Related papers: Bayesian evidence as a tool for comparing datasets
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…
This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an…
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…
Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…
Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an…
In light of the growing number of cosmological observations, it is important to develop versatile tools to quantify the constraining power and consistency of cosmological probes. Originally motivated from information theory, we use the…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses…
Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…
We build a Bayesian contextual classification model using an optimistic score ratio for robust binary classification when there is limited information on the class-conditional, or contextual, distribution. The optimistic score searches for…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…