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We propose a copula based method to handle missing values in multivariate data of mixed types in multilevel data sets. Building upon the extended rank likelihood of \cite{hoff2007extending} and the multinomial probit model, our model is a…
The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent…
Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis,…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
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…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…
We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the…
Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of…
The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Small expectation values are difficult to measure in Monte Carlo calculations as they tend to get swamped by noise. Recently an algorithm has been proposed by Luscher and Weisz which allows one to measure expectation values which previously…
Estimating mutual information (MI) is a fundamental task in data science and machine learning. Existing estimators mainly rely on either highly flexible models (e.g., neural networks), which require large amounts of data, or overly…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…