Related papers: Bayesian Modeling and MCMC Computation in Linear L…
This paper discusses the challenges presented by tall data problems associated with Bayesian classification (specifically binary classification) and the existing methods to handle them. Current methods include parallelizing the likelihood,…
Bayesian variable selection (BVS) depends critically on the specification of a prior distribution over the model space, particularly for controlling sparsity and multiplicity. This paper examines the practical consequences of different…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…
Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and…
When modelling censored observations, a typical approach in current regression methods is to use a censored-Gaussian (i.e. Tobit) model to describe the conditional output distribution. In this paper, as in the case of missing data, we argue…
These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…
Multilevel network meta-regression (ML-NMR) enables population-adjusted indirect treatment comparisons by combining individual patient data (IPD) with aggregate data. When individual-level covariates are unavailable, ML-NMR marginalizes…
Predicting with missing inputs challenges even parametric models, as parameter estimation alone is insufficient for prediction on incomplete data. While several works study prediction in linear models, we focus on logistic models, where…
We investigate the complexity of logistic regression models which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
Mixed effects regression models are widely used by language researchers. However, these regressions are implemented with an algorithm which may not converge on a solution. While convergence issues in linear mixed effects models can often be…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…