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R. A. Fisher founded modern statistical inference in 1922 and identified its fundamental problems to be: specification, estimation and distribution. Since then the problem of statistical model specification has received scant attention in…

Initially applied in astronomy and geodesy, the linear regression model aimed to find the best estimates for parameters with predefined meanings. E.g., orbital elements, geodetic constants. As its use expanded to other disciplines, often to…

Fiducial inference was introduced in the first half of the 20th century by Fisher (1935) as a means to get a posterior-like distribution for a parameter without having to arbitrarily define a prior. While the method originally fell out of…

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…

Social inequality is a topic of interest since ages, and has attracted researchers across disciplines to ponder over it origin, manifestation, characteristics, consequences, and finally, the question of how to cope with it. It is manifested…

Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…

Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is…

Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…

The importance of research teams' diversity for the progress of science is highlighted extensively. Despite the seemingly hegemonic role of hypothesis testing in modern quantitative research, little attention has been devoted to the…

The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…

Data privacy has increasingly become a daunting challenge because it limits data availability, which is essential in estimating statistical models such as generalized linear mixed models. Access to personal data often involves considerable…