Related papers: Hypothesis testing for Markov chain Monte Carlo

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a…

Effective sample size is a standard summary of Markov chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinate-wise…

Instead of testing solely a precise hypothesis, it is often useful to enlarge it with alternatives that are deemed to differ from it negligibly. For instance, in a bioequivalence study one might consider the hypothesis that the…

Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted…

Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable…

Most genome assemblers construct point estimates, choosing a genome sequence from among many alternative hypotheses that are supported by the data. We present a Markov Chain Monte Carlo approach to sequence assembly that instead generates…

Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their…

Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform…

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…

Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

In a Monte-Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones.…

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a…

We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via…