Related papers: A Conversation with Donald B. Rubin
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on finite inference of recursive functions, since…
Imputation procedures in biomedical fields have turned into statistical practice, since further analyses can be conducted ignoring the former presence of missing values. In particular, non-parametric imputation schemes like the random…
Meta-analysis is a statistical method used in evidence synthesis for combining, analyzing and summarizing studies that have the same target endpoint and aims to derive a pooled quantitative estimate using fixed and random effects models or…
We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern…
Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's $h$-transform, as well as a summary of Doob's three books. Finally, Doob's `stochastic triangle' is viewed…
Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…
The Statistics Consortium at the University of Maryland, College Park, hosted a two-day workshop on Bayesian Methods that Frequentists Should Know during April 30--May 1, 2008. The event was co-sponsored by the Institute of Mathematical…
Respondent-driven sampling (RDS) is an approach to sampling design and analysis which utilizes the networks of social relationships that connect members of the target population, using chain-referral methods to facilitate sampling. RDS…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
This article, produced as a result of the Symposium on Statistical Inference, is an introduction to the literature on the function of expertise, judgment, and choice in the practice of statistics and scientific research. In particular,…
The notation of mutually unbiased bases(MUB) was first introduced by Ivanovic to reconstruct density matrixes\cite{Ivanovic}. The subject about how to use MUB to analyze, process, and utilize the information of the second moments between…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
The 2021 Nobel Prize in Economics recognized an epistemology of causal inference based on the Rubin causal model (Rubin 1974), which merits broader attention in philosophy. This model, in fact, presupposes a logical principle of…
This special volume of Statistical Sciences presents some innovative, if not provocative, ideas in the area of reliability, or perhaps more appropriately named, integrated system assessment. In this age of exponential growth in science,…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
Suppose you are told that taking a statin will reduce your risk of a heart attack or stroke by 3% in the next ten years, or that women have better emotional intelligence than men. You may wonder how accurate the 3% is, or how confident we…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
Robert Vincent Hogg was born on November 8, 1924 in Hannibal, Missouri. He earned a Ph.D. in statistics at the University of Iowa in 1950, where his advisor was Allen Craig. Following graduation, he joined the mathematics faculty at the…