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Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in…
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 problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion,…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…
This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…
The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data…
We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…