相关论文: An alternative inference tool to total probability…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

A product of two Gaussians (or normal distributions) is another Gaussian. That's a valuable and useful fact! Here we use it to derive a refactoring of a common product of multivariate Gaussians: The product of a Gaussian likelihood times a…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

The mutual information of two random variables i and j with joint probabilities t_ij is commonly used in learning Bayesian nets as well as in many other fields. The chances t_ij are usually estimated by the empirical sampling frequency…

This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…

An overview is presented of a general theory of statistical inference that is referred to as the fiducial-Bayes fusion. This theory combines organic fiducial inference and Bayesian inference. The aim is that the reader is given a clear…

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…

Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…