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Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…
The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and…
A new method for the computation of the posterior distribution of the number k of components in a finite mixture is presented. Two aspects of prior specification are also studied: an argument is made for the use of a Poisson(1) distribution…
Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
Causal inference relies on the untestable assumption of no unmeasured confounding. Sensitivity analysis can be used to quantify the impact of unmeasured confounding on causal estimates. Among sensitivity analysis methods proposed in the…
Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with…
Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective "unsupervised" implies that the number of mixing components is unknown and has to be determined, ideally by data…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…
We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…
Unit-level models for survey data offer many advantages over their area-level counterparts, such as potential for more precise estimates and a natural benchmarking property. However two main challenges occur in this context: accounting for…