We argue that Bayesian decision theory provides a good theoretical framework for visual perception. Such a theory involves a likelihood function specifying how the scene generates the image(s), a prior assumption about the scene, and a decision rule to determine the scene interpretation. This is illustrated by describing Bayesian theories for individual visual cues and showing that perceptual biases found in psychophysical experiments can be interpreted as biases towards prior assumptions made by the visual system. We then describe the implications of this framework for the integration of different cues. We argue that the dependence of cues on prior assumptions means that care must be taken to model these dependencies during integration. This suggests that a number of proposed schemes for cue integration, which only allow weak interaction between cues, are not adequate and instead stronger coupling is often required. These theories require the choice of decision rules and we argue that...

In a probability-based reasoning system, Bayes’ theorem and its variations are often used to revise the system’s beliefs. However, if the explicit conditions and the implicit conditions of probability assignments are properly distinguished,it follows that Bayes ’ theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that Jeffrey’s rule and its variations are not revision rules, either. Without these distinctions, the limitation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, cannot be done in the Bayesian approach, because a probability distribution function alone does not contain the information needed by the operation. 1

This paper develops a means-ends analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions–including prescriptions for when exactly to introduce hidden particles.

Attributing higher "probability" to a sentence of form p-and-q compared to p is a reasoning fallacy only if (a) the word "probability" carries its modern, technical meaning, and (b) the sentence p is interpreted as a conjunct of the conjunction p-and-q. Legitimate doubts arise about both conditions in classic demonstrations of the conjunction fallacy. We use betting paradigms to reduce these sources of ambiguity about conjunctive reasoning. Reality of the conjunction fallacy 1 Introduction The conjunction fallacy Here is the famous Linda story, to be labeled E (for "evidence") in what follows. (E) Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. The task is to rank various statements "by their probability," including these two. (B) Linda is a bank teller. (B # F ) Linda is a bank teller and is activ...

This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.

Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the Johnson-Carnap continuum of inductive methods, as well as the Nix-Paris continuum, and show how inductive influence can

This paper pursues a thorough-going instrumentalist, or meansends, approach to the theory of inductive inference. I consider three epistemic aims: convergence to a correct theory, fast convergence to a correct theory and steady con- vergence to a correct theory (avoiding retractions). For each of these, two questions arise: (1) What is the structure of inductive problems in which these aims are feasible ? (2) When feasible, what are the inference methods that attain them? Formal learning theory provides the tools for a complete set of answers to these questions.

14. Sponsoring Agency Code Traffic accident reconstruction has been defined as the effort to determine, from whatever evidence is available, how an accident happened. Traffic accident reconstruction can be treated as a problem in uncertain reasoning about a particular event, and developments in modeling uncertain reasoning for artificial intelligence can be applied to this problem. Physical principles can usually be used to develop a structural model of the accident and this model, together with an expert assessment of prior uncertainty regarding the accident’s initial conditions, can be represented as a Bayesian network. Posterior probabilities for the accident’s initial conditions, given evidence collected at the accident scene, can then be computed by updating the Bayesian network. Using a possible worlds semantics, truth conditions for counterfactual claims about the accident can be defined and used to rigorously implement a “but for ” test of whether or not a speed limit violation could be considered a cause of an accident. The logic of this approach is illustrated for a simplified version of a

This paper describes the cornerstones of a means-ends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the "limit of inquiry". I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Means-ends vindications of (a version of) Occam's Razor and the natural generalizations in a Goodmanian Riddle of Induction illustrate the power of this approach. The paper establishes a hierarchy of means-ends notions of empirical success, and discusses a number of issues, results and applications of means-ends epistemology.

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective