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Statistical learning (SL) includes methods that extract knowledge from complex data. SL methods beyond generalized linear models are being increasingly implemented in public health research and epidemiology because they can perform better…

We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…

Traditionally, heritability has been estimated using family-based methods such as twin studies. Advancements in molecular genomics have facilitated the development of alternative methods that utilise large samples of unrelated or related…

Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…

Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…

Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…

The increasing availability of time --and space-- resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world datasets can often…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…

The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" --…

In genetic studies of complex diseases, the underlying mode of inheritance is often not known. Thus, the most powerful test or other optimal procedure for one model, e.g. recessive, may be quite inefficient if another model, e.g. dominant,…

Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure…

Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and…

Randomized experiments are a crucial tool for causal inference in many different fields. Rerandomization addresses any covariate imbalance in such experiments by resampling treatment assignments until certain balance criteria are satisfied.…

Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…

Estimation of social influence in networks can be substantially biased in observational studies due to homophily and network correlation in exposure to exogenous events. Randomized experiments, in which the researcher intervenes in the…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…