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We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small…
Mediation analysis is widely used for exploring treatment mechanisms; however, it faces challenges when nonignorable missing confounders are present. Efficient inference of mediation effects and the efficiency loss due to nonignorable…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…
Recent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly…
Trials enroll a large number of subjects in order to attain power, making them expensive and time-consuming. Sample size calculations are often performed with the assumption of an unadjusted analysis, even if the trial analysis plan…
Approximate statistical inference via determination of the asymptotic distribution of a statistic is routinely used for inference in applied medical statistics (e.g. to estimate the standard error of the marginal or conditional risk ratio).…
Diffusion models have led to significant advancements in generative modelling. Yet their widespread adoption poses challenges regarding data attribution and interpretability. In this paper, we aim to help address such challenges in…
Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
This article considers nonparametric regression models with multivariate covariates and with responses missing at random. We estimate the regression function with a local polynomial smoother. The residual-based empirical distribution…
There is a long-standing debate in the statistical, epidemiological and econometric fields as to whether nonparametric estimation that uses data-adaptive methods, like machine learning algorithms in model fitting, confer any meaningful…
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
No man is an island, as individuals interact and influence one another daily in our society. When social influence takes place in experiments on a population of interconnected individuals, the treatment on a unit may affect the outcomes of…