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Estimating uncertainty of machine learning models is essential to assess the quality of the predictions that these models provide. However, there are several factors that influence the quality of uncertainty estimates, one of which is the…
We study the problem of conditional predictive inference on multiple outcomes missing at random (MAR) -- or equivalently, under covariate shift. While the weighted conformal prediction offers a tool for inference under covariate shift with…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…
Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is…
Surrogate models (including deep neural networks and other machine learning algorithms in supervised learning) are capable of approximating arbitrarily complex, high-dimensional input-output problems in science and engineering, but require…
Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data.…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…
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…
In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…