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The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…

Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modeling of data with heteroscedastic and possibly correlated measurement errors and intrinsic scatter. The method fully accounts for time evolution.…

In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…

Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…

Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…

Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…

In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem…

The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…

The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…

This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…

In February 1700, Isaac Newton needed a precise tropical year to design a new universal calendar that would supersede the Gregorian one. However, 17th-Century astronomers were uncertain of the long-term variation in the inclination of the…

Research at the intersection of machine learning and the social sciences has provided critical new insights into social behavior. At the same time, a variety of critiques have been raised ranging from technical issues with the data used and…

Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…

Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…