scholarly journals A Bayesian framework for identifying consistent patterns of microbial abundance between body sites

2019 ◽  
Author(s):  
Richard Meier ◽  
Jeffrey A Thompson ◽  
Mei Chung ◽  
Naisi Zhao ◽  
Karl T. Kelsey ◽  
...  
Keyword(s):  
Disease Status ◽  
Operational Taxonomic Unit ◽  
Bayesian Framework ◽  
Bayesian Regression ◽  
Microbial Abundance ◽  
Simulation Studies ◽  
Disease Subtype ◽  
Strength Of Association ◽  
Formal Test ◽  
Correlation Statistic

AbstractRecent studies have found that the microbiome in both gut and mouth are associated with diseases of the gut, including cancer. If resident microbes could be found to exhibit consistent patterns between the mouth and gut, disease status could potentially be assessed non-invasively through profiling of oral samples. Currently, there exists no generally applicable method to test for such associations. Here we present a Bayesian framework to identify microbes that exhibit consistent patterns between body sites, with respect to a phenotypic variable. For a given operational taxonomic unit (OTU), a Bayesian regression model is used to obtain Markov-Chain Monte Carlo estimates of abundance among strata, calculate a correlation statistic, and conduct a formal test based on its posterior distribution. Extensive simulation studies demonstrate overall viability of the approach, and provide information on what factors affect its performance. Applying our method to a dataset containing oral and gut microbiome samples from 77 pancreatic cancer patients revealed several OTUs exhibiting consistent patterns between gut and mouth with respect to disease subtype. Our method is well powered for modest sample sizes and moderate strength of association and can be flexibly extended to other research settings using any currently established Bayesian analysis programs.

scholarly journals A Bayesian framework for identifying consistent patterns of microbial abundance between body sites

2019 ◽  
Vol 18 (6) ◽  
Author(s):  
Richard Meier ◽  
Jeffrey A. Thompson ◽  
Mei Chung ◽  
Naisi Zhao ◽  
Karl T. Kelsey ◽  
...  
Keyword(s):  
Disease Status ◽  
Operational Taxonomic Unit ◽  
Bayesian Framework ◽  
Bayesian Regression ◽  
Microbial Abundance ◽  
Simulation Studies ◽  
Disease Subtype ◽  
Strength Of Association ◽  
Formal Test ◽  
Correlation Statistic

Abstract Recent studies have found that the microbiome in both gut and mouth are associated with diseases of the gut, including cancer. If resident microbes could be found to exhibit consistent patterns between the mouth and gut, disease status could potentially be assessed non-invasively through profiling of oral samples. Currently, there exists no generally applicable method to test for such associations. Here we present a Bayesian framework to identify microbes that exhibit consistent patterns between body sites, with respect to a phenotypic variable. For a given operational taxonomic unit (OTU), a Bayesian regression model is used to obtain Markov-Chain Monte Carlo estimates of abundance among strata, calculate a correlation statistic, and conduct a formal test based on its posterior distribution. Extensive simulation studies demonstrate overall viability of the approach, and provide information on what factors affect its performance. Applying our method to a dataset containing oral and gut microbiome samples from 77 pancreatic cancer patients revealed several OTUs exhibiting consistent patterns between gut and mouth with respect to disease subtype. Our method is well powered for modest sample sizes and moderate strength of association and can be flexibly extended to other research settings using any currently established Bayesian analysis programs.

