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Stats
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Bayes and Empirical Bayes Inference
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Bayes and Empirical Bayes Inference

A special issue of Stats (ISSN 2571-905X).

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 9788

Special Issue Editor

Prof. Dr. Wenhao Gui

E-Mail Website
Guest Editor
Department of Data Science, School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Interests: statistical inference; reliability analysis; applied statistics; distribution theory; Bayesian statistics

Special Issue Information

Dear Colleagues,

I am pleased to announce a Special Issue on “Bayes and Empirical Bayes Inference”. The Bayesian method is an effective estimation method, which is suitable for both parametric and nonparametric models. Because of the combination of prior information, estimation results of the Bayesian method are more accurate. Empirical Bayes modeling permits statisticians to incorporate additional information into problems by viewing the parameters as a second stochastic process with an unknown but restricted class of distribution. Bayes and empirical Bayes inference have a broad range of applications in practical fields. This Special Issue will present a collection of the latest developments in Bayes and empirical Bayes inference and their applications to practical problems.

I look forward to receiving your submissions.

Prof. Dr. Wenhao Gui
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Stats is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bayes estimation
  • empirical Bayes estimation
  • asymptotic optimality
  • loss functions
  • empirical process
  • likelihood function
  • data science
  • statistical software

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Published Papers (5 papers)

