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The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
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…
High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or…
We propose a model for stochastic formation of opinion clusters, modelled by an evolving network, and herd behaviour to account for the observed fat-tail distribution in returns of financial-price data. The only parameter of the model is h,…
Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total…
The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
Bayesian penalized regression techniques, such as the Bayesian lasso and the Bayesian horseshoe estimator, have recently received a significant amount of attention in the statistics literature. However, software implementing…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous…
In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…
We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…
We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the…