Aging research relies on varied statistical methods, and applying these methods appropriately is important for scientific rigor. However, proper use of these statistical techniques is a challenge. We discuss two categories of statistical methods in aging research: (a) emerging methods requiring further validation, including techniques to examine compression of morbidity, maximum lifespan, immortal time bias, molecular aging clocks, and treatment response heterogeneity, and (b) classic and existing methods needing reconsideration and improvement, such as stepwise regression, generalized linear models, methods for accounting for clustering and nesting effects, methods for testing for group differences, methods for mediation and moderation analyses, and nonlinear models. For each method, we review its relevance to aging research, highlight statistical issues, and suggest improvements or alternatives with examples from aging research. We urge researchers to refine traditional approaches and embrace emerging methods tailored to the unique challenges of aging research. This review will help researchers identify and apply sound statistical methods, thereby improving statistical rigor in aging research.

With advancements in technology and the decreasing cost of data acquisition, high-throughput omics data have become increasingly prevalent in biomedical research. These data are often collected across multiple omics modalities at different molecular levels, offering a comprehensive perspective on underlying biological mechanisms. However, the multimodal nature of multiomics data presents unique and complex challenges for statistical analysis. In this article, we provide a comprehensive review of recent advancements in statistical methods for multiomics data integration. We discuss key topics in unsupervised learning (including dimension reduction, clustering, and network analysis), supervised learning (including regression, classification, and mediation analysis), and other areas. Finally, we highlight unresolved challenges and propose promising directions for future research to further advance the field.

With increased data collection, the need to fuse data sources has emerged as an important and rapidly growing research activity in the statistical community. In considering spatial and spatio-temporal datasets to examine complex environmental and ecological processes of interest, we often have multiple sources that are jointly informative about features of interest of the processes. Model-based data fusion aims to leverage information from these sources to improve inference and prediction. In the spatial statistics setting, these data could be geostatistical; areal; or point patterns with varying spatial resolutions, supports, and domains. Given two or more sources, we explore stochastic modeling to implement a suitable fusion with full inference and uncertainty quantification. We illustrate these ideas using three environmental and ecological examples: precipitation, marine mammal abundance, and joint species distributions.

Generalized additive models are generalized linear models in which the linear predictor includes a sum of smooth functions of covariates, where the shape of the functions is to be estimated. They have also been generalized beyond the original generalized linear model setting to distributions outside the exponential family and to situations in which multiple parameters of the response distribution may depend on sums of smooth functions of covariates. The widely used computational and inferential framework in which the smooth terms are represented as latent Gaussian processes, splines, or Gaussian random effects is reviewed, paying particular attention to the case in which computational and theoretical tractability is obtained by prior rank reduction of the model terms. An empirical Bayes approach is taken, and its relatively good frequentist performance discussed, along with some more overtly frequentist approaches to model selection. Estimation of the degree of smoothness of component functions via cross validation or marginal likelihood is covered, alongside the computational strategies required in practice, including when data and models are reasonably large. It is briefly shown how the framework extends easily to location-scale modeling, and, with more effort, to techniques such as quantile regression. Also covered are the main classes of smooths of multiple covariates that may be included in models: isotropic splines and tensor product smooth interaction terms.

Causal mediation analysis provides an attractive framework for integrating diverse types of exposure, genomic, and phenotype data. Recently, this field has seen a surge of interest, largely driven by the increasing need for causal mediation analyses in health and social sciences. This article aims to provide a review of recent developments in mediation analysis, encompassing mediation analysis of a single mediator and a large number of mediators, as well as mediation analysis with multiple exposures and mediators. Our review focuses on the recent advancements in statistical inference for causal mediation analysis, especially in the context of high-dimensional mediation analysis. We delve into the complexities of testing mediation effects, especially addressing the challenge of testing a large number of composite null hypotheses. Through extensive simulation studies, we compare the existing methods across a range of scenarios. We also include an analysis of data from the Normative Aging Study, which examines DNA methylation CpG sites as potential mediators of the effect of smoking status on lung function. We discuss the pros and cons of these methods and future research directions.

In recent years, there has been a growing trend of applying reinforcement learning (RL) in financial applications. This approach has shown great potential for decision-making tasks in finance. In this review, we present a comprehensive study of the applications of RL in finance and conduct a series of meta-analyses to investigate the common themes in the literature, such as the factors that most significantly affect RL's performance compared with traditional methods. Moreover, we identify challenges, including explainability, Markov decision process modeling, and robustness, that hinder the broader utilization of RL in the financial industry and discuss recent advancements in overcoming these challenges. Finally, we propose future research directions, such as benchmarking, contextual RL, multi-agent RL, and model-based RL, to address these challenges and to further enhance the implementation of RL in finance.

Entity resolution is the process of merging and removing duplicate records from multiple data sources, often in the absence of unique identifiers. Bayesian models for entity resolution allow one to include a priori information, quantify uncertainty in important applications, and directly estimate a partition of the records. Markov chain Monte Carlo (MCMC) sampling is the primary computational method for approximate posterior inference in this setting, but due to the high dimensionality of the space of partitions, there are no agreed upon standards for diagnosing nonconvergence of MCMC sampling. In this article, we review Bayesian entity resolution, with a focus on the specific challenges that it poses for the convergence of a Markov chain. We review prior methods for convergence diagnostics, discussing their weaknesses. We provide recommendations for using MCMC sampling for Bayesian entity resolution, focusing on the use of modern diagnostics that are commonplace in applied Bayesian statistics. Using simulated data, we find that a commonly used Gibbs sampler performs poorly compared with two alternatives.

Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to find the low-dimensional structure of data. Dimension reduction for large, high-dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high-dimensional point clouds and allow one to visualize, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all from a practicing statistician's perspective. It describes the trade-offs and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

Data are distributed across different sites due to computing facility limitations or data privacy considerations. Conventional centralized methods—those in which all datasets are stored and processed in a central computing facility—are not applicable in practice. Therefore, it has become necessary to develop distributed learning approaches that have good inference or predictive accuracy while remaining free of individual data or obeying policies and regulations to protect privacy. In this article, we introduce the basic idea of distributed learning and conduct a selected review on various distributed learning methods, which are categorized by their statistical accuracy, computational efficiency, heterogeneity, and privacy. This categorization can help evaluate newly proposed methods from different aspects. Moreover, we provide up-to-date descriptions of the existing theoretical results that cover statistical equivalency and computational efficiency under different statistical learning frameworks. Finally, we provide existing software implementations and benchmark datasets, and we discuss future research opportunities.