arXiv subjects

Mark F. J. Steel

Publications and source records attributed to Mark F. J. Steel.

9 recordsLinked to original sources

arXiv2026

Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$χ^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

stat.ME↗

arXiv2025

Media Bias and Polarization through the Lens of a Markov Switching Latent Space Network Model

News outlets are now more than ever incentivized to provide their audience with slanted news, while the intrinsic homophilic nature of online social media may exacerbate polarized opinions. Here, we propose a new dynamic latent space model for time-varying online audience-duplication networks, which exploits social media content to conduct inference on media bias and polarization of news outlets. We contribute to the literature in several directions: 1) Our model provides a novel measure of media bias that combines information from both network data and text-based indicators; 2) we endow our model with Markov-Switching dynamics to capture polarization regimes while maintaining a parsimonious specification; 3) we contribute to the literature on the statistical properties of latent space network models. The proposed model is applied to a set of data on the online activity of national and local news outlets from four European countries in the years 2015 and 2016. We find evidence of a strong positive correlation between our media slant measure and a well-grounded external source of media bias. In addition, we provide insight into the polarization regimes across the four countries considered.

stat.AP↗

arXiv2025

Scalable Variable Selection and Model Averaging for Latent Regression Models Using Approximate Variational Bayes

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii) exponentially large model spaces, and (iii) computational costs in large samples. We introduce a novel integrated likelihood approximation based on mean-field variational posterior approximations and establish its asymptotic model selection consistency under broad conditions. To reduce the computational burden, we develop an approximate variational Bayes scheme that fixes the latent regression outcomes for all models at initial estimates obtained under a baseline null model. Despite its simplicity, this approach locally and asymptotically preserves the model-selection behavior of the full variational Bayes approach to first order, at a fraction of the computational cost. Extensive numerical studies - covering probit, tobit, semi-parametric count data models and Poisson log-normal regression - demonstrate accurate inference and large speedups, often reducing runtime from days to hours with comparable accuracy. Applications to real-world data further highlight the practical benefits of the methods for Bayesian inference in large samples and under model uncertainty.

stat.ME↗

arXiv2025

Model Uncertainty in Latent Gaussian Models with Univariate Link Function

We consider a class of latent Gaussian models with a univariate link function (ULLGMs). These are based on standard likelihood specifications (such as Poisson, Binomial, Bernoulli, Erlang, etc.) but incorporate a latent normal linear regression framework on a transformation of a key scalar parameter. We allow for model uncertainty regarding the covariates included in the regression. The ULLGM class typically accommodates extra dispersion in the data and has clear advantages for deriving theoretical properties and designing computational procedures. We formally characterize posterior existence under a convenient and popular improper prior and show that ULLGMs inherit the consistency properties from the latent Gaussian model. We propose a simple and general Markov chain Monte Carlo algorithm for Bayesian model averaging in ULLGMs. Simulation results suggest that the framework provides accurate results that are robust to some degree of misspecification. The methodology is successfully applied to measles vaccination coverage data from Ethiopia and to data on bilateral migration flows between OECD countries.

stat.ME↗

arXiv2021

Probabilistic sequential matrix factorization

We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme, which makes the resulting method particularly efficient. PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We also introduce a robust version of PSMF, called rPSMF, which uses Student-t filters to handle model misspecification. We show that PSMF can be used in multiple contexts: modeling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing data in several high-dimensional time-series, such as measurements of pollutants across London.

stat.ML↗

arXiv2019

Model Averaging and its Use in Economics

The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal response to model uncertainty in a Bayesian framework, and most of the paper deals with Bayesian model averaging. The important role of the prior assumptions in these Bayesian procedures is highlighted. In addition, frequentist model averaging methods are also discussed. Numerical methods to implement these methods are explained, and I point the reader to some freely available computational resources. The main focus is on uncertainty regarding the choice of covariates in normal linear regression models, but the paper also covers other, more challenging, settings, with particular emphasis on sampling models commonly used in economics. Applications of model averaging in economics are reviewed and discussed in a wide range of areas, among which growth economics, production modelling, finance and forecasting macroeconomic quantities.

stat.AP↗

arXiv2014

Bayesian Survival Modelling of University Outcomes

The aim of this paper is to model the length of registration at university and its associated academic outcome for undergraduate students at the Pontificia Universidad Católica de Chile. Survival time is defined as the time until the end of the enrollment period, which can relate to different reasons - graduation or two types of dropout - that are driven by different processes. Hence, a competing risks model is employed for the analysis. The issue of separation of the outcomes (which precludes maximum likelihood estimation) is handled through the use of Bayesian inference with an appropriately chosen prior. We are interested in identifying important determinants of university outcomes and the associ- ated model uncertainty is formally addressed through Bayesian model averaging. The methodology introduced for modelling university outcomes is applied to three selected degree programmes, which are particularly affected by dropout and late graduation.

stat.AP↗

arXiv2013

On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors

Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference for the Student-$t$ linear regression model under objective priors that are based on the Jeffreys rule. Posterior propriety results presented in Fonseca et al. (2008) are revisited and corrected. In particular, it is shown that the standard Jeffreys-rule prior precludes the existence of a proper posterior distribution.

stat.ME↗

arXiv2013

Adaptive MC^3 and Gibbs algorithms for Bayesian Model Averaging in Linear Regression Models

The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each iteration using uniform selection probabilities and then propose to update that variable. This may be computationally inefficient if the number of variables is large and many variables are redundant. In this work, we introduce adaptive versions of these samplers that retain their simplicity in implementation and reduce the selection probabilities of the many redundant variables. The improvements in efficiency for the adaptive samplers are illustrated in real and simulated datasets.

stat.CO↗