Related papers: Marginal inferential models: prior-free probabilis…
Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…
Pre-trained machine learning (ML) predictions have been increasingly used to complement incomplete data to enable downstream scientific inquiries, but their naive integration risks biased inferences. Recently, multiple methods have been…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…
Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors…
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data,…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding…
Causal inference deals with identifying which random variables "cause" or control other random variables. Recent advances on the topic of causal inference based on tools from statistical estimation and machine learning have resulted in…
Copula models are widely employed in multivariate time series analysis because they permit flexible modelling of marginal distributions independently of the dependence structure, which is fully characterised by the copula function. However,…
A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially…
The Invariant Risk Minimization (IRM) framework aims to learn invariant features from a set of environments for solving the out-of-distribution (OOD) generalization problem. The underlying assumption is that the causal components of the…
This paper is concerned with Bayesian inference when the likelihood is analytically intractable but can be unbiasedly estimated. We propose an annealed importance sampling procedure for estimating expectations with respect to the posterior.…
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This…