Related papers: The look-elsewhere effect from a unified Bayesian …
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
We suggest a method for statistical tests which does not suffer from a posteriori manipulations with tested samples (e.g. cuts optimization) and does not require a somewhat obscure procedure of the penalty estimate. The idea of the method…
Several experiments in high-energy physics and astrophysics can be treated as on/off measurements, where an observation potentially containing a new source or effect ("on" measurement) is contrasted with a background-only observation free…
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are…
We propose an analytical solution to the on-off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a…
In high-energy astrophysics, it is common practice to account for the background overlaid with the counts from the source of interest with the help of auxiliary measurements carried on by pointing off-source. In this "on/off" measurement,…
We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all…
A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the coexistence of…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
Bayes factors have become a popular tool in exoplanet spectroscopy for testing atmosphere models against one another. We show that the commonly used method for converting these values into significance "sigmas" is invalid. The formula is…
For decades researchers have studied the On/Off counting problem, where a measured rate consists of two parts. One due to a signal process and another due to a background process, of which both magnitudes are unknown. While most frequentist…
Different ways of extracting parameters of interest from combined data sets of separate experiments are investigated accounting for the systematic errors. It is shown, that the frequentist approach may yield larger $\chi^2$ values when…
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…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…
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…
We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…