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

Improved weather indices based Bayesian regression model for forecasting crop yield

MAUSAM ◽  
2021 ◽  
Vol 72 (4) ◽  
pp. 879-886
Author(s):  
M. YEASIN ◽  
K. N. SINGH ◽  
A. LAMA ◽  
B. GURUNG
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Crop Yield ◽  
Wheat Yield ◽  
Bayesian Framework ◽  
Bayesian Regression ◽  
Estimation Of Parameters ◽  
Yield Data ◽  
Conjugate Priors ◽  
Modern Era

As agriculture is the backbone of the Indian economy, Government needs a reliable forecast of crop yield for planning new schemes. The most extensively used technique for forecasting crop yield is regression analysis. The significance of parameters is one of the major problems of regression analysis. Non-significant parameters lead to absurd forecast values and these forecast values are not reliable. In such cases, models need to be improved. To improve the models, we have incorporated prior knowledge through the Bayesian technique and investigate the superiority of these models under the Bayesian framework. The Bayesian technique is one of the most powerful methodologies in the modern era of statistics. We have discussed different types of prior (informative, non-informative and conjugate priors). The Markov chain Monte Carlo (MCMC) methodology has been briefly discussed for the estimation of parameters under Bayesian framework. To illustrate these models, production data of banana, mango and wheat yield data are taken under consideration. We compared the traditional regression model with the Bayesian regression model and conclusively infer that the models estimated under Bayesian framework provided superior results as compared to the models estimated under the classical approach.

scholarly journals A measure of association for ordered categorical data in population-based studies

2016 ◽  
Vol 27 (3) ◽  
pp. 812-831 ◽  
Author(s):  
Kerrie P Nelson ◽  
Don Edwards
Keyword(s):  
Categorical Data ◽  
Large Scale ◽  
Intraclass Correlation ◽  
Disease Status ◽  
Population Based ◽  
Simulation Studies ◽  
Ordered Categorical Data ◽  
Measure Of Association ◽  
Ordered Categorical ◽  
Categorical Scale

Ordinal classification scales are commonly used to define a patient’s disease status in screening and diagnostic tests such as mammography. Challenges arise in agreement studies when evaluating the association between many raters’ classifications of patients’ disease or health status when an ordered categorical scale is used. In this paper, we describe a population-based approach and chance-corrected measure of association to evaluate the strength of relationship between multiple raters’ ordinal classifications where any number of raters can be accommodated. In contrast to Shrout and Fleiss’ intraclass correlation coefficient, the proposed measure of association is invariant with respect to changes in disease prevalence. We demonstrate how unique characteristics of individual raters can be explored using random effects. Simulation studies are conducted to demonstrate the properties of the proposed method under varying assumptions. The methods are applied to two large-scale agreement studies of breast cancer screening and prostate cancer severity.

scholarly journals Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yuliang Yin ◽  
Baoren Li
Keyword(s):  
Credible Interval ◽  
Bayesian Framework ◽  
New Method ◽  
Simulation Studies ◽  
Normal Populations ◽  
Normal Means ◽  
Bayesian Evidence ◽  
The Difference

The Behrens-Fisher problem concerns the inferences for the difference between the means of two normal populations without making any assumption about the variances. Although the problem has been extensively studied in the literature, researchers cannot agree on its solution at present. In this paper, we propose a new method for dealing with the Behrens-Fisher problem in the Bayesian framework. The Bayesian evidence for testing the equality of two normal means and a credible interval at a specified level for the difference between the means are derived. Simulation studies are carried out to evaluate the performance of the provided Bayesian evidence.

scholarly journals Augmented mixed models for clustered proportion data

2014 ◽  
Vol 26 (2) ◽  
pp. 880-897 ◽  
Author(s):  
Dipankar Bandyopadhyay ◽  
Diana M Galvis ◽  
Victor H Lachos
Keyword(s):  
Monte Carlo ◽  
Mixed Models ◽  
Disease Status ◽  
Beta Regression ◽  
Simulation Studies ◽  
Case Deletion ◽  
Covariate Effects ◽  
Influence Diagnostics ◽  
Study Population ◽  
Disease Free

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

scholarly journals Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

2018 ◽  
Author(s):  
Paul - Christian Bürkner ◽  
Emmanuel Charpentier
Keyword(s):  
Regression Models ◽  
Prior Information ◽  
Estimation Method ◽  
Predictive Performance ◽  
R Package ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Interaction Terms ◽  
Fully Bayesian ◽  
Ordinal Predictors

