Bayesian paradigm has been widely acknowledged as a coherent approach to learning putative probability model structures from a finite class of candidate models. Bayesian learning is based on measuring the predictive ability of a model in terms of the corresponding marginal data distribution, which equals the expectation of the likelihood with respect to a prior distribution for model parameters. The main controversy related to this learning method stems from the necessity of specifying proper prior distributions for all unknown (...) parameters of a model, which ensures a complete determination of the marginal data distribution. Even for commonly used models, subjective priors may be difficult to specify precisely, and therefore, several automated learning procedures have been suggested in the literature. Here we introduce a novel Bayesian learning method based on the predictive entropy of a probability model, that can combine both subjective and objective probabilistic assessment of uncertain quantities in putative models. It is shown that our approach can avoid some of the limitations of the earlier suggested objective Bayesian methods. (shrink)

The objectivity of Bayesian induction relies on the ability of evidence to produce a convergence to agreement among agents who initially disagree about the plausibilities of hypotheses. I will describe three sorts of Bayesian convergence. The first reduces the objectivity of inductions about simple "occurrent events" to the objectivity of posterior probabilities for theoretical hypotheses. The second reveals that evidence will generally induce converge to agreement among agents on the posterior probabilities of theories only if the convergence is (...) 0 or 1. The third establishes conditions under which evidence will very probably compel posterior probabilities of theories to converge to 0 or 1. (shrink)

본고는 딥러닝의 이미지 인식 원리와 유아의 이미지 인식 원리를 종합하면서, 이미지-개념 학습을 위한 새로운 교수학습모델, 즉 “베이지안 구조구성주의 교수학습모델”(Bayesian Structure-constructivist Teaching-learning Model: BSTM)을 제안한다. 달리 말하면, 기계학습 원리와 인간학습 원리를 비교함으로써 얻게 되는 시너지 효과를 바탕으로, 유아들의 이미지-개념 학습을 위한 새로운 교수 모델을 구성하는 것을 목표로 한다. 이런 맥락에서 본고는 전체적으로 3가지 차원에서 논의된다. 첫째, 아동의 이미지 학습에 대한 역사적 중요 이론인 “대상 전체론적 가설”, “분류학적 가설”, “배타적 가설”, “기본 수준 범주 가설” 등을 역사 비판적 관점에서 검토한다. 둘째, 컴퓨터 (...) 공학에서 전개된 머신러닝의 이미지 학습 원리 및 그 구조의 역사적 변형들에 대해서 비판적으로 분석하면서, 특히 딥러닝의 교육 인식론적 의미를 도출한다. 셋째, 선행하는 논의들을 토대로 이미지와 개념을 연결시키는 학습, 즉 단어학습을 위한 필자의 고유한 이론인 구조구성주의 개념교수모델을 제안한다. 이때 필자는 피아제의 명제논리학적 학습 가설, 즉 논리-수학적 구조를 중시하는 기존의 피아제 학파의 학습 가설과 최근의 베이지안 학습 이론에서 강조된 확률론적 추론 가설, 특히 “교육학적 추론 가설”을 동시에 포함할 수 있는 교수학습모델의 구조 및 주요 지향점들을 제안한다. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases (...) of the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)

Infant language learners are faced with the difficult inductive problem of determining how new words map to novel or known objects in their environment. Bayesian inference models have been successful at using the sparse information available in natural child-directed speech to build candidate lexicons and infer speakers’ referential intentions. We begin by asking how a Bayesian model optimized for monolingual input generalizes to new monolingual or bilingual corpora and find that, especially in the case of the bilingual input, (...) the model shows a significant decrease in performance. In the next experiment, we propose the ME Model, a modified Bayesian model, which approximates infants’ mutual exclusivity bias to support the differential demands of monolingual and bilingual learning situations. The extended model is assessed using the same corpora of real child-directed speech, showing that its performance is more robust against varying input and less dependent than the Intentional Model on optimization of its parsimony parameter. We argue that both monolingual and bilingual demands on word learning are important considerations for a computational model, as they can yield significantly different results than when only one such context is considered. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic (...) in character and are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, brings together two important research topics: how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. (...) Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of (...) the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results. (shrink)

BackgroundBayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.MethodsThe sample consisted of 102 mother-adolescent dyads. (...) Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.ResultsThe prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.ConclusionA systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations, and may also be affected by pragmatic considerations regarding the impact of the previous results at hand. (shrink)

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons critically. Lastly, I highlight a number of challenges for avalanche educators when incorporating the Bayesian perspective in their curriculum.

This chapter describes the logic of inductive inference as seen through the eyes of the modern theory of personal probability, including a number of its recent refinements and extensions. The structure of the chapter is as follows. After a brief discussion of mathematical probability, to establish notation and terminology, it recounts the gradual evolution of the probabilistic explication of induction from Bayes to the present. The focus is not in this history per se, but in its use to highlight the (...) key assumptions, criticisms, refinements, and achievements of that theory. Along the way, the structure of the modern theory is presented, and its relation to the problem of induction discussed. (shrink)

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the (...) individuals without the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71.. (shrink)

The paper discusses Bayesian convergence when the truth is excluded from the analysis by means of a simple coin-tossing example. In the fair-balance paradox a fair coin is tossed repeatedly. A Bayesian agent, however, holds the a priori view that the coin is either biased towards heads or towards tails. As a result the truth is ignored by the agent. In this scenario the Bayesian approach tends to confirm a false model as the data size goes to (...) infinity. I argue that the fair-balance paradox reveals an unattractive feature of the Bayesian approach to scientific inference and explore a modification of the paradox. (shrink)

