This article compares inference to the best explanation with Bayes’s rule in a social setting, specifically, in the context of a variant of the Hegselmann–Krause model in which agents not only update their belief states on the basis of evidence they receive directly from the world, but also take into account the belief states of their fellow agents. So far, the update rules mentioned have been studied only in an individualistic setting, and it is known that in such (...) a setting both have their strengths as well as their weaknesses. It is shown here that in a social setting, inference to the best explanation outperforms Bayes’s rule according to every desirable criterion. 1 What Is Inference to the Best Explanation?2 Judging the Rules—By Which Lights?3 From an Individualistic to a Social Perspective 3.1 The Hegselmann–Krause model 3.2 A probabilistic extension of the Hegselmann–Krause model 3.3 Simulations4 Results and Discussion5 Interpretation6 Conclusion. (shrink)

On a widely held view, episodes of inner speech provide at least one way in which we become conscious of our thoughts. However, it can be argued, on the one hand, that consciousness of thoughts in virtue of inner speech presupposes interpretation of the simulated speech. On the other hand, the need for such self-interpretation seems to clash with distinctive first-personal characteristics that we would normally ascribe to consciousness of one’s own thoughts: a special reliability; a lack of conscious ambiguity (...) and incomprehensibility; and a sense of causal agency. I try to resolve this puzzle by proposing an account for the requisite self-interpretation of inner speech in terms of Bayesian probabilistic inference. Drawing on “perceptual loop” accounts of speech control, I argue that such interpretive probabilistic inferences are used for the control of inner speech, and that as a consequence of this function, they are biased toward the correct interpretations. I conclude by showing how this model can explain the first-personal characteristics of consciousness of one’s own thoughts. In the case of the sense of causal agency, the resulting explanation yields novel accounts for “audible thoughts” and thought insertion. (shrink)

On a widely held view, episodes of inner speech provide at least one way in which we become conscious of our thoughts. However, it can be argued, on the one hand, that consciousness of thoughts in virtue of inner speech presupposes interpretation of the simulated speech. On the other hand, the need for such self-interpretation seems to clash with distinctive first-personal characteristics that we would normally ascribe to consciousness of one’s own thoughts: a special reliability; a lack of conscious ambiguity (...) and incomprehensibility; and a sense of causal agency. I try to resolve this puzzle by proposing an account for the requisite self-interpretation of inner speech in terms of Bayesian probabilistic inference. Drawing on “perceptual loop” accounts of speech control, I argue that such interpretive probabilistic inferences are used for the control of inner speech, and that as a consequence of this function, they are biased toward the correct interpretations. I conclude by showing how this model can explain the first-personal characteristics of consciousness of one’s own thoughts. In the case of the sense of causal agency, the resulting explanation yields novel accounts for “audible thoughts” and thought insertion. (shrink)

Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs, consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs (...) joining some of the nodes, representing dependency relations among them. This chapter describes and comments on two different approaches to inference network construction. In the first approach, a DAG network structure is explicitly constructed as a vehicle for probabilistic analyses. Since the associated computations can be regarded as generalising the use of Bayes' rule, such networks are commonly called Bayesian networks. The second approach stems from the work of the American jurist John H. Wigmore who was the very first person to attempt a systematic study of inference networks. (shrink)

Certain hypotheses cannot be directly confirmed for theoretical, practical, or moral reasons. For some of these hypotheses, however, there might be a workaround: confirmation based on analogical reasoning. In this paper we take up Dardashti, Hartmann, Thébault, and Winsberg’s (in press) idea of analyzing confirmation based on analogical inference Baysian style. We identify three types of confirmation by analogy and show that Dardashti et al.’s approach can cover two of them. We then highlight possible problems with their model as (...) a general approach to analogical inference and argue that these problems can be avoided by supplementing Bayesian update with Jeffrey conditionalization. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary (...) formal learning theory. In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary (...) formal learning theory.In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in (...) which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

