Related papers: Feldman-Cousins Confidence Levels - Toy MC Method
The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only ("null") hypothesis. A typical approach uses toy Monte Carlo experiments to build an…
We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter…
In this note we present studies of coverage and power for confidence intervals for a Poisson process with known background calculated using the Likelihood ratio (aka Feldman & Cousins) ordering with Bayesian treatment of uncertainties in…
When searching for new physics effects, collaborations will often wish to publish upper limits and intervals with a lower confidence level than the threshold they would set to claim an excess or a discovery. However, confidence intervals…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…
In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties.…
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should…
In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full…
In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a…
Researchers often calculate ratios of measured quantities. Specifying confidence limits for ratios is difficult and the appropriate methods are often unknown. Appropriate methods are described (Fieller, Taylor, special bootstrap methods).…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
We study frequentist confidence intervals based on graphical profile likelihoods (Wilks' theorem, likelihood integration), and the Feldman-Cousins (FC) prescription, a generalisation of the Neyman belt construction, in a setting with…
We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…