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We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…

Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance sampling-based…

Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…

Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…

Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…

The class of $\alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails,…

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…

When language model (LM) users aim to improve the quality of its generations, it is crucial to specify concrete behavioral attributes that the model should strive to reflect. However, curating such principles across many domains, even…

This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…

Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…

This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…

In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…

Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…

We present a practical implementation of a Monte Carlo method to estimate the significance of cross-correlations in unevenly sampled time series of data, whose statistical properties are modeled with a simple power-law power spectral…