Bayes factor consistency in linear models when p grows with n

2009 ◽  
Author(s):  
Ruixin Guo
Keyword(s):  
Bayes Factor ◽  
Linear Models

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 Brain disconnectivity mapping of post-stroke fatigue

2020 ◽  
Author(s):  
Kristine M. Ulrichsen ◽  
Knut K. Kolskår ◽  
Geneviève Richard ◽  
Dag Alnæs ◽  
Erlend S. Dørum ◽  
...  
Keyword(s):  
Bayes Factor ◽  
Linear Models ◽  
Chronic Phase ◽  
Stroke Patients ◽  
Lesion Location ◽  
Post Stroke ◽  
Novel Approach ◽  
Alternative Hypotheses ◽  
Brain Correlates ◽  
Methodological Considerations

AbstractStroke patients commonly suffer from post stroke fatigue (PSF). Despite a general consensus that brain perturbations constitute a precipitating event in the multifactorial etiology of PSF, the specific predictive value of conventional lesion characteristics such as size and localization remain unclear. The current study represents a novel approach to assess the neural correlates of PSF in chronic stroke patients. While previous research has focused primarily on lesion location or size, with mixed or inconclusive results, we targeted the extended structural network implicated by the lesion, and evaluated the added explanatory value of a disconnectivity approach with regards to the brain correlates of PSF. To this end, we estimated individual brain disconnectome maps in 84 stroke survivors in the chronic phase (≥ 3 months post stroke) using information about lesion location and normative white matter pathways obtained from 170 healthy individuals. PSF was measured by the Fatigue Severity Scale (FSS). Voxel wise analyses using non-parametric permutation-based inference were conducted on disconnectome maps to estimate regional effects of disconnectivity. Associations between PSF and global disconnectivity and clinical lesion characteristics were tested by linear models, and we estimated Bayes factor to quantify the evidence for the null and alternative hypotheses, respectively. The results revealed no significant associations between PSF and disconnectome measures or lesion characteristics, with moderate evidence in favor of the null hypothesis. These results suggest that symptoms of post-stroke fatigue are not simply explained by lesion characteristics or brain disconnectome measures in stroke patients in a chronic phase, and are discussed in light of methodological considerations.

scholarly journals Food-provisioning negatively affects calf survival and female reproductive success in bottlenose dolphins

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
V. Senigaglia ◽  
F. Christiansen ◽  
K. R. Sprogis ◽  
J. Symons ◽  
L. Bejder
Keyword(s):  
Reproductive Success ◽  
Bayes Factor ◽  
Linear Models ◽  
Southern Oscillation ◽  
Bottlenose Dolphins ◽  
Food Provisioning ◽  
Female Reproductive Success ◽  
Climatic Fluctuations ◽  
Calf Survival

AbstractFood-provisioning of wildlife can facilitate reliable up-close encounters desirable by tourists and, consequently, tour operators. Food-provisioning can alter the natural behavior of an animal, encouraging adverse behavior (e.g. begging for food handouts), and affect the reproductive success and the viability of a population. Studies linking food-provisioning to reproductive success are limited due to the lack of long-term datasets available, especially for long-lived species such as marine mammals. In Bunbury, Western Australia, a state-licensed food-provisioning program offers fish handouts to a limited number of free-ranging bottlenose dolphins (Tursiops aduncus). Coupled with long-term historical data, this small (<200 individuals), resident dolphin population has been extensively studied for over ten years, offering an opportunity to examine the effect of food-provisioning on the reproductive success of females (ntotal = 63;nprovisioned females = 8). Female reproductive success was estimated as the number of weaned calves produced per reproductive years and calf survival at year one and three years old was investigated. The mean reproductive success of provisioned and non-provisioned females was compared using Bayes factor. We also used generalized linear models (GLMs) to examine female reproductive success in relation to the occurrence of food-provisioning, begging behavior and location (within the study area). Furthermore, we examined the influence of these variables and birth order and climatic fluctuations (e.g. El Niño Southern Oscillation) on calf survival. Bayes factor analyses (Bayes factor = 6.12) and results from the best fitting GLMs showed that female reproductive success and calf survival were negatively influenced by food-provisioning. The negative effects of food-provisioning, although only affecting a small proportion of the adult females’ population (13.2%), are of concern, especially given previous work showing that this population is declining.

scholarly journals A Caveat on the Savage-Dickey Density Ratio: The Case of Computing Bayes Factors for Regression Parameters

2018 ◽  
Author(s):  
Daniel W. Heck
Keyword(s):  
Regression Models ◽  
Bayes Factor ◽  
Linear Models ◽  
Nonlinear Models ◽  
Density Ratio ◽  
Equality Constraint ◽  
Process Models ◽  
Linear Regression Models ◽  
Simple Method ◽  
Regression Parameters

The Savage-Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an effect on the dependent variable. However, the Savage-Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition is violated for multiple regression models with a Jeffreys-Zellner-Siow (JZS) prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage-Dickey ratio is especially relevant when analytical solutions for the Bayes factor are not available. This is the case for generalized linear models, nonlinear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage-Dickey density ratio.

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