Lindley’s Bayesian thoughts
Lindley Bayesian Thoughts Interview, 2004.
“Ultimately, in my extreme view, all reasoning reduces to probability calculations.”
This Lindley’s mature view, but lacking in detail. Some time I should check my interpretation.
He approves of de Finetti.
- Approves of Savage’s proof.
- Advocates maximization of expected utility
- States that non-Bayesian methods are always dominated by Bayesian methods (Wald’s admissibility?)
- Bayesian methods create ‘an organized subject’.
- He states that any measure of uncertainty must be additive, like probability, but unlike likelihood.
“The main danger is that they will be used automatically. In the application of Bayesian methods, you first need to assign some basic probabilities (and perhaps utilities) to give the problem structure;… . One must think about the basic values and it is not usually satisfactory to use a normal density and non-informative priors. You must think about the real quantities involved, like temperature or blood pressure, and not about symbols that represent them. This distinction between the thinking you and the unthinking, calculating personal computer is essential.”
“Savage, around 1960, is reported to have said to his colleagues: “In 1954 I proved that the only sound methods were Bayesian; yet you continue to use non-Bayesian ideas without pointing out a flaw in either my premises or my proof, why?””
“In the assessment of probabilities. …
I have emphasised the need to think when using Bayes. Yet we devote too little effort to doing so, and we know almost nothing about assessing probabilities for four, or more, quantities … . This is despite the development of powerful methods for handling large data sets with many variables. Here the computer has overtaken the thinker … .”
In principle, Lindley is a fundamentalist Bayesian. But he recognizes that the assessment of initial probabilities is problematic, such that anyone who lacks confidence in their assessment might be said to have Knightian uncertainty.
I intend to rise to Lindley’s challenge – but politely – later.
A 2013 interview. Lindley’s approach is clearly pragmatic, based on the likelihood principle and utility maximization. Like Keynes, all probabilities are conditional on some ‘small’ model world. If the model is wrong, one should change it. If one has doubts about the model, one should develop a more general model about which one has no doubts.
He regards the axioms as falsifiable, and to work in practice. He regards criticisms of Bayesianism as not being directed at specific axioms, and hence not valid. His method of working is like that of Boole, Keynes and Good, in which one iteratively develops candidate probabilities until one has a solution. Thus:
- Lindley seems unaware of Keynes’ criticisms of specific axioms in his Treatise.
- He does not deal with the case (common in the social sciences and real life) where there seems no possibility of a model that encompasses all possibilities.
- He implicitly assumes that the process of iteration of probability estimates will converge, which ought to be a theorem conditional on the situation being modelled (e.g., that it is stable and ergodic).
My notes on Probability.