Causal Bayes nets (CBNs) provide one of the most powerful tools for modelling coarse-grained type-level causal structure. As in other fields (e.g., thermodynamics) the question arises how such coarse-grained characterisations are related to the characterisation of their underlying structure (in this case: token-level causal relations). Answering this question meets what is called a “coherence-requirement” in the reduction debate: How are different accounts of one and the same system (or kind of system) related to each other. We argue that CBNs (...) as tools for type-level causal inference are abstract enough to roughly fit any current token-level theory of causation as long as certain modelling assumptions are satisfied, but accounts of actual causation, i.e. accounts that attempt to infer token-causation based on CBNs, for the very same reason, face certain limitations. (shrink)

Causal Bayes nets have been developed in philosophy, statistics, and computer sciences to provide a formalism to represent causal structures, to induce causal structure from data and to derive predictions. Causal Bayes nets have been used as psychological theories in at least two ways. They were used as rational, computational models of causal reasoning and they were used as formal models of mental causal models. A crucial assumption made by them is the Markov condition, which informally states that (...) variables are independent of other variables that are not their direct or indirect effects conditional on their immediate causes. Whether people’s inferences conform to the causal Markov and the faithfulness condition has recently been investigated empirically. A review of respective research indicates that inferences frequently violate these conditions. This finding challenges some uses of causal Bayes nets in psychology. They entail that causal Bayes nets may not be appropriate to derive predictions for causal model theories of causal reasoning. They also question whether causal Bayes nets as a rational model are empirically descriptive. They do not challenge, however, causal Bayes nets as normative models and their usage as formal models of causal reasoning. (shrink)

According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this article is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of the epistemological challenges to these claims; and some of the implications of these claims. We address two questions: (i) How are Bayesian models used in theoretical neuroscience? (ii) From the use of (...) Bayesian models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people's performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the three-level framework laid out by David Marr ( [1982] ). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects' perceptual performance and features of the underlying neural mechanisms. (shrink)

While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions (...) under which Bayesian agents would be rational. The proposal is illustrated with a characterization of costs inspired by thermodynamics. (shrink)

This book grew out of previously published papers of mine composed over a period of years; they have been reworked (sometimes beyond recognition) so as to form a reasonably coherent whole. Part One treats of informative inference. I argue (Chapter 2) that the traditional principle of induction in its clearest formulation (that laws are confirmed by their positive cases) is clearly false. Other formulations in terms of the 'uniformity of nature' or the 'resemblance of the future to the past' (...) seem to me hopelessly unclear. From a Bayesian point of view, 'learning from experience' goes by conditionalization (Bayes' rule). The traditional stum bling block for Bayesians has been to fmd objective probability inputs to conditionalize upon. Subjective Bayesians allow any probability inputs that do not violate the usual axioms of probability. Many subjectivists grant that this liberality seems prodigal but own themselves unable to think of additional constraints that might plausibly be imposed. To be sure, if we could agree on the correct probabilistic representation of 'ignorance' (or absence of pertinent data), then all probabilities obtained by applying Bayes' rule to an 'informationless' prior would be objective. But familiar contra dictions, like the Bertrand paradox, are thought to vitiate all attempts to objectify 'ignorance'. BuUding on the earlier work of Sir Harold Jeffreys, E. T. Jaynes, and the more recent work ofG. E. P. Box and G. E. Tiao, I have elected to bite this bullet. In Chapter 3, I develop and defend an objectivist Bayesian approach. (shrink)

We used a new method to assess how people can infer unobserved causal structure from patterns of observed events. Participants were taught to draw causal graphs, and then shown a pattern of associations and interventions on a novel causal system. Given minimal training and no feedback, participants in Experiment 1 used causal graph notation to spontaneously draw structures containing one observed cause, one unobserved common cause, and two unobserved independent causes, depending on the pattern of associations and interventions they saw. (...) We replicated these findings with less‐informative training (Experiments 2 and 3) and a new apparatus (Experiment 3) to show that the pattern of data leads to hidden causal inferences across a range of prior constraints on causal knowledge. (shrink)

