2021

A Bayesian Inference Primer

“When you have eliminated the impossible, all that remains, no matter how improbable, must be the truth.” – Sherlock Holmes (Arthur Conan Doyle) For a long time Bayesian inference was something I understood without really understanding it. I only really got it it after reading Chapter 2 of John K. Kruschke’s textbook Doing Bayesian Data Analysis, where he describes Bayesian Inference as Reallocation of Credibility Across Possibilities I now understand Bayesian Inference to be essentially Sherlock Holmes’ pithy statement about eliminating the impossible quoted above, taken to its mathematical conclusion.

The Deliberati Argument Model

In this article we introduce an argument model: a set of terms for analyzing arguments by naming their parts. There are various argument models in the academic literature on argumentation theory and related fields but none provide us with precise definitions for all the concepts behind our algorithms for improving for online conversations. So we will define those concepts here. Our model incorporates the basic ideas from the influential Toulmin model of argumentation first introduced in 1948.

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Necessity and Sufficiency

Argument and Information In the previous essay in this series, we introduced the idea of relevance, and said that a premise is relevant to the conclusion iff $P(A \vert B) > P(A \vert \bar{B})$. Consider the argument (𝐴) this is a good candidate for the job because (𝐵) he has a pulse. Having a pulse may not be a very persuasive reason to hire somebody, but it is probably quite relevant, because if the candidate did not have a pulse, the subject would probably be much less likely to want to hire him.

A Bayesian Account of Argumentation

In this essay, we present an account of argumentation as the exchange of information between Bayesian rational agents. The basic idea of the Bayesian view of probability is that probabilities represent subjective degrees of belief. So if we know the beliefs of some rational “subject”, we can precisely define and measure various concepts relating to the quality of an argument in the mind of the subject. In other words we can objectively measure the subjective quality of an argument.