Related papers: On The Distribution of Bayesian Evidences
Bayesian linear mixed-effects models and Bayesian ANOVA are increasingly being used in the cognitive sciences to perform null hypothesis tests, where a null hypothesis that an effect is zero is compared with an alternative hypothesis that…
Bayesian evidence ratios are widely used to quantify the statistical consistency between different experiments. However, since the evidence ratio is prior dependent, the precise translation between its value and the degree of…
Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign…
For several decades, legal and scientific scholars have argued that conclusions from forensic examinations should be supported by statistical data and reported within a probabilistic framework. Multiple models have been proposed to quantify…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on…
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…
We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
The Bayes factor is the gold-standard figure of merit for comparing fits of models to data, for hypothesis selection and parameter estimation. However it is little used because it is computationally very intensive. Here it is shown how…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic…
Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…
Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor)…