On appelle « biais de confirmation » la tendance supposée des humains à sélectionner les informations qui vont dans le sens de ce qu’ils croient (ou veulent croire) et à interpréter celles dont ils disposent en faveur de leurs hypothèses favorites. Cet article vise à porter un regard critique sur certains usages de cette notion, et plus généralement sur le recours aux « biais cognitifs » pour expliquer tout un ensemble de phénomènes sociaux interprétés comme les marques d’une forme d’irrationalité. (...) Remettant en question le caractère probant des résultats expérimentaux destinés à mettre en évidence une déviation qui nous conduirait systématiquement à des représentations inexactes, je suggère que l’approche bayésienne en psychologie du raisonnement permet de rendre compte de certains de ces résultats en faisant l’hypothèse que nos inférences se conforment à une telle norme. (shrink)

A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making (...) inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (shrink)

Bayesians have traditionally taken a dim view of the Inference to the Best Explanation, arguing that, if IBE is at variance with Bayes ' rule, then it runs afoul of the dynamic Dutch book argument. More recently, Bayes ' rule has been claimed to be superior on grounds of conduciveness to our epistemic goal. The present paper aims to show that neither of these arguments succeeds in undermining IBE.

Bayesian learning theory and evolutionary theory both formalize adaptive competition dynamics in possibly high‐dimensional, varying, and noisy environments. What do they have in common and how do they differ? In this paper, we discuss structural and dynamical analogies and their limits, both at a computational and an algorithmic‐mechanical level. We point out mathematical equivalences between their basic dynamical equations, generalizing the isomorphism between Bayesian update and replicator dynamics. We discuss how these mechanisms provide analogous answers to the challenge of adapting (...) to stochastically changing environments at multiple timescales. We elucidate an algorithmic equivalence between a sampling approximation, particle filters, and the Wright‐Fisher model of population genetics. These equivalences suggest that the frequency distribution of types in replicator populations optimally encodes regularities of a stochastic environment to predict future environments, without invoking the known mechanisms of multilevel selection and evolvability. A unified view of the theories of learning and evolution comes in sight. (shrink)

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or “Bayes nets”. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- (...) to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism. (shrink)

Reichenbach held that all scientific inference reduces, via probability calculus, to induction, and he held that induction can be justified. He sees scientific knowledge in a practical context and insists that any rational assessment of actions requires a justification of induction. Gaps remain in his justifying argument; for we can not hope to prove that induction will succeed if success is possible. However, there are good prospects for completing a justification of essentially the kind he sought by showing that (...) while induction may succeed, no alternative is a rational way of trying.Reichenbach's claim that probability calculus, especially via Bayes' Theorem, can help to exhibit the structure of inference to theories is a valuable insight. However, his thesis that the weighting of all hypotheses rests only on frequency data is too restrictive, especially given his scientific realism. Other empirical factors are relevant. Any satisfactory account of scientific inference must be deeply indebted to Reichenbach's foundation work. (shrink)

This article reports results from two studies of how people answer counterfactual questions about simple machines. Participants learned about devices that have a specific configuration of components, and they answered questions of the form “If component X had not operated [failed], would component Y have operated?” The data from these studies indicate that participants were sensitive to the way in which the antecedent state is described—whether component X “had not operated” or “had failed.” Answers also depended on whether the device (...) is deterministic or probabilistic—whether X's causal parents “always” or only “usually” cause X to operate. Participants' explanations of their answers often invoked non-operation of causally prior components or unreliability of prior connections. They less often mentioned independence from these causal elements. (shrink)

