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Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
In many scientific fields, researchers are interested in discovering features with substantial effect on the response from a large number of features while controlling the proportion of false discoveries. By incorporating the knockoff…
Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian Optimization (BO) employs…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
This paper discusses the efficient Bayesian estimation of a multivariate factor stochastic volatility (Factor MSV) model with leverage. We propose a novel approach to construct the sampling schemes that converges to the posterior…
For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…
In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of…
Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models…
We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal…
This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…
Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…
We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…
Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…