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the contained information. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modeling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter $b$ representing the direction and size of the effect and a simplex parameter $\zeta$ modeling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may not only be applied to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies, we show that the model is well calibrated and, in case of monotonicity, has similar or even better predictive performance than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects, which allows to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

Uncertainty Quantification for Multiscale Simulations1

2001 ◽  
Vol 124 (1) ◽  
pp. 29-41 ◽  
Author(s):  
B. DeVolder ◽  
J. Glimm ◽  
J. W. Grove ◽  
Y. Kang ◽  
Y. Lee ◽  
...  
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
Uncertainty Quantification ◽  
Confidence Intervals ◽  
Petroleum Reservoirs ◽  
Bayesian Framework ◽  
Simulation Studies ◽  
Error Statistics ◽  
Key Issues ◽  
Leading Term

A general discussion of the quantification of uncertainty in numerical simulations is presented. A principal conclusion is that the distribution of solution errors is the leading term in the assessment of the validity of a simulation and its associated uncertainty in the Bayesian framework. Key issues that arise in uncertainty quantification are discussed for two examples drawn from shock wave physics and modeling of petroleum reservoirs. Solution error models, confidence intervals and Gaussian error statistics based on simulation studies are presented.

scholarly journals On Default Priors for Robust Bayesian Estimation with Divergences

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 29
Author(s):  
Tomoyuki Nakagawa ◽  
Shintaro Hashimoto
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Methods ◽  
Posterior Distribution ◽  
Bayesian Framework ◽  
Moment Matching ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Prior Distributions ◽  
Matching Priors ◽  
Selection Of

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.

scholarly journals Not That Close to Mommy: Horizontal Transmission Seeds the Microbiome Associated with the Marine Sponge Plakina cyanorosea

2020 ◽  
Vol 8 (12) ◽  
pp. 1978
Author(s):  
Bruno F. R. Oliveira ◽  
Isabelle R. Lopes ◽  
Anna L. B. Canellas ◽  
Guilherme Muricy ◽  
Alan D. W. Dobson ◽  
...  
Keyword(s):  
Environmental Samples ◽  
Developmental Stages ◽  
Horizontal Transmission ◽  
Operational Taxonomic Unit ◽  
Marine Sponges ◽  
Microbial Abundance ◽  
Dominant Member ◽  
Strict Core ◽  
Surrounding Seawater ◽  
Unique Otus

Marine sponges are excellent examples of invertebrate–microbe symbioses. In this holobiont, the partnership has elegantly evolved by either transmitting key microbial associates through the host germline and/or capturing microorganisms from the surrounding seawater. We report here on the prokaryotic microbiota during different developmental stages of Plakina cyanorosea and their surrounding environmental samples by a 16S rRNA metabarcoding approach. In comparison with their source adults, larvae housed slightly richer and more diverse microbial communities, which are structurally more related to the environmental microbiota. In addition to the thaumarchaeal Nitrosopumilus, parental sponges were broadly dominated by Alpha- and Gamma-proteobacteria, while the offspring were particularly enriched in the Vibrionales, Alteromonodales, Enterobacterales orders and the Clostridia and Bacteroidia classes. An enterobacterial operational taxonomic unit (OTU) was the dominant member of the strict core microbiota. The most abundant and unique OTUs were not significantly enriched amongst the microbiomes from host specimens included in the sponge microbiome project. In a wider context, Oscarella and Plakina are the sponge genera with higher divergence in their associated microbiota compared to their Homoscleromorpha counterparts. Our results indicate that P. cyanorosea is a low microbial abundance sponge (LMA), which appears to heavily depend on the horizontal transmission of its microbial partners that likely help the sponge host in the adaptation to its habitat.

Sign in / Sign up

Export Citation Format

Share Document