keep or discard aberrant common items are discussed, with recommendations for future research into more informed and formal ways of dealing with misbehaving common items. (shrink)
Most of the existing literature on social preferences either tests whether certain characteristics of the social context (like intentions of others) influence individual decisions, or tries to estimate parameters of social preference functions describing such behavior at the level of the entire population. In the present paper, we are concerned with measuring parameters of social preference functions at the individual level. We draw upon concepts developed for eliciting other types of utility functions, in particular the literature on decision making under (...) incomplete information. Our method derives parameters of social preference functions from indifference statements about the distribution of payoffs a group. We apply our method in a controlled social preference experiment to establish the external validity of estimated parameters. Our results show the expected relationships to some external factors (like educational background of subjects) and also a strong correspondence between parameter estimates and factors that, according to the subjects’ own descriptions, influenced their behavior. We also find that some concepts discussed in the literature on social preferences, in particular envy toward players receiving a larger payoff, have very diverse and complex effects at the individual level. (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)
We consider the procedure for small-sample estimation of reliability parameters. The main shortcomings of the classical methods and the Bayesian approach are analyzed. Models that find robust Bayesian estimates are proposed. The sensitivity of the Bayesian estimates to the choice of the prior distribution functions is investigated using models that find upper and lower bounds. The proposed models reduce to optimization problems in the space of distribution functions.
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)
The stop-signal paradigm is frequently used to study response inhibition. In this paradigm, participants perform a two-choice response time task where the primary task is occasionally interrupted by a stop-signal that prompts participants to withhold their response. The primary goal is to estimate the latency of the unobservable stop response (stop signal reaction time or SSRT). Recently, Matzke, Dolan, Logan, Brown, and Wagenmakers (in press) have developed a Bayesian parametric approach that allows for the estimation of the entire distribution (...) of SSRTs. The Bayesian parametric approach assumes that SSRTs are ex-Gaussian distributed and uses Markov chain Monte Carlo sampling to estimate the parameters of the SSRT distri- bution. Here we present an efficient and user-friendly software implementa- tion of the Bayesian parametric approach —BEESTS— that can be applied to individual as well as hierarchical stop-signal data. BEESTS comes with an easy-to-use graphical user interface and provides users with summary statistics of the posterior distribution of the parameters as well various diag- nostic tools to assess the quality of the parameter estimates. The software is open source and runs on Windows and OS X operating systems. In sum, BEESTS allows experimental and clinical psychologists to estimate entire distributions of SSRTs and hence facilitates the more rigorous analysis of stop-signal data. (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)
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 purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system. Joint estimation involves the application of a multiply parameterized operator-valued measure. An example related to the simultaneous estimation of the position and velocity of a particle is given. Conceptual difficulties attending simultaneous measurement of noncommuting observables are avoided by this formation.
Distance function-based diffusion-generated motion, a highly efficient numerical algorithm, is used to simulate a classical model of recrystallization in unprecedented detail and in physically relevant parameter regimes not attainable with many previous techniques. The algorithm represents interfaces implicitly and is closely related to the level set method. In particular, it allows for automatic topological changes and arbitrarily large time-steps. Large-scale simulations of recrystallization for physically relevant parameter values are presented in detail. In addition, new analytical estimates for the (...) distribution of surviving nuclei are obtained and compared with the numerical results. (shrink)
The thermal expansion of magnesium oxide has been measured below room temperature from 140°K to 284.5°K, using an interferometric method. The accuracy of measurement is better than 3% in the temperature range studied. The agreement of these results with Durand's is quite good, but consistently higher over most of the range by 2 or 3%, for the most part within the estimated experimental error. The Grüneisen parameter remains constant at about 1.51 over the present experimental range; but an isolated (...) measurement of Durand at 85°K suggests that at lower temperatures it rises quite sharply above this value. This possibility is therefore investigated theoretically. With a non-central force model to represent MgO, ?(?3) and ?(2) are calculated and it is found that ?(?3) > ?(2), again suggesting that the Grüneisen parameter increases with falling temperature. Of the two reported experimental values for the infra-red absorption frequency, correlation with the heat capacity strongly indicates a wavelength of 25.26?m rather than 17.3?m. Thermal expansion measurements at still lower temperatures must be carried out to confirm definitely the rise in the Grüneisen parameter. (shrink)