Related papers: Modelling Correlated Bernoulli Data Part II: Infer…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…
Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…
Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based…
Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about…
In this article, a general family of bivariate distributions is used to model competing risks data with dependent factors. The general structure of competing risks data considered here includes ties. A comprehensive inferential framework…
When variable selection methods are applied to bootstrapped and multiply imputed datasets, the set of selected variables typically varies across iterations. Aggregating results via the union rule can lead to overly dense models. We propose…
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate…
We present a dynamic prediction framework for binary sequences that is based on a Bernoulli generalization of the auto-regressive process. Our approach lends itself easily to variants of the standard link prediction problem for a sequence…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Doubly robust learning offers a robust framework for causal inference from observational data by integrating propensity score and outcome modeling. Despite its theoretical appeal, practical adoption remains limited due to perceived…
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…
In recurrent event studies, panel binary data arise when subjects are observed at discrete time points and only the recurrent event status within each observation window is recorded. Such data frequently occur in longitudinal studies due to…