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Research

15 pages, 385 KiB  
Article
Empirical Inferences Under Bayesian Framework to Identify Cellwise Outliers
by Luca Sartore, Lu Chen and Valbona Bejleri
Stats 2024, 7(4), 1244-1258; https://doi.org/10.3390/stats7040073 - 19 Oct 2024
Viewed by 813
Abstract
Outliers are typically identified using frequentist methods. The data are classified as “outliers” or “not outliers” based on a test statistic that measures the magnitude of the difference between a value and the majority part of the data. The threshold for a data [...] Read more.
Outliers are typically identified using frequentist methods. The data are classified as “outliers” or “not outliers” based on a test statistic that measures the magnitude of the difference between a value and the majority part of the data. The threshold for a data value to be an outlier is typically defined by the user. However, a subjective choice of the threshold increases the uncertainty associated with outlier status for each data value. A cellwise outlier detection algorithm named FuzzyHRT is used to automate the editing process in repeated surveys. This algorithm uses Bienaymé–Chebyshev’s inequality and fuzzy logic to detect four different types of outliers resulting from format inconsistencies, historical, tail, and relational anomalies. However, fuzzy logic is not suited for probabilistic reasoning behind the identification of anomalous cells. Bayesian methods are well suited for quantifying the uncertainty associated with the identification of outliers. Although, as suggested by the literature, there exist well-developed Bayesian methods for record-level outlier detection, Bayesian methods for identifying outliers within individual records (i.e., at the cell level) remain unexplored. This paper presents two approaches from the Bayesian perspective to study the uncertainty associated with identifying outliers. A Bayesian bootstrap approach is explored to study the uncertainty associated with the output scores from the FuzzyHRT algorithm. Empirical likelihoods in a Bayesian setting are also considered for probabilistic reasoning behind the identification of anomalous cells. NASS survey data for livestock and major crop yield (such as corn) are considered for comparing the performances of the two proposed approaches with recent cellwise outlier methods. Full article
(This article belongs to the Special Issue Bayes and Empirical Bayes Inference)
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13 pages, 947 KiB  
Article
A Spatial Gaussian-Process Boosting Analysis of Socioeconomic Disparities in Wait-Listing of End-Stage Kidney Disease Patients across the United States
by Sounak Chakraborty, Tanujit Dey, Lingwei Xiang and Joel T. Adler
Stats 2024, 7(2), 508-520; https://doi.org/10.3390/stats7020031 - 7 Jun 2024
Viewed by 1261
Abstract
In this study, we employed a novel approach of combining Gaussian processes (GPs) with boosting techniques to model the spatial variability inherent in End-Stage Kidney Disease (ESKD) data. Our use of the Gaussian processes boosting, or GPBoost, methodology underscores the efficacy of this [...] Read more.
In this study, we employed a novel approach of combining Gaussian processes (GPs) with boosting techniques to model the spatial variability inherent in End-Stage Kidney Disease (ESKD) data. Our use of the Gaussian processes boosting, or GPBoost, methodology underscores the efficacy of this hybrid method in capturing intricate spatial dynamics and enhancing predictive accuracy. Specifically, our analysis demonstrates a notable improvement in out-of-sample prediction accuracy regarding the percentage of the population remaining on the wait list within geographic regions. Furthermore, our investigation unveils race and gender-based factors that significantly influence patient wait-listing. By leveraging the GPBoost approach, we identify these pertinent factors, shedding light on the complex interplay between demographic variables and access to kidney transplantation services. Our findings underscore the imperative for a multifaceted strategy aimed at reducing spatial disparities in kidney transplant wait-listing. Key components of such an approach include mitigating gender disparities, bolstering access to healthcare services, fostering greater awareness of transplantation options, and dismantling structural barriers to care. By addressing these multifactorial challenges, we can strive towards a more equitable and inclusive landscape in kidney transplantation. Full article
(This article belongs to the Special Issue Bayes and Empirical Bayes Inference)
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16 pages, 476 KiB  
Article
The Flexible Gumbel Distribution: A New Model for Inference about the Mode
by Qingyang Liu, Xianzheng Huang and Haiming Zhou
Stats 2024, 7(1), 317-332; https://doi.org/10.3390/stats7010019 - 13 Mar 2024
Cited by 3 | Viewed by 2370
Abstract
A new unimodal distribution family indexed via the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and [...] Read more.
A new unimodal distribution family indexed via the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and flexibility in capturing heavy-tailed data that exhibit different directions of skewness over a wide range. Both frequentist and Bayesian methods are developed to infer parameters in the new distribution. Simulation studies are conducted to demonstrate satisfactory performance of both methods. By fitting the proposed model to simulated data and data from an application in hydrology, it is shown that the proposed flexible distribution is especially suitable for data containing extreme values in either direction, with the mode being a location parameter of interest. Using the proposed unimodal distribution, one can easily formulate a regression model concerning the mode of a response given covariates. We apply this model to data from an application in criminology to reveal interesting data features that are obscured by outliers. Full article
(This article belongs to the Special Issue Bayes and Empirical Bayes Inference)
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23 pages, 424 KiB  
Article
Informative g-Priors for Mixed Models
by Yu-Fang Chien, Haiming Zhou, Timothy Hanson and Theodore Lystig
Stats 2023, 6(1), 169-191; https://doi.org/10.3390/stats6010011 - 16 Jan 2023
Cited by 3 | Viewed by 2639
Abstract
Zellner’s objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure [...] Read more.
Zellner’s objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure noise. In this paper, we propose a novel yet remarkably simple g-prior specification when a subject matter expert has information on the marginal distribution of the response yi. The approach is extended for use in mixed models with some surprising but intuitive results. Simulation studies are conducted to compare the model fitting under the proposed g-prior with that under other existing priors. Full article
(This article belongs to the Special Issue Bayes and Empirical Bayes Inference)
21 pages, 1344 KiB  
Article
Closed Form Bayesian Inferences for Binary Logistic Regression with Applications to American Voter Turnout
by Kevin Dayaratna, Jesse Crosson and Chandler Hubbard
Stats 2022, 5(4), 1174-1194; https://doi.org/10.3390/stats5040070 - 17 Nov 2022
Viewed by 2101
Abstract
Understanding the factors that influence voter turnout is a fundamentally important question in public policy and political science research. Bayesian logistic regression models are useful for incorporating individual level heterogeneity to answer these and many other questions. When these questions involve incorporating individual [...] Read more.
Understanding the factors that influence voter turnout is a fundamentally important question in public policy and political science research. Bayesian logistic regression models are useful for incorporating individual level heterogeneity to answer these and many other questions. When these questions involve incorporating individual level heterogeneity for large data sets that include many demographic and ethnic subgroups, however, standard Markov Chain Monte Carlo (MCMC) sampling methods to estimate such models can be quite slow and impractical to perform in a reasonable amount of time. We present an innovative closed form Empirical Bayesian approach that is significantly faster than MCMC methods, thus enabling the estimation of voter turnout models that had previously been considered computationally infeasible. Our results shed light on factors impacting voter turnout data in the 2000, 2004, and 2008 presidential elections. We conclude with a discussion of these factors and the associated policy implications. We emphasize, however, that although our application is to the social sciences, our approach is fully generalizable to the myriads of other fields involving statistical models with binary dependent variables and high-dimensional parameter spaces as well. Full article
(This article belongs to the Special Issue Bayes and Empirical Bayes Inference)
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