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1. Prediction intervals for Poisson‐based regression models

   https://doi.org/10.1002/wics.1568  

   Kim, Taeho ; Lieberman, Benjamin ; Luta, George ; Peña, Edsel A. ( June 2021 , WIREs Computational Statistics)

   This paper provides a review of the literature regarding methods for constructing prediction intervals for counting variables, with particular focus on those whose distributions are Poisson or derived from Poisson and with an over‐dispersion property. Independent and identically distributed models and regression models are both considered. The motivating problem for this review is that of predicting the number of daily and cumulative cases or deaths attributable to COVID‐19 at a future date.

   This article is categorized under:

   Applications of Computational Statistics > Clinical Trials

   Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

   Statistical Models > Generalized Linear Models

    

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2. Interaction Selection and Prediction Performance in High-Dimensional Data: A Comparative Study of Statistical and Tree-Based Methods

   https://doi.org/10.6339/24-JDS1127  

   Nzekwe, Chinedu J ; Kim, Seongtae ; Mostafa, Sayed A ( May 2024 , Journal of Data Science)

   Predictive modeling often ignores interaction effects among predictors in high-dimensional data because of analytical and computational challenges. Research in interaction selection has been galvanized along with methodological and computational advances. In this study, we aim to investigate the performance of two types of predictive algorithms that can perform interaction selection. Specifically, we compare the predictive performance and interaction selection accuracy of both penalty-based and tree-based predictive algorithms. Penalty-based algorithms included in our comparative study are the regularization path algorithm under the marginality principle (RAMP), the least absolute shrinkage selector operator (LASSO), the smoothed clipped absolute deviance (SCAD), and the minimax concave penalty (MCP). The tree-based algorithms considered are random forest (RF) and iterative random forest (iRF). We evaluate the effectiveness of these algorithms under various regression and classification models with varying structures and dimensions. We assess predictive performance using the mean squared error for regression and accuracy, sensitivity, specificity, balanced accuracy, and F1 score for classification. We use interaction coverage to judge the algorithm’s efficacy for interaction selection. Our findings reveal that the effectiveness of the selected algorithms varies depending on the number of predictors (data dimension) and the structure of the data-generating model, i.e., linear or nonlinear, hierarchical or non-hierarchical. There were at least one or more scenarios that favored each of the algorithms included in this study. However, from the general pattern, we are able to recommend one or more specific algorithm(s) for some specific scenarios. Our analysis helps clarify each algorithm’s strengths and limitations, offering guidance to researchers and data analysts in choosing an appropriate algorithm for their predictive modeling task based on their data structure.

    

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3. Information criteria for model selection

   https://doi.org/10.1002/wics.1607  

   Zhang, Jiawei ; Yang, Yuhong ; Ding, Jie ( February 2023 , WIREs Computational Statistics)

   The rapid development of modeling techniques has brought many opportunities for data‐driven discovery and prediction. However, this also leads to the challenge of selecting the most appropriate model for any particular data task. Information criteria, such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC), have been developed as a general class of model selection methods with profound connections with foundational thoughts in statistics and information theory. Many perspectives and theoretical justifications have been developed to understand when and how to use information criteria, which often depend on particular data circumstances. This review article will revisit information criteria by summarizing their key concepts, evaluation metrics, fundamental properties, interconnections, recent advancements, and common misconceptions to enrich the understanding of model selection in general.

   This article is categorized under:

   Data: Types and Structure > Traditional Statistical Data

   Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

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   Statistical Models > Model Selection

    

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4. Nearest‐neighbor sparse Cholesky matrices in spatial statistics

   https://doi.org/10.1002/wics.1574  

   Datta, Abhirup ( December 2021 , WIREs Computational Statistics)

   Gaussian process (GP) is a staple in the toolkit of a spatial statistician. Well‐documented computing roadblocks in the analysis of large geospatial datasets using GPs have now largely been mitigated via several recent statistical innovations. Nearest neighbor Gaussian process (NNGP) has emerged as one of the leading candidates for such massive‐scale geospatial analysis owing to their empirical success. This article reviews the connection of NNGP to sparse Cholesky factors of the spatial precision (inverse‐covariance) matrix. Focus of the review is on these sparse Cholesky matrices which are versatile and have recently found many diverse applications beyond the primary usage of NNGP for fast parameter estimation and prediction in the spatial (generalized) linear models. In particular, we discuss applications of sparse NNGP Cholesky matrices to address multifaceted computational issues in spatial bootstrapping, simulation of large‐scale realizations of Gaussian random fields, and extensions to nonparametric mean function estimation of a GP using random forests. We also review a sparse‐Cholesky‐based model for areal (geographically aggregated) data that addresses long‐established interpretability issues of existing areal models. Finally, we highlight some yet‐to‐be‐addressed issues of such sparse Cholesky approximations that warrant further research.

   This article is categorized under:

   Algorithms and Computational Methods > Algorithms

   Algorithms and Computational Methods > Numerical Methods

    

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5. Sequential change‐point detection: Computation versus statistical performance

   https://doi.org/10.1002/wics.1628  

   Wang, Haoyun ; Xie, Yao ( July 2023 , WIREs Computational Statistics)

   Change‐point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large‐scale, high‐dimensional, and complex streaming data call for computationally (memory) efficient sequential change‐point detection algorithms that are also statistically powerful. This gives rise to a computation versus statistical power trade‐off, an aspect less emphasized in the past in classic literature. This tutorial takes this new perspective and reviews several sequential change‐point detection procedures, ranging from classic sequential change‐point detection algorithms to more recent non‐parametric procedures that consider computation, memory efficiency, and model robustness in the algorithm design. Our survey also contains classic performance analysis, which provides useful techniques for analyzing new procedures.

   This article is categorized under:

   Statistical Models > Time Series Models

   Algorithms and Computational Methods > Algorithms

   Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

    

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