Bayes, Hume, Price, and Miracles

This chapter discusses the Bayesian analysis of miracles. It is set in the context of the eighteenth-century debate on miracles. The discussion is focused on the probable response of Thomas Bayes to David Hume's celebrated argument against miracles. The chapter presents the claim that the criticisms Richard Price made against Hume's argument against miracles were largely solid.

Bayesianism—its Scope and Limits

This chapter discusses the scope and limits of Bayesianism. The first topics discussed are the math and philosophy embedded in Bayesianism and the standard objection to Bayesianism. The concept of likelihood in Bayesianism is examined, and a problem of the best-case strategy of dealing with nuisance parameters is studied. Finally, the main weakness of strong Bayesianism is identified.

Bayesianism in Statistics

This chapter discusses Bayesianism in statistics. The first section of the chapter is devoted to the First Bayesian Theory, which is immediately followed by a discussion of significance tests and the Second Bayesian Theory. Lindley's Paradox and the Neyman-Pearson Theory are examined in detail, along with the concept of priors and likelihood. The final portion of the chapter focuses on the Second Bayesian theory as logic.

Introduction*

This chapter introduces Bayes' Theorem, which is primarily concerned with probability. It discusses some of the different kinds of probability, such as statistical probability, before moving on to a discussion of probability axioms. Bayesianism, prior probability and simplicity, and countable additivity are also studied in the chapter.

Propensities May Satisfy Bayes’s Theorem

This chapter discusses the question of whether the propensity interpretation of probability is a genuine interpretation of the calculus of probability. One of the main points of interest can be found in the difficulty of understanding the term P(A\C), when the occurrence A is temporally or causally anterior to the occurrence C. The chapter is able to determine that an intelligible interpretation of the calculus of probability as a calculus of propensities exists. Although it is not obviously a correct interpretation, it is a factual matter whether propensities obey the calculus of probability.

Bayes’s Theorem and Weighing Evidence by Juries

This chapter discusses Bayes's theorem and the weighing of evidence by the juries. It first examines statistics and the law, before moving on to testing between two hypotheses in court. Identification evidence and databases and search are examined as well. The chapter concludes with a brief discussion of some problems of legal reasoning that have been greatly clarified by examining them from a Bayesian perspective.