Conor Mayo-Wilson | Searcharxiv

arXiv2022

Robust Bayesianism and Likelihoodism

We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988], and a variety of other widely-accepted "statistical principles", e.g., the sufficiency principle [Birnbaum, 1962, 1972] and stopping-rule principle [Berger and Wolpert, 1988]. The main technical contribution of this paper is to extend some of those results to a qualitative framework in which experimenters are justified only in making comparative, non-numerical judgments of the form "A given B is more likely than C given D."

math.ST↗

arXiv2012

Causal Conclusions that Flip Repeatedly and Their Justification

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method from non-experimental data is subject to reversal as the sample size increases any finite number of times. That result, called the causal flipping theorem, extends prior results to the effect that causal discovery cannot be reliable on a given sample size. We argue that since repeated flipping of causal conclusions is unavoidable in principle for consistent methods, the best possible discovery methods are consistent methods that retract their earlier conclusions no more than necessary. A series of simulations of various methods across a wide range of sample sizes illustrates concretely both the theorem and the principle of comparing methods in terms of retractions.

cs.LG↗