Related papers: Backtesting Expected Shortfall: Accounting for bot…
We investigate the phenomenon of posterior collapse in variational autoencoders (VAEs) from the perspective of statistical physics, and reveal that it constitutes a phase transition governed jointly by data structure and model…
We address the problem of estimating the expected shortfall risk of a financial loss using a finite number of i.i.d. data. It is well known that the classical plug-in estimator suffers from poor statistical performance when faced with…
Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…
The closure principle is a standard tool for achieving strong family-wise error rate (FWER) control in multiple testing problems. We develop an e-value-based closed testing framework that inherits nice properties of e-values, which are…
Single-call stochastic extragradient methods, like stochastic past extragradient (SPEG) and stochastic optimistic gradient (SOG), have gained a lot of interest in recent years and are one of the most efficient algorithms for solving…
Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…
These notes are based on lectures delivered by G. Schehr at the XVIth School on Fundamental Problems in Statistical Physics (FPSP), held in Oropa (Italy) from 30 June to 11 July 2025. After a brief introduction to extreme value statistics…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…
The problem of estimation error of Expected Shortfall is analyzed, with a view of its introduction as a global regulatory risk measure.
A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general…
While the inverse probability of treatment weighting (IPTW) is a commonly used approach for treatment comparisons in observational data, the resulting estimates may be subject to bias and excessively large variance when there is lack of…
Estimation of heterogeneous treatment effects is an essential component of precision medicine. Model and algorithm-based methods have been developed within the causal inference framework to achieve valid estimation and inference. Existing…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contains derivatives instruments. In this paper, we postpone to estimate…
The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in…
Competing risks models for a repairable system subject to several failure modes are discussed. Under minimal repair, it is assumed that each failure mode has a power law intensity. An orthogonal reparametrization is used to obtain an…
The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile.…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…