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Laura Ventura

Publications and source records attributed to Laura Ventura.

12 recordsLinked to original sources
arXiv2026

Box Confidence Depth: simulation-based inference with hyper-rectangles

This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations fail to provide accurate results. The method leverages the concept of data depth and depends on creating random hyper-rectangles, i.e. boxes, in the sample space generated through simulations from the model, varying the input parameters. A probabilistic acceptance rule allows to retrieve a Depth-Confidence Distribution for the model parameters from which point estimators as well as calibrated confidence sets can be read-off. The method is designed to address cases where both the parameters and test statistics are multivariate.

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arXiv2025

Bayesian Discrepancy Measure: Higher-order and Skewed approximations

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order asymptotic approximations and skewed approximations for univariate posterior distributions, also in the presence of nuisance parameters, demonstrating improved accuracy in capturing posterior shape with little additional computational cost over simple first-order approximations. For the third-order approximations, connections to frequentist inference via matching priors are highlighted. Moreover, the definition of the Bayesian Discrepancy Measure and the proposed methodology are extended to the multivariate setting, employing tractable skew-normal posterior approximations obtained via derivative matching at the mode. Accurate multivariate approximations for the Bayesian Discrepancy Measure are then derived by defining credible regions based on the Optimal Transport map, that transforms the skew-normal approximation to a standard multivariate normal distribution. The performance and practical benefits of these higher-order and skewed approximations are illustrated through two examples.

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arXiv2022

On approximate robust confidence distributions

A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $ψ$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests along with measures of evidence for statements of the type "$ψ> ψ_0$" or "$ψ_1 \leq ψ\leq ψ_2$", to derive confidence intervals, comparing the parameter of interest with other parameters from other studies, etc. The aim of this contribution is to discuss robust confidence distributions derived from unbiased $M-$estimating functions, which provide robust inference for $ψ$ when the assumed distribution is just an approximate parametric model or in the presence of deviant values in the observed data. Paralleling likelihood-based results and extending results available for robust scoring rules, we first illustrate how robust confidence distributions can be derived from the asymptotic theory of robust pivotal quantities. Then, we discuss the derivation of robust confidence distributions via simulation methods. An application and a simulation study are illustrated in the context of non-inferiority testing, in which null hypotheses of the form $H_0: ψ\leq ψ_0$ are of interest.

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arXiv2022

A new Bayesian discrepancy measure

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a given hypothesis with respect to the available information (prior law and data). To summarise this information, the posterior median is employed, allowing a simple assessment of the discrepancy with a fixed hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a single hypothesis with the observed data, as opposed to the more common comparative approach where a hypothesis is rejected in favour of a competing hypothesis. The proposed measure of evidence has properties of consistency and invariance. After presenting the definition of the measure for a parameter of interest, both in the absence and in the presence of nuisance parameters, we illustrate some examples showing its conceptual and interpretative simplicity. Finally, we compare the BDT with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses.

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arXiv2021

Robust confidence distributions from proper scoring rules

A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to reach point estimates, to assess their precision, to set up tests along with measures of evidence, to derive confidence intervals, comparing the parameter of interest with other parameters from other studies, etc. A general recipe for deriving confidence distributions is based on classical pivotal quantities and their exact or approximate distributions. However, in the presence of model misspecifications or outlying values in the observed data, classical pivotal quantities, and thus confidence distributions, may be inaccurate. The aim of this paper is to discuss the derivation and application of robust confidence distributions. In particular, we discuss a general approach based on the Tsallis scoring rule in order to compute a robust confidence distribution. Examples and simulation results are discussed for some problems often encountered in practice, such as the two-sample heteroschedastic comparison, the receiver operating characteristic curves and regression models.

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arXiv2019

Robust approximate Bayesian inference

We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics in ABC algorithms. The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method. An R implementation is also provided in the robustBLME package.

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arXiv2019

Objective Bayesian inference with proper scoring rules

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications is required. In these situations, we suggest to resort to a posterior distribution for the parameter of interest based on proper scoring rules. Scoring rules are loss functions designed to measure the quality of a probability distribution for a random variable, given its observed value. Important examples are the Tsallis score and the Hyvärinen score, which allow us to deal with model misspecifications or with complex models. Also the full and the composite likelihoods are both special instances of scoring rules. The aim of this paper is twofold. Firstly, we discuss the use of scoring rules in the Bayes formula in order to compute a posterior distribution, named SR-posterior distribution, and we derive its asymptotic normality. Secondly, we propose a procedure for building default priors for the unknown parameter of interest that can be used to update the information provided by the scoring rule in the SR-posterior distribution. In particular, a reference prior is obtained by maximizing the average $α-$divergence from the SR-posterior distribution. For $0 \leq |α|<1$, the result is a Jeffreys-type prior that is proportional to the square root of the determinant of the Godambe information matrix associated to the scoring rule. Some examples are discussed.

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arXiv2016

Improved Laplace Approximation for Marginal Likelihoods

Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the integrand function may be far from that of the Gaussian density, and thus the standard Laplace approximation can be inaccurate. We propose an improved Laplace approximation that reduces the asymptotic error of the standard Laplace formula by one order of magnitude, thus leading to third-order accuracy. We also show, by means of practical examples of various complexity, that the proposed method is extremely accurate, even in high dimensions, improving over the standard Laplace formula. Such examples also demonstrate that the accuracy of the proposed method is comparable with that of other existing methods, which are computationally more demanding. An R implementation of the improved Laplace approximation is also provided through the R package iLaplace available on CRAN.

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arXiv2015

Approximate Bayesian Computation with composite score functions

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

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arXiv2014

Minimum scoring rule inference

Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper we develop some basic scoring rule estimation theory, and explore robustness and interval estimation properties by means of theory and simulations.

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arXiv2012

A note on marginal posterior simulation via higher-order tail area approximations

We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar parameter of interest, in the presence of nuisance parameters. Its advantage over MCMC methods is that samples are drawn independently with lower computational time and the implementation requires only standard maximum likelihood routines. The method is illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model.

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