JOHN WILCOX
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The seven requirements of highly accurate Bayesians

8/9/2024

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TL;DR key points

  • We all form judgments about the world, and we need these to be accurate in order to make good decisions
  • In epistemology and philosophy of science, “Bayesianism” is the dominating theory about how to form rational judgments
  • However, not all of us are always Bayesians, and not all Bayesians are always accurate 
  • This post then articulates seven requirements to be an accurate Bayesian, some of which are widely-known to some (i.e. requirements 1 to 3) while others may be less so (i.e. requirements 4 to 7)
  • The requirements are as follows:
               1. Assign likelihoods to evidence
               2. Assign prior probabilities to the hypotheses
               3. Update using Bayes’ theorem
               4. Use calibrated probabilities
               5. Recognize auxiliary hypotheses
               6. Recognize consilience
               7. Be cautious about fallible heuristics

​THE IMPORTANCE OF BAYESIANISM​

As discussed elsewhere, in many important contexts, we need to form accurate judgments about the world: this is true of medical diagnosis and treatment, of law proceedings, of policy analysis and indeed of a myriad other domains. And as discussed elsewhere, more accurate judgments often means better decisions, including in contexts where they can be a matter of life and death—such as medicine and law.

In analytic epistemology and philosophy of science, “Bayesianism” is the dominant theory of how we should form rational judgments of probability. Additionally, as I discuss elsewhere, Bayesian thinking can help us recognize strong evidence and find the truth in cases where others cannot. 

But there’s ample evidence that humans are not Bayesians, and there’s ample arguments that Bayesians can still end up with inaccurate judgments if they start from the wrong place (i.e. the wrong “priors”).

So, given the importance of accurate judgments and given Bayesianism’s potential to facilitate such accuracy, how can one be an accurate Bayesian?

Here, I argue that there are seven requirements of highly accurate Bayesians (somewhat carrying on the Steven Covey-styled characterization of rationality which I outlined here). Some requirements will be well-known to relevant experts (such as requirements 1 to 3) while others might be less so (such as requirements 4 to 7). In any case, this post is written for both the expert and novice, hoping to say something unfamiliar to both—while the familiar remainder can be easily skipped.

With that caveat, let us consider the first requirement.


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How to calculate probabilities: The Bayesian calculator

11/10/2021

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the tl;dr key points

  • This post describes and provides a Bayesian calculator to supplement a philosophy of science course taught at Stanford University
  • The calculator is potentially useful for a variety of purposes, including calculating the probability of propositions in philosophical, scientific and mundane contexts
  • The calculator also features some examples of Bayesian calculations, just to help others get an intuition for how to use the calculator

THE BAYESIAN CALCULATOR: WHY YOU SHOULD CARE ABOUT IT

Tomorrow, I'll be giving my last lecture on Bayesianism for the course "Phil 60: Introduction to Philosophy of Science" at Stanford University. 

There, I'll be talking about a Bayesian solution to the problem of underdetermination, associated with Pierre Duhem and Willard van Orman Quine.

The problem essentially concerns the limited ability of evidence to support or rule out isolated hypotheses. For example, if you run an experiment to test whether a putative piece of iron melts at 1538 degrees Celsius, and the piece doesn't melt at that temperature, then you have at least two possible responses: you could rule out the hypothesis that iron melts at 1538 degrees Celsius, or you could instead rule out the hypothesis that the piece of metal was actually iron as opposed to another substance. As Duhem put it, the experiment itself does not tell you which specific hypothesis is false: 
​

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    John Wilcox

    Cognitive scientist
    @ Columbia University
    Founder
    @ Alethic Innovations

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  • Home
  • Curriculum Vitae
  • Teaching
    • Accuracy of Human Judgment
    • Introduction to Psychology
    • Teaching Methods
    • Philosophy of Science
    • Ethics in a Human Life
    • Epistemology & Probability
    • Logic
    • Applied Research Methods
    • Teaching Evaluations
  • John's Blog