Related papers: Discussion: On Arguments Concerning Statistical Pr…
Rejoinder of "On the Birnbaum Argument for the Strong Likelihood Principle" by Deborah G. Mayo [arXiv:1302.7021].
Deborah Mayo claims to have refuted Birnbaum's argument that the Likelihood Principle is a logical consequence of the Sufficiency and Conditionality Principles. However, this claim fails because her interpretation of the Conditionality…
This is an invited contribution to the discussion on Professor Deborah Mayo's paper, "On the Birnbaum argument for the strong likelihood principle," to appear in Statistical Science. Mayo clearly demonstrates that statistical methods…
We discuss Birnbaum's result, its relevance to statistical reasoning, Mayo's objections and the result in [Electron. J. Statist. 7 (2013) 2645-2655] that the proof of this result doesn't establish what is commonly believed.…
The paper by Mayo claims to provide a new clarification and critique of Birnbaum's argument for showing that sufficiency and conditionality principles imply the likelihood principle. However, much of the arguments go back to arguments made…
The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability,…
The new book by philosopher Deborah Mayo is relevant to data science for topical reasons, as she takes various controversial positions regarding hypothesis testing and statistical practice, and also as an entry point to thinking about the…
In this discussion we demonstrate that fiducial distributions provide a natural example of an inference paradigm that does not obey Strong Likelihood Principle while still satisfying the Weak Conditionality Principle. [arXiv:1302.7021]
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…
Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].
Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].
An essential component of inference based on familiar frequentist notions, such as $p$-values, significance and confidence levels, is the relevant sampling distribution. This feature results in violations of a principle known as the strong…
Comment on ``Lancaster Probabilities and Gibbs Sampling'' [arXiv:0808.3852]
In this note, we provide critical commentary on two articles that cast doubt on the validity and implications of Birnbaum's theorem: Evans (2013) and Mayo (2014). In our view, the proof is correct and the consequences of the theorem are…
Discussion of "Likelihood Inference for Models with Unobservables: Another View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
Discussion of "Likelihood Inference for Models with Unobservables: Another View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
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],…
For many years, philosopher-of-statistics Deborah Mayo has been advocating the concept of severe testing as a key part of hypothesis testing. Her recent book, Statistical Inference as Severe Testing, is a comprehensive exposition of her…
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.