Related papers: Multiple testing with anytime-valid Monte Carlo p-…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a…
Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is…
In contemporary research, data scientists often test an infinite sequence of hypotheses $H_1,H_2,\ldots$ one by one, and are required to make real-time decisions without knowing the future hypotheses or data. In this paper, we consider such…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Given a composite null hypothesis H, test supermartingales are non-negative supermartingales with respect to H with initial value 1. Large values of test supermartingales provide evidence against H. As a result, test supermartingales are an…
Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern…
For a bucket test with a single criterion for success and a fixed number of samples or testing period, requiring a $p$-value less than a specified value of $\alpha$ for the success criterion produces statistical confidence at level $1 -…
Monte Carlo permutation tests are a cornerstone of valid, model-free statistical inference. A widely held practical intuition is that increasing the number of sampled permutations improves test performance, in particular that statistical…
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is…
The rank envelope test (Myllym\"aki et al., Global envelope tests for spatial processes, arXiv:1307.0239 [stat.ME]) is proposed as a solution to multiple testing problem for Monte Carlo tests. Three different situations are recognized: 1) a…
Genome assembly, the process of reconstructing a long genetic sequence by aligning and merging short fragments, or reads, is known to be NP-hard, either as a version of the shortest common superstring problem or in a Hamiltonian-cycle…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur…
Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing. Applications of this control abound in drug discovery, forensics, anomaly detection, and, in particular, machine learning,…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…