Related papers: An Alternative Perspective on the Robust Poisson M…

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…

Generalized linear models, such as logistic regression, are widely used to model the association between a treatment and a binary outcome as a function of baseline covariates. However, the coefficients of a logistic regression model…

Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…

In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…

Species distribution modeling (SDM) plays a crucial role in investigating habitat suitability and addressing various ecological issues. While likelihood analysis is commonly used to draw ecological conclusions, it has been observed that its…

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case…

Survival outcomes are common in comparative effectiveness studies and require unique handling because they are usually incompletely observed due to right-censoring. A ``once for all'' approach for causal inference with survival outcomes…

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…

In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…

Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent…

Poisson random effect models with a shared random effect have been widely used in actuarial science for analyzing the number of claims. In particular, the random effect is a key factor in a posteriori risk classification. However, the…

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…

This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous…