Related papers: Bayesian Posteriors Without Bayes' Theorem
We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the…
Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…
Estimation of the population size $n$ from $k$ i.i.d.\ binomial observations with unknown success probability $p$ is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously…
This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
In recent years, large-scale Bayesian learning draws a great deal of attention. However, in big-data era, the amount of data we face is growing much faster than our ability to deal with it. Fortunately, it is observed that large-scale…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…
The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…