Published in Annual Review of Statistics and Its Application
Introduced more than a half-century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity of this framework for inferring causal relationships among time series has remained the topic of continuous de...
Published in Annual Review of Statistics and Its Application
Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is postprocessed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not a...
Published in Annual Review of Statistics and Its Application
With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical...
Published in Annual Review of Statistics and Its Application
This article reviews current advances and developments in neural networks. This requires recalling some of the earlier work in the field. We emphasize Bayesian approaches and their benefits compared to more standard maximum likelihood treatments. Several representative experiments using varied modern neural architectures are presented.
Published in Annual Review of Statistics and Its Application
Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications. For MCMC simulation to produce reliable outcomes, it needs to generate observations representative of the target distribution, and it must be long enough so that the errors of Monte Carlo est...
Published in Annual Review of Statistics and Its Application
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well developed, methods for high-dimensional and complex data sets are still scarce. Appropriate notions of sparsity and connections to other fields such as machine learning, grap...
Published in Annual Review of Statistics and Its Application
This article considers simulation and analysis of incidence data using stochastic compartmental models in well-mixed populations. Several simulation approaches are described and compared. Thereafter, we provide an overview of likelihood estimation for stochastic models. We apply one such method to a real-life outbreak data set and compare models as...
Published in Annual Review of Statistics and Its Application
The data science of networks is a rapidly developing field with myriad applications. In neuroscience, the brain is commonly modeled as a connectome, a network of nodes connected by edges. While there have been thousands of papers on connectomics, the statistics of networks remains limited and poorly understood. Here, we provide an overview from the...
Published in Annual Review of Statistics and Its Application
Online learning is a framework for the design and analysis of algorithms that build predictive models by processing data one at the time. Besides being computationally efficient, online algorithms enjoy theoretical performance guarantees that do not rely on statistical assumptions on the data source. In this review, we describe some of the most imp...
Published in Annual Review of Statistics and Its Application
Demand for access to data, especially data collected using public funds, is ever growing. At the same time, concerns about the disclosure of the identities of and sensitive information about the respondents providing the data are making the data collectors limit the access to data. Synthetic data sets, generated to emulate certain key information f...
