A Note on the Subtleties of Bayesian Inference (original) (raw)

Bayesianism II: Applications and Criticisms

Philosophy Compass, 2011

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemology, and statistics, and criticisms of these applications.

Bayesianism I: Introduction and Arguments in Favor

Philosophy Compass, 2011

Bayesianism is a popular position (or perhaps, positions) in the philosophy of science, epistemology, statistics, and other related areas, which represents belief as coming in degrees, measured by a probability function. In this article, I give an overview of the unifying features of the different positions called 'Bayesianism', and discuss several of the arguments traditionally used to support them.

The limitation of Bayesianism

Artificial Intelligence, 2004

In the current discussion about the capacity of Bayesianism in reasoning under uncertainty, there is a conceptual and notational confusion between the explicit condition and the implicit condition of a probability evaluation. Consequently, the limitation of Bayesianism is often seriously underestimated. To represent the uncertainty of a belief system where revision is needed, it is not enough to assign a probability value to each belief.

Bayesianism: Explanations from Asterix, Tintin, and Captain Haddock

2024

This note compares Bayesianism and frequentism, two approaches to probability. Bayesians view probabilities as subjective beliefs adjusted by data using Bayes' formula, while frequentists treat them as objective frequencies to test hypotheses. Through examples drawn from Asterix, Tintin, and Captain Haddock, we show that Bayesians update their beliefs in response to new information, while frequentists reject or accept a hypothesis based on its likelihood. Although different, these approaches share a common goal: improving decision-making in a rational manner, enriching both practice and modern theories such as those in economics and game theory.

A Bayesian account of establishing

The British Journal for the Philosophy of Science, 2021

When a proposition is established, it can be taken as evidence for other propositions. Can the Bayesian theory of rational belief and action provide an account of establishing? I argue that it can, but only if the Bayesian is willing to endorse objective constraints on both probabilities and utilities, and willing to deny that it is rationally permissible to defer wholesale to expert opinion. I develop a new account of deference that accommodates this latter requirement.

Jon Williamson and David Corfield Introduction: Bayesianism Into the 21ST Century

2014

Bayesian theory now incorporates a vast body of mathematica l, statistical and computational techniques that are widely applied in a panop ly of disciplines, from artificial intelligence to zoology. Yet Bayesians rarely ag ree on the basics, even on the question of what Bayesianism actually is. This book is about the basics — about the opportunities, questions and problems that face B y sianism today. So what is Bayesianism, roughly? Most Bayesians maintain th t an individual’s degrees of belief ought to obey the axioms of the probability calculus. If, for example, you believe to degree 0.4 that you will be rained on tomorrow, then you should also believe that you will not be rained on tomorrow to degree0.6. Most Bayesians also maintain that an individual’s degrees of bel ief should take prior knowledge and beliefs into account. According to the Bayesian conditionalisation principle, if you come to learn that you will be in Manchester tomorrow (m) then your degree of belief in being...

Objective Bayesianism, Bayesian conditionalisation and voluntarism

Synthese, 2009

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 Bayesian norms are tied up in the very notion of degrees of belief.

Bayesianism: Objections and Rebuttals

Philosophical Foundations of Evidence Law, 2021

While the laws of probability are rarely disputed, the question of how we should interpret probability judgments is less straightforward. Broadly, there are two ways to conceive of probability—either as an objective feature of the world, or as a subjective measure of our uncertainty. Both notions have their place in science, but it is the latter subjective notion (the Bayesian approach) that is crucial in legal reasoning. This chapter explains the advantages of using Bayesian networks in adjudicative factfinding. It addresses a number of common objections to the Bayesian approach, such as “There is no such thing as a probability of a single specified event”; “The Bayesian approach only works with statistical evidence”; “The Bayesian approach is too difficult for legal factfinders to comprehend”; and “A Bayesian network can never capture the full complexity of a legal case.” Fenton and Lagnado offer rebuttals to each of these objections.

Bayesianism without learning

Research in Economics, 1999

According to the standard definition, a Bayesian agent is one who forms his posterior belief by conditioning his prior belief on what he has learned, that is, on facts of which he has become certain. Here it is shown that Bayesianism can be described without assuming that the agent acquires any certain information; an agent is Bayesian if his prior, when conditioned on his posterior belief, agrees with the latter. This condition is shown to characterize Bayesian models.