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The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular…
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially…
This paper introduces a new Importance Sampling scheme, called Adaptive Twisted Importance Sampling, which is adequate for the improved estimation of rare event probabilities in he range of moderate deviations pertaining to the empirical…
How to deal with missing data in observational studies is a common concern for causal inference. When the covariates are missing at random (MAR), multiple approaches have been provided to help solve the issue. However, if the exposure is…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…
Generalized linear models are often assumed to fit propensity scores, which are used to compute inverse probability weighted (IPW) estimators. In order to derive the asymptotic properties of IPW estimators, the propensity score is supposed…
A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads…
Large-scale rare events data are commonly encountered in practice. To tackle the massive rare events data, we propose a novel distributed estimation method for logistic regression in a distributed system. For a distributed framework, we…
We study predictive probability inference in classification tasks using random forests under class imbalance. We focus on two simplified variants of Breiman's algorithm, namely subsampling Infinite Random Forests (IRFs) and under-sampling…
Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
Balancing weights have been widely applied to single or monotone missingness due to empirical advantages over likelihood-based methods and inverse probability weighting approaches. This paper considers non-monotone missing data under the…
The paper analyzes theoretically and empirically the performance of likelihood weighting (LW) on a subset of nodes in Bayesian networks. The proposed scheme requires fewer samples to converge due to reduction in sampling variance. The…
A key methodological challenge in observational studies with interference between units is twofold: (1) each unit's outcome may depend on many others' treatments, and (2) treatment assignments may exhibit complex dependencies across units.…
Surveys usually suffer from non-response, which decreases the effective sample size. Item non-response is typically handled by means of some form of random imputation if we wish to preserve the distribution of the imputed variable. This…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
The propensity score is widely used for causal inference in observational studies, but common parametric estimators can produce biased and inefficient effect estimates when model assumptions are violated. Nonparametric approaches reduce…
In this paper, we propose two variable selection methods for adjusting the censoring information for survival times, such as the restricted mean survival time. To adjust for the influence of censoring, we consider an inverse survival…