Related papers: Frequentism and Bayesianism: A Python-driven Prime…

The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…

There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…

The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…

Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence…

Standard statistical theory has arguably proved to be unsuitable as a basis for constructing a satisfactory completely general framework for performing statistical inference. For example, frequentist theory has never come close to providing…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of…

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…

We perform extensive Monte Carlo simulations to systematically compare the frequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goal is to investigate whether the Bayesian period search is advantageous over the…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…

The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…

In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).…

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.…

Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…

In this article, we consider the problem of estimating the parameters of the Fr\'echet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood,…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

It is shown that all the Frequentist methods are equivalent from a statistical point of view, but the physical significance of the confidence intervals depends on the method. The Bayesian Ordering method is presented and confronted with the…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…