Probabilistic inference forms lead from point probabilities of the premises to interval probabilities of the conclusion. The probabilistic version of Modus Ponens, for example, licenses the inference from \({P(A) = \alpha}\) and \({P(B|A) = \beta}\) to \({P(B)\in [\alpha\beta, \alpha\beta + 1 - \alpha]}\) . We study generalized inference forms with three or more premises. The generalized Modus Ponens, for example, leads from \({P(A_{1}) = \alpha_{1}, \ldots, P(A_{n})= \alpha_{n}}\) and \({P(B|A_{1} \wedge \cdots \wedge A_{n}) = \beta}\) to an (...) according interval for P(B). We present the probability intervals for the conclusions of the generalized versions of Cut, Cautious Monotonicity, Modus Tollens, Bayes’ Theorem, and some SYSTEM O rules. Recently, Gilio has shown that generalized inference forms “degrade”—more premises lead to less precise conclusions, i.e., to wider probability intervals of the conclusion. We also study Adam’s probability preservation properties in generalized inference forms. Special attention is devoted to zero probabilities of the conditioning events. These zero probabilities often lead to different intervals in the coherence and the Kolmogorov approach. (shrink)

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been revived for (...) a new generation of readers. (shrink)

Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin-1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal (...) variable; through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables are found, all the problems of quantum field theory and of quantum gravity might melt away. (shrink)

Many of our decisions pertain to causal systems. Nevertheless, only recently has it been claimed that people use causal models when making judgments, decisions and predictions, and that causal Bayes nets allow us to formally describe these inferences. Experimental research has been limited to simple, artificial problems, which are unrepresentative of the complex dynamic systems we successfully deal with in everyday life. For instance, in social interactions, we can explain the actions of other's on the fly and we can (...) generalize from limited observations to predict future actions and their consequences. Our main argument is that none of these inferences (i.e., induction, generalization, explanation, and prediction) can be achieved without causal reasoning. As a case in point we use the popular television series desperate housewives and show how causal Bayes nets are able to explain the inferences made in social contexts. Crucially, causal Bayes nets also allow us to understand why we can infer so much from so little when making sense of a protagonist's behavior. (shrink)

Bayesianism and Inference to the best explanation are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretations of prior probabilities: “IBE-Bayesianism” and “frequentist-Bayesianism”. After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: endorses a role for explanatory value in the assessment (...) of scientific hypotheses; avoids a purely subjectivist reading of prior probabilities; and fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned. (shrink)

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In (...) addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study. (shrink)

We outline a cognitive and computational account of causal learning in children. We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent representation of the causal relations among events. This kind of knowledge can be perspicuously represented by the formalism of directed graphical causal models, or “Bayes nets”. Human causal learning and inference may involve computations similar to those for learnig causal Bayes nets and (...) for predicting with them. Preliminary experimental results suggest that 2- to 4-year-old children spontaneously construct new causal maps and that their learning is consistent with the Bayes-Net formalism. (shrink)

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...) are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your (...) evidence. (shrink)

Two long-standing arguments in cognitive science invoke the assumption that holistic inference is computationally infeasible. The first is Fodor’s skeptical argument toward computational modeling of ordinary inductive reasoning. The second advocates modular computational mechanisms of the kind posited by Cosmides, Tooby and Sperber. Based on advances in machine learning related to Bayes nets, as well as investigations into the structure of scientific and ordinary information, I maintain neither argument establishes its architectural conclusion. Similar considerations also undermine Fodor’s decades-long (...) diagnosis of artificial intelligence research as confounded by an inability to circumscribe the amount of information relevant to inferential processes. This diagnosis is particularly inapposite with respect to Bayes nets, since one of their strengths as machine learning systems has been their capacity to reason probabilistically about large data sets whose size overwhelms the capacities of individual human reasoners. A general moral follows from these criticisms: Insights into artificial and human cognitive systems are likely to be cultivated by focusing greater attention on the structure and density of connections among items of information that are available to them. (shrink)

The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although (...) it had been stated by Price. The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n → ∞, the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter. (shrink)

In this essay, we will try to provide a formal analysis of practical inference, attentive to the various phases in which it is articulated, and being so capable of explaining both the logical conclusiveness of the inference and the probabilistic nature of its conclusion. An innovative purpose of this article is to show how the final deliberation leading to action—the ultimate practical judgment—takes place according to a logic consistent with the use of Bayes’ theorem. This is why (...) we refer to Bayesian practical inference in the title of this essay. (shrink)

