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Count data with an excessive number of zeros frequently arise in fields such as economics, medicine, and public health. Traditional count models often fail to adequately handle such data, especially when the relationship between the…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure…
We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…
We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…
Estimating an individual's counterfactual outcomes under interventions is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, facial images) and…
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…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…
Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
It is generally difficult to make any statements about the expected prediction error in an univariate setting without further knowledge about how the data were generated. Recent work showed that knowledge about the real underlying causal…
Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…
Recommender systems are seen as an effective tool to address information overload, but it is widely known that the presence of various biases makes direct training on large-scale observational data result in sub-optimal prediction…
Ecological studies involving counts of abundance, presence-absence or occupancy rates often produce data having a substantial proportion of zeros. Furthermore, these types of processes are typically multivariate and only adequately…
Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…