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The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without…
Population control is an essential component of any projector Monte Carlo algorithm. This control mechanism usually introduces a bias in the sampled quantities that is inversely proportional to the population size. In this paper, we…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
In this paper, a Monte Carlo based approach for the quantification of the importance of the scattering input parameters with respect to the failure probability is presented. Using the basic idea of the alpha-factors of the First Order…
Unbiased assessment of the predictivity of models learnt by supervised machine-learning methods requires knowledge of the learned function over a reserved test set (not used by the learning algorithm). The quality of the assessment depends,…
We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that ensures reliability of said inferences. The catch is that…
Machine learning models $-$ now commonly developed to screen, diagnose, or predict health conditions $-$ are evaluated with a variety of performance metrics. An important first step in assessing the practical utility of a model is to…
Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…