Can statistical inference shed any worthwhile light on theory change? For many years I have believed that the answer is “Yes.” Let me try to explain why I think so. On my first reading of Thomas S. Kuhn’s The Structure of Scientific Revolutions (1962) I was so deeply shocked at his repudiation of the distinction between the context of discovery and the context of justification that I put the book down without finishing it. By 1969, when a conference was (...) held at the Minnesota Center for Philosophy of Science on the relations between the history of science and the philosophy of science, I had returned to Structure and formed the view that Kuhn’s rejection of this fundamental distinction resulted from his adoption of an inadequate conception of scientific justification. It appeared that he saw scientific confirmation in terms of the traditional hypothetico-deductive (H-D) schema, according to which a scientific hypothesis (or theory) is confirmed by observing the truth of its logical consequences. (shrink)

Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a (...) 2×2-table, a unit square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

It can be demonstrated in a very straightforward way that confirmation and evidence as spelled out by us can vary from one case to the next, that is, a hypothesis may be weakly confirmed and yet the evidence for it can be strong, and conversely, the evidence may be weak and the confirmation strong. At first glance, this seems puzzling; the puzzlement disappears once it is understood that confirmation is of single hypotheses, in which there is an initial degree of (...) belief which is adjusted up or down as data accumulate, whereas evidence always has to do with a comparison of one hypothesis against another with respect to the data and is belief-independent. Confusing them is, we suggest, a plausible source of the so-called “base-rate fallacy” identified by Kahneman and Tversky which leads most of us to make mistaken statistical inferences. It is also in the background, or so we argue in some detail, of the important policy controversies concerning human-induced global warming. (shrink)

Lately in the past couple of years, there are an increasing in the normal rate of playing computer games or video games compared to the E-learning content that are introduced for the safety of our children, and the impact of the video game addictiveness that ranges from (Musculoskeletal issues, Vision problems and Obesity). Furthermore, this paper introduce an intelligent tutoring system for both parent and their children for enhancement the experience of gaming and tell us about the health problems and (...) how we can solve them, with an easy user interface that way can our children be happy and excited about the information and their health. (shrink)

We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability (...) measure. If a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.

Newsome ((2003). The debate between current versions of covariation and mechanism approaches to causal inference. Philosophical Psychology, 16, 87-107.) recently published a critical review of psychological theories of human causal inference. In that review, he characterized covariation and mechanism theories, the two dominant theory types, as competing, and offered possible ways to integrate them. I argue that Newsome has misunderstood the theoretical landscape, and that covariation and mechanism theories do not directly conflict. Rather, they rely on distinct sets (...) of reliable indicators of causation, and focus on different types of causation (type vs. token). There are certainly debates in the research field, but the theoretical landscape is not as fractured as Newsome suggests, and a potential unifying framework has already emerged using causal Bayes nets. Philosophical work on causal epistemology matters for psychologists, but not in the way Newsome suggests. (shrink)

A pocket-sized collection of mindfulness practices anyone can do anytime--from the author of Mindful Eating. Mindfulness can reduce stress, improve physical health and quality of life, and give you deep insight. Meditation practice is one way to do it, but not the only way. In fact, there are easy ways to fit it into your everyday life. Jan Chozen Bays provides here 25 practices that can be used on the go to cultivate mindfulness. The three-breath practice, the mindfulness of entering (...) rooms, offering compliments, tasting your food one careful bite at a time--these deceptively simple practices can have a cumulative effect for the better. The book is an abridgment of Bays's longer collection How to Train a Wild Elephant: And Other Adventures in Mindfulness. (shrink)

