Artículos con la etiqueta ‘Statistics Theory (math.ST)’

Foundations of statistical inference, revisited

Por • 31 dic, 2013 • Category: Leyes

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 violating the likelihood principle need not violate either the sufficiency or conditionality principle, thus refuting Birnbaum’s claim. With the constraints of Birnbaum’s theorem lifted, we revisit issues related to the foundations of statistical inference, focusing on some new foundational principles, the inferential model framework, and connections with sufficiency and conditioning.

A Tricentenary history of the Law of Large Numbers

Por • 27 sep, 2013 • Category: Educacion

The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli’s Theorem in 1713, through De Moivre’s Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob Bernoulli’s Theorem: 1. As limit theorem (sample size $n\to\infty$), and: 2. Determining sufficiently large sample size for specified precision, for known and also unknown p (the inversion problem), are studied, in frequentist and Bayesian settings. The Bienaym\'{e}-Chebyshev Inequality is shown to be a meeting point of the French and Russian directions in the history. Particular emphasis is given to less well-known aspects especially of the Russian direction, with the work of Chebyshev, Markov (the organizer of Bicentennial celebrations), and S.N. Bernstein as focal points.

Measurement of statistical evidence on an absolute scale following thermodynamic principles

Por • 27 jun, 2012 • Category: Crítica

Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p-values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically-based framework in which measurement of E on an absolute scale, for which “one degree” always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.