frequentist/Bayesian

Guest Post: Larry Laudan. Why Presuming Innocence is Not a Bayesian Prior

DSCF3726“Why presuming innocence has nothing to do with assigning low prior probabilities to the proposition that defendant didn’t commit the crime”

by Professor Larry Laudan
Philosopher of Science*

Several of the comments to the July 17 post about the presumption of innocence suppose that jurors are asked to believe, at the outset of a trial, that the defendant did not commit the crime and that they can legitimately convict him if and only if they are eventually persuaded that it is highly likely (pursuant to the prevailing standard of proof) that he did in fact commit it. Failing that, they must find him not guilty. Many contributors here are conjecturing how confident jurors should be at the outset about defendant’s material innocence.

That is a natural enough Bayesian way of formulating the issue but I think it drastically misstates what the presumption of innocence amounts to.  In my view, the presumption is not (or at least should not be)  an instruction about whether jurors believe defendant did or did not commit the crime.  It is, rather, an instruction about their probative attitudes.wavy capital

There are three reasons for thinking this:

a). asking a juror to begin a trial believing that defendant did not commit a crime requires a doxastic act that is probably outside the jurors’ control.  It would involve asking jurors  to strongly believe an empirical assertion for which they have no evidence whatsoever.  It is wholly unclear that any of us has the ability to talk ourselves into resolutely believing x if we have no empirical grounds for asserting x. By contrast, asking juries to believe that they have seen as yet no proof of defendant’s guilt is an easy belief to acquiesce in since it is obviously true. Continue reading

Categories: frequentist/Bayesian, PhilStatLaw, Statistics | 28 Comments

Mayo Commentary on Gelman & Robert

The following is my commentary on a paper by Gelman and Robertforthcoming (in early 2013) in the The American Statistician* (submitted October 3, 2012).

_______________________

mayo 2010 conference IphoneDiscussion of Gelman and Robert, “Not only defended but also applied”: The perceived absurdity of Bayesian inference”
Deborah G. Mayo

1. Introduction

I am grateful for the chance to comment on the paper by Gelman and Robert. I welcome seeing statisticians raise philosophical issues about statistical methods, and I entirely agree that methods not only should be applicable but also capable of being defended at a foundational level. “It is doubtful that even the most rabid anti-Bayesian of 2010 would claim that Bayesian inference cannot apply” (Gelman and Robert 2012, p. 6). This is clearly correct; in fact, it is not far off the mark to say that the majority of statistical applications nowadays are placed under the Bayesian umbrella, even though the goals and interpretations found there are extremely varied. There are a plethora of international societies, journals, post-docs, and prizes with “Bayesian” in their name, and a wealth of impressive new Bayesian textbooks and software is available. Even before the latest technical advances and the rise of “objective” Bayesian methods, leading statisticians were calling for eclecticism (e.g., Cox 1978), and most will claim to use a smattering of Bayesian and non-Bayesian methods, as appropriate. George Casella (to whom their paper is dedicated) and Roger Berger in their superb textbook (2002) exemplify a balanced approach. Continue reading

Categories: frequentist/Bayesian, Statistics | 24 Comments

Blog at WordPress.com.