相关论文: Generalizations related to hypothesis testing with…

In the simple vs composite hypothesis test with a proper prior, the Bayes Factor (BF) is shown to be the posterior mean of the Likelihood Ratio (LR). Therefore, the posterior standard deviation of the LR or rather its posterior cumulative…

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…

In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…

Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for…

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…

Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…

We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…

The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…

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…

Establishing the frequentist properties of Bayesian approaches widens their appeal and offers new understanding. In hypothesis testing, Bayesian model averaging addresses the problem that conclusions are sensitive to variable selection. But…

\citet{Rosenbaum83ps} introduced the notion of the propensity score and discussed its central role in causal inference with observational studies. Their paper, however, caused a fundamental incoherence with an early paper by…

When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…

The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

The local false discovery rate (lfdr) of Efron et al. (2001) enjoys major conceptual and decision-theoretic advantages over the false discovery rate (FDR) as an error criterion in multiple testing, but is only well-defined in Bayesian…

The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical…

For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal…

Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…