Related papers: Sequential Monte-Carlo testing by betting
AB testing evaluates the difference between a control and a treatment in a statistically rigorous manner. Continuous monitoring allows statistical evaluation of an AB test as it proceeds. One goal of continuous monitoring is early stopping…
We consider the computation of the permanent of a binary n by n matrix. It is well- known that the exact computation is a #P complete problem. A variety of Markov chain Monte Carlo (MCMC) computational algorithms have been introduced in the…
Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…
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…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
We introduce a principled probabilistic framework for reward-guided decoding in large language models, addressing the limitations of standard decoding methods that optimize token-level likelihood rather than sequence-level quality. Our…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
We develop conservative tests for the mean of a bounded population under stratified sampling and apply them to risk-limiting post-election audits. The tests are ``anytime valid'' under sequential sampling, allowing optional stopping in each…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
We compare two theoretically distinct approaches to generating artificial (or ``surrogate'') data for testing hypotheses about a given data set. The first and more straightforward approach is to fit a single ``best'' model to the original…
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…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
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…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves…