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Classical statistics deals with determined and precise data analysis. But in reality, there are many cases where the information is not accurate and a degree of impreciseness, uncertainty, incompleteness, and vagueness is observed. In these…
Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…
Spurious correlations in training data significantly hinder the generalization capability of machine learning models when faced with distribution shifts, leading to the proposition of numberous debiasing methods. However, it remains to be…
Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…
In their fundamental paper on cubic variance functions, Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families on the real line, their characterization through…
A novel method for estimating Bayesian network (BN) parameters from data is presented which provides improved performance on test data. Previous research has shown the value of representing conditional probability distributions (CPDs) via…
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…
Machine learning tools have empowered a qualitatively new way to perform differential cross section measurements whereby the data are unbinned, possibly in many dimensions. Unbinned measurements can enable, improve, or at least simplify…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…
In behavioral and psychiatric research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This kind of clustered binary data are usually non-normally distributed, which can…
Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…
Although the independent censoring assumption is commonly used in survival analysis, it can be violated when the censoring time is related to the survival time, which often happens in many practical applications. To address this issue, we…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to…
The Drift-Diffusion Model (DDM) is widely used in neuropsychological studies to understand the decision process by incorporating both reaction times and subjects' responses. Various models have been developed to estimate DDM parameters,…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…
Response-biased sampling, in which samples are drawn from a popula- tion according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. In particular, the complete obser- vations in…
Models such as the zero-inflated and zero-altered Poisson and zero-truncated binomial are well-established in modern regression analysis. We propose a super model that jointly and maximally unifies alteration, inflation, truncation and…