The exponential growth of social data both in volume and complexity has increasingly exposed many of the shortcomings of the conventional frequentist approach to statistics. The scientific community has called for careful usage of the approach and its inference. Meanwhile, the alternative method, Bayesian statistics, still faces considerable barriers toward a more widespread application. The bayesvl R package is an open program, designed for implementing Bayesian modeling and analysis using the Stan language’s no-U-turn (NUTS) sampler. The package combines (...) the ability to construct Bayesian network models using directed acyclic graphs (DAGs), the Markov chain Monte Carlo (MCMC) simulation technique, and the graphic capability of the ggplot2 package. As a result, it can improve the user experience and intuitive understanding when constructing and analyzing Bayesian network models. A case example is offered to illustrate the usefulness of the package for Big Data analytics and cognitive computing. (shrink)

According to the comparative Bayesian concept of confirmation, rationalized versions of creationism come out as empirically confirmed. From a scientific viewpoint, however, they are pseudo-explanations because with their help all kinds of experiences are explainable in an ex-post fashion, by way of ad-hoc fitting of an empirically empty theoretical framework to the given evidence. An alternative concept of confirmation that attempts to capture this intuition is the use novelty criterion of confirmation. Serious objections have been raised against this criterion. (...) In this paper I suggest solutions to these objections. Based on them, I develop an account of genuine confirmation that unifies the UN-criterion with a refined probabilistic confirmation concept that is explicated in terms of the confirmation of evidence-transcending content parts of the hypothesis. (shrink)

The plausibility of uncommon events and miracles based on testimony of such an event has been much discussed. When analyzing the probabilities involved, it has mostly been assumed that the common events can be taken as data in the calculations. However, we usually have only testimonies for the common events. While this difference does not have a significant effect on the inductive part of the inference, it has a large influence on how one should view the reliability of testimonies. In (...) this work, a full Bayesian solution is given for the more realistic case, where one has a large number of testimonies for a common event and one testimony for an uncommon event. A free-running parameter is given for the unreliability of testimony, to be determined from data. It is seen that, in order for there to be a large amount of testimonies for a common event, the testimonies will probably be quite reliable. For this reason, because the testimonies are quite reliable based on the testimonies for the common events, the probability for the uncommon event, given a testimony for it, is also higher. Perhaps surprisingly, in the simple case, the increase in plausibility from testimony for the uncommon events is of the same magnitude as the decrease in plausibility from induction. In summary, one should be more open-minded when considering the plausibility of uncommon events. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for (...) inductive probability given the agent’s evidence. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

(2013). Evolutionary modules and Bayesian facilitation: The role of general cognitive resources. Thinking & Reasoning: Vol. 19, No. 1, pp. 27-53. doi: 10.1080/13546783.2012.713177.

This paper is part of a larger campaign against moderation in foundational epistemology. I think the only plausible responses to a kind of Humean sceptic are, radical responses. The Humean sceptic I have in mind tells us about a sceptical scenario, ss, where our evidence is just as it actually is, but some purported piece of knowledge of ours is false. The sceptic names the proposition You aren’t in ss as s, and calls on us to respond to the following (...) argument. (shrink)

Grounded cognition offers a natural approach for integrating Bayesian accounts of optimality with mechanistic accounts of cognition, the brain, the body, the physical environment, and the social environment. The constructs of simulator and situated conceptualization illustrate how Bayesian priors and likelihoods arise naturally in grounded mechanisms to predict and control situated action.

In a criminal trial, evidence is used to draw conclusions about what happened concerning a supposed crime. Traditionally, the three main approaches to modeling reasoning with evidence are argumentative, narrative and probabilistic approaches. Integrating these three approaches could arguably enhance the communication between an expert and a judge or jury. In previous work, techniques were proposed to represent narratives in a Bayesian network and to use narratives as a basis for systematizing the construction of a Bayesian network for (...) a legal case. In this paper, these techniques are combined to form a design method for constructing a Bayesian network based on narratives. This design method is evaluated by means of an extensive case study concerning the notorious Dutch case of the Anjum murders. (shrink)

In Practical and Scientific Rationality: A Difficulty for Levi's Epistemology, Wayne Backman points to genuine difficulties in Isaac Levi's epistemology, difficulties that Backman attributes to Levi's having required, and for no good reason, that a rational person adopt but one standard of possibility for all her endeavors practical and scientific. I argue that Levi's requirement has, in fact, a deep and compelling motivation that tips the scales in favor of a different diagnosis of Levi's ills — i.e., that Levi's error (...) lies simply in his having set insufficiently high qualifications for admission into the corpus that determines a person's standard of possibility. (shrink)

It has been argued recently that dogmatism in epistemology is incompatible with Bayesianism. That is, it has been argued that dogmatism cannot be modelled using traditional techniques for Bayesian modelling. I argue that our response to this should not be to throw out dogmatism, but to develop better modelling techniques. I sketch a model for formal learning in which an agent can discover a posteriori fundamental epistemic connections. In this model, there is no formal objection to dogmatism.

A major open question in the borderlands between epistemology and philosophy of science concerns whether Bayesian updating and abductive inference are compatible. Some philosophers—most influentially Bas van Fraassen—have argued that they are not. Others have disagreed, arguing that abduction, properly understood, is indeed compatible with Bayesianism. Here we present two formal results that allow us to tackle this question from a new angle. We start by formulating what we take to be a minimal version of the claim that abduction (...) is a rational pattern of reasoning. We then show that this minimal abductivist principle, when combined with Bayesian updating by conditionalization, places surprisingly strong and controversial constraints on how we must measure explanatory power. The lesson is not that Bayesianism is definitely incompatible with abduction, but that both compatibilism and incompatibilism have hitherto unrecognized consequences. We end the paper by formulating these consequences in the form of a trilemma. (shrink)