Plagiarism detection is the process of finding similarities on electronic based documents. Recently, this process is highly required because of the large number of available documents on the internet and the ability to copy and paste the text of relevant documents with simply Control+C and Control+V commands. The proposed solution is to investigate and develop an easy, fast, and multi-language support plagiarism detector with the easy of one click to detect the document plagiarism. This process will be done with the (...) support of intelligent system that can learn, change and adapt to the input document and make a cross-fast search for the content on the local repository and the online repository and link the content of the file with the matching content everywhere found. Furthermore, the supported document type that we will use is word, text and in some cases, the pdf files –where is the text can be extracting from them- and this made possible by using the DLL file from Word application that Microsoft provided on OS. The using of DLL will let us to not constrain on how to get the text from files; and will help us to apply the file on our Delphi project and walk throw our methodology and read the file word by word to grantee the best working scenarios for the calculation. In the result, this process will help in the uprising the documents quality and enhance the writer experience related to his work and will save the copyrights for the official writer of the documents by providing a new alternative tool for plagiarism detection problem for easy and fast use to the concerned Institutions for free. (shrink)

Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...) on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit. (shrink)

Originally published as a long essay in Mind and Cosmos, Volume II of the University of Pittsburgh series in the philosophy of science, this study admirably fills the need for an elementary survey of problems in the area of probability and induction. But it is more than an introduction. The author is working on the general thesis that Bayes' theorem of the probability calculus holds the key to the understanding of scientific inference. Guided by this idea he attempts (...) to salvage what he thinks is of value in various current theories of probability and scientific inference, particularly, the frequency theory of probability as defended by Reichenbach, Popper's views on the falsifiability of theories, and Hanson's work on the logic of discovery. These attempts to develop a theory in the latter part of the book follow discussions of Hume's critique of induction, the probability calculus and five past and present interpretations of the calculus. This is a well-written and challenging introduction to the field.—R. H. K. (shrink)

This paper examines Patrick Suppes’ probabilistic theory of causality understood as a theory of causal inference, and draws some lessons for empirical economics and contemporary debates in the foundations of econometrics. It argues that a standard method of empirical economics, multiple regression, is inadequate for most but the simplest applications, that the Bayes’ nets approach, which can be understood as a generalisation of Suppes’ theory, constitutes a considerable improvement but is still subject to important limitations, and that the (...) currently fashionable ‘design-based approach’ suffers from the same flaws Suppes anticipated a long time ago. It then sketches an alternative in response, one that differs drastically from the formalisms Suppes endorsed but is consistent with his pragmatic general take on science. (shrink)

The Problem of Old Evidence (POE) states that Bayesian confirmation theory cannot explain why a theory H can be confirmed by a piece of evidence E already known. Different dimensions of POE have been highlighted. Here, I consider the dynamic and static dimension. In the former, we want to explain how the discovery that H accounts for E confirms H. In the latter, we want to understand why E is and will be a reason to prefer H over its competitors. (...) The aim of the paper is twofold. Firstly, I stress that two recent solutions to the dynamic dimension, recently proposed by Eva and Hartmann, can be read in terms of Inference to the Best Explanation (IBE). On this base, I gauge the weaknesses and strengths of the two models. Namely, I show that the two authors endorse a particular IBE’s formulation, and that it is still unsure if it is the one descriptively used. Moreover, I contend that, while one condition of their first model is not expression of this formulation, the only condition of their second model is. Secondly, I focus on the static dimension of POE which, now, has to be expressed in IBE terms. To solve it, I rely on the counterfactual approach, and on a version of IBE in which explanatory considerations help to evaluate the terms in Bayes’ theorem. However, it turns out that the problems of the counterfactual approach recur even when it is used to solve the static POE in IBE terms. (shrink)

In order to explore whether and how Jewish teachings influence the attitudes of strictly-orthodox Jews to clinical trials, 10 strictly-orthodox Jews were purposively selected and interviewed, using a semi-structured schedule. Relevant literature was searched for similar studies and for publications covering relevant Jewish teachings. Thematic analysis was used to analyse transcribed interviews and explore relationships between attitudes and Jewish teachings identified in the review. Participants’ attitudes were influenced in a variety of ways: by Jewish teachings on the over-riding importance of (...) preserving life—the need to avoid risks affecting life and health, while taking risks to preserve life—and the religious obligation to help others, as well as by previous experience. Attitudes mirrored those in the general population, enabling many participants to reach conclusions that did not differ materially from those of the general population or research ethics committees. (shrink)