scholarly journals Computing Bayes factors from data with missing values

2021 ◽  
Author(s):  
Herbert Hoijtink ◽  
Xin Gu ◽  
Joris Mulder ◽  
Yves Rosseel
Keyword(s):  
Missing Values ◽  
Bayes Factor ◽  
Equality Constraints ◽  
Bayes Factors ◽  
Multiple Imputations

The Bayes factor is increasingly used for the evaluation of hypotheses. These may betraditional hypotheses specified using equality constraints among the parameters of thestatistical model of interest or informative hypotheses specified using equality andinequality constraints. So far no attention has been given to the computation of Bayesfactors from data with missing values. A key property of such a Bayes factor should bethat it is only based on the information in the observed values. This paper will show thatsuch a Bayes factor can be obtained using multiple imputations of the missing values.

scholarly journals A Bayesian solution to the Behrens–Fisher problem

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Fco. Javier Girón ◽  
Carmen del Castillo
Keyword(s):  
Closed Form ◽  
Hierarchical Model ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Simple Solution ◽  
Asymptotic Approximations ◽  
Normal Distributions ◽  
Fisher Distribution ◽  
Leibler Divergence

AbstractA simple solution to the Behrens–Fisher problem based on Bayes factors is presented, and its relation with the Behrens–Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens–Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback–Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.

scholarly journals Simulation Studies as a Tool to Understand Bayes Factors

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592097262
Author(s):  
Don van Ravenzwaaij ◽  
Alexander Etz
Keyword(s):  
Simulation Study ◽  
Prior Distribution ◽  
Bayes Factor ◽  
R Package ◽  
Bayes Factors ◽  
Simulation Studies ◽  
Social Scientists ◽  
Simple Simulation ◽  
Set Up

When social scientists wish to learn about an empirical phenomenon, they perform an experiment. When they wish to learn about a complex numerical phenomenon, they can perform a simulation study. The goal of this Tutorial is twofold. First, it introduces how to set up a simulation study using the relatively simple example of simulating from the prior. Second, it demonstrates how simulation can be used to learn about the Jeffreys-Zellner-Siow (JZS) Bayes factor, a currently popular implementation of the Bayes factor employed in the BayesFactor R package and freeware program JASP. Many technical expositions on Bayes factors exist, but these may be somewhat inaccessible to researchers who are not specialized in statistics. In a step-by-step approach, this Tutorial shows how a simple simulation script can be used to approximate the calculation of the Bayes factor. We explain how a researcher can write such a sampler to approximate Bayes factors in a few lines of code, what the logic is behind the Savage-Dickey method used to visualize Bayes factors, and what the practical differences are for different choices of the prior distribution used to calculate Bayes factors.

Do sexist jokes increase rape proclivity among males high in hostile sexism? Evidence from two pre-registered direct replications of Thomae & Viki (2013)

2021 ◽  
Author(s):  
Neil McLatchie ◽  
Manuela Thomae
Keyword(s):  
Bayes Factor ◽  
Alternative Hypothesis ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Original Study ◽  
Bayes Factors ◽  
Hostile Sexism ◽  
Replication Studies ◽  
Open Research ◽  
Rape Proclivity

Thomae and Viki (2013) reported that increased exposure to sexist humour can increase rape proclivity among males, specifically those who score high on measures of Hostile Sexism. Here we report two pre-registered direct replications (N = 530) of Study 2 from Thomae and Viki (2013) and assess replicability via (i) statistical significance, (ii) Bayes factors, (iii) the small-telescope approach, and (iv) an internal meta-analysis across the original and replication studies. The original results were not supported by any of the approaches. Combining the original study and the replications yielded moderate evidence in support of the null over the alternative hypothesis with a Bayes factor of B = 0.13. In light of the combined evidence, we encourage researchers to exercise caution before claiming that brief exposure to sexist humour increases male’s proclivity towards rape, until further pre-registered and open research demonstrates the effect is reliably reproducible.

Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

2021 ◽  
Author(s):  
John K. Kruschke
Keyword(s):  
Posterior Distribution ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Prior Model ◽  
Bayesian Hypothesis Testing ◽  
Bayesian Model Comparison ◽  
Posterior Model Probability ◽  
Model Probability

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

scholarly journals Estimating Bayes factors from minimal summary statistics in repeated measures analysis of variance designs

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Thomas Faulkenberry
Keyword(s):  
Analysis Of Variance ◽  
Repeated Measures ◽  
Bayes Factor ◽  
Linear Models ◽  
Repeated Measurements ◽  
Bayes Factors ◽  
Complex Method ◽  
Summary Statistics ◽  
Minimal Set ◽  
Repeated Measures Analysis

In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the F-statistic, the number of subjects, and the number of repeated measurements per subject, is based on the BIC approximation of the Bayes factor, a common default method for Bayesian computation with linear models. In addition to providing computational examples, I report a simulation study in which I demonstrate that the formula compares favorably to a recently developed, more complex method that accounts for correlation between repeated measurements. The minimal BIC method provides a simple way for researchers to estimate Bayes factors from a minimal set of summary statistics, giving users a powerful index for estimating the evidential value of not only their own data, but also the data reported in published studies.

scholarly journals A Markov chain representation of the multiple testing problem

2016 ◽  
Vol 27 (2) ◽  
pp. 364-383 ◽  
Author(s):  
Stefano Cabras
Keyword(s):  
Markov Chain ◽  
Multiple Testing ◽  
Bayes Factor ◽  
Alternative Hypothesis ◽  
Multiple Hypothesis Testing ◽  
Bayes Factors ◽  
Rna Seq ◽  
Markov Transition ◽  
Improper Priors ◽  
Alternative Hypotheses

The problem of multiple hypothesis testing can be represented as a Markov process where a new alternative hypothesis is accepted in accordance with its relative evidence to the currently accepted one. This virtual and not formally observed process provides the most probable set of non null hypotheses given the data; it plays the same role as Markov Chain Monte Carlo in approximating a posterior distribution. To apply this representation and obtain the posterior probabilities over all alternative hypotheses, it is enough to have, for each test, barely defined Bayes Factors, e.g. Bayes Factors obtained up to an unknown constant. Such Bayes Factors may either arise from using default and improper priors or from calibrating p-values with respect to their corresponding Bayes Factor lower bound. Both sources of evidence are used to form a Markov transition kernel on the space of hypotheses. The approach leads to easy interpretable results and involves very simple formulas suitable to analyze large datasets as those arising from gene expression data (microarray or RNA-seq experiments).

scholarly journals The Effects of Missing Data Characteristics on the Choice of Imputation Techniques

2020 ◽  
Vol 07 (02) ◽  
pp. 161-177
Author(s):  
Oyekale Abel Alade ◽  
Ali Selamat ◽  
Roselina Sallehuddin
Keyword(s):  
Missing Data ◽  
Missing Values ◽  
Health Management ◽  
Support Vector ◽  
Multiple Imputations ◽  
Original Dataset ◽  
Learning Machine ◽  
Elm Classifier ◽  
The Right

One major characteristic of data is completeness. Missing data is a significant problem in medical datasets. It leads to incorrect classification of patients and is dangerous to the health management of patients. Many factors lead to the missingness of values in databases in medical datasets. In this paper, we propose the need to examine the causes of missing data in a medical dataset to ensure that the right imputation method is used in solving the problem. The mechanism of missingness in datasets was studied to know the missing pattern of datasets and determine a suitable imputation technique to generate complete datasets. The pattern shows that the missingness of the dataset used in this study is not a monotone missing pattern. Also, single imputation techniques underestimate variance and ignore relationships among the variables; therefore, we used multiple imputations technique that runs in five iterations for the imputation of each missing value. The whole missing values in the dataset were 100% regenerated. The imputed datasets were validated using an extreme learning machine (ELM) classifier. The results show improvement in the accuracy of the imputed datasets. The work can, however, be extended to compare the accuracy of the imputed datasets with the original dataset with different classifiers like support vector machine (SVM), radial basis function (RBF), and ELMs.

Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors

2021 ◽  
pp. 1471082X2098131
Author(s):  
Alan Agresti ◽  
Francesco Bartolucci ◽  
Antonietta Mira
Keyword(s):  
Bayesian Inference ◽  
Mixture Models ◽  
Random Effects ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Posterior Mean ◽  
Bayesian Paradigm ◽  
Research Publications ◽  
Nonparametric Mixture ◽  
Mixed Modelling

We describe two interesting and innovative strands of Murray Aitkin's research publications, dealing with mixture models and with Bayesian inference. Of his considerable publications on mixture models, we focus on a nonparametric random effects approach in generalized linear mixed modelling, which has proven useful in a wide variety of applications. As an early proponent of ways of implementing the Bayesian paradigm, Aitkin proposed an alternative Bayes factor based on a posterior mean likelihood. We discuss these innovative approaches and some research lines motivated by them and also suggest future related methodological implementations.

scholarly journals Implementation of a Physician-Based Stroke Unit in a Remote Hospital of North-East India-Tezpur Model

2021 ◽  
Vol 12 (02) ◽  
pp. 356-361
Author(s):  
Lydia John ◽  
Akanksha William ◽  
Dimple Dawar ◽  
Himani Khatter ◽  
Pratibha Singh ◽  
...  
Keyword(s):  
Stroke Unit ◽  
Missing Values ◽  
Nearest Neighbor ◽  
Length Of Hospital Stay ◽  
Stroke Severity ◽  
Christian Mission ◽  
Multiple Imputations ◽  
North East India ◽  
North East ◽  
Remote Hospital

Abstract Objective The study aims to determine the effects of implementing stroke unit (SU) care in a remote hospital in North-East India. Materials and Methods This before-and-after implementation study was performed at the Baptist Christian Mission Hospital, Tezpur, Assam between January 2015 and December 2017. Before the implementation of stroke unit care (pre-SU), we collected information on usual stroke care and 1-month outcome of 125 consecutive stroke admissions. Staff was then trained in the delivery of SU care for 1 month, and the same information was collected in a second (post-SU) cohort of 125 patients. Statistical Analysis Chi-square and Mann–Whitney U test were used to compare group differences. The loss to follow-up was imputed by using multiple imputations using the Markov Chain Monto Carlo method. The sensitivity analysis was also performed by using propensity score matching of the groups for baseline stroke severity (National Institute of Health Stroke Scale) using the nearest neighbor approach to control for confounding, and missing values were imputed by using multiple imputations. The adjusted odds ratio was calculated in univariate and multivariate regression analysis after adjusting for baseline variables. All the analysis was done by using SPSS, version 21.0., IBM Corp and R version 4.0.0., Armonk, New York, United States. Results The pre-SU and post-SU groups were age and gender matched. The post-SU group showed higher rates of swallow assessment (36.8 vs. 0%, p < 0.001), mobility assessment, and re-education (100 vs. 91.5%, p = 0.037). The post-SU group also showed reduced complications (28 vs. 45%, p = 0.006) and a shorter length of hospital stay (4 ± 2.16 vs. 5 ± 2.68 days, p = 0.026). The functional outcome (modified ranking scale) at 1-month showed no difference between the groups, good outcome in post-SU (39.6%) versus pre-SU (35.7%), p = 0.552. Conclusion The implementation of this physician-based SU care model in a remote hospital in India shows improvements in quality measures, complications, and possibly patient outcomes.

scholarly journals Simulation Studies as a Tool to Understand Bayes Factors

2020 ◽  
Author(s):  
Don van Ravenzwaaij ◽  
Alexander Etz
Keyword(s):  
Simulation Study ◽  
Prior Distribution ◽  
Bayes Factor ◽  
R Package ◽  
Bayes Factors ◽  
Simulation Studies ◽  
Social Scientists ◽  
Simple Simulation ◽  
Set Up

When social scientists wish to learn about an empirical phenomenon, they perform an experiment. When they wish to learn about a complex numerical phenomenon,they can perform a simulation study. The goal of this paper is twofold. Firstly, this paper introduces how to set up a simulation study using the relatively simple example of simulating from the prior. Secondly, this paper demonstrates how simulation can be used to learn about the Jeffreys-Zellner-Siow (JZS) Bayes factor: a currently popular implementation of the Bayes factor employed in the BayesFactor R-package and freeware program JASP. Many technical expositions exist on JZS Bayes factors, but these may be somewhat inaccessible to researchers that are not specialized in statistics. This paper aims to show in a step-by-step approach how a simple simulation script can be used to approximate the calculation of the JZS Bayes factor. We explain how a researcher can write such a sampler to approximate JZS Bayes factors in a few lines of code, what the logic is behind the Savage Dickey method used to visualize JZS Bayes factors, and what the practical differences are for different choices of the prior distribution for calculating Bayes factors.

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