Related papers: Bayesian inference: More than Bayes's theorem

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of…

In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…

The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…

Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive…

Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…

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…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…

Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…