相关论文: From $p$-Values to Posterior Probabilities of Hypo…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

Investigators often use the data to generate interesting hypotheses and then perform inference for the generated hypotheses. P-values and confidence intervals must account for this explorative data analysis. A fruitful method for doing so…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

The end of LEP and SLC is a good moment to review the way to summarize search results in order to exploit at best, in future analyses and speculations, the pieces of information coming from all experiments. Some known problems with the…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal…

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…

We describe Bayes factors based on z, t, $\chi^2$, and F statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. 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…

Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign…

We study a variation of Bayesian M-ary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an…

The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model…

A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation…

Posterior predictive p-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribution is not uniform under the hypothesis…

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…