Related papers: Frequentist and Bayesian Confidence Intervals

The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…

Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…

When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…

Practical employment of Bayesian trial designs is still rare. Even if accepted in principle, the regulators have commonly required that such designs be calibrated according to an upper bound for the frequentist type I error rate. This…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis…

In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

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…

In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm.…

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

We argue that the Bayesian paradigm, of a prior which represents the beliefs of the statistician before observing the data, is not feasible in ultra-high-dimensional models. We claim that natural priors that represent the a priori beliefs…

The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses and for its assessment Bayesian methods are widespread in the forensic field. However, the Bayesian `recipe' for the LR…

In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

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…

Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…