scholarly journals Inferring the Allelic Series at QTL in Multiparental Populations

Genetics ◽  
2020 ◽  
Vol 216 (4) ◽  
pp. 957-983
Author(s):  
Wesley L. Crouse ◽  
Samir N. P. Kelada ◽  
William Valdar
Keyword(s):  
Dirichlet Process ◽  
Bayesian Regression ◽  
Allelic Series ◽  
Posterior Inference ◽  
True Number ◽  
Tests Of Association ◽  
Selection Framework ◽  
Effect Estimation ◽  
Functional Alleles ◽  
Fully Bayesian

Multiparental populations (MPPs) are experimental populations in which the genome of every individual is a mosaic of known founder haplotypes. These populations are useful for detecting quantitative trait loci (QTL) because tests of association can leverage inferred founder haplotype descent. It is difficult, however, to determine how haplotypes at a locus group into distinct functional alleles, termed the allelic series. The allelic series is important because it provides information about the number of causal variants at a QTL and their combined effects. In this study, we introduce a fully Bayesian model selection framework for inferring the allelic series. This framework accounts for sources of uncertainty found in typical MPPs, including the number and composition of functional alleles. Our prior distribution for the allelic series is based on the Chinese restaurant process, a relative of the Dirichlet process, and we leverage its connection to the coalescent to introduce additional prior information about haplotype relatedness via a phylogenetic tree. We evaluate our approach via simulation and apply it to QTL from two MPPs: the Collaborative Cross (CC) and the Drosophila Synthetic Population Resource (DSPR). We find that, although posterior inference of the exact allelic series is often uncertain, we are able to distinguish biallelic QTL from more complex multiallelic cases. Additionally, our allele-based approach improves haplotype effect estimation when the true number of functional alleles is small. Our method, Tree-Based Inference of Multiallelism via Bayesian Regression (TIMBR), provides new insight into the genetic architecture of QTL in MPPs.

scholarly journals Inferring the Allelic Series at QTL in Multiparental Populations

2020 ◽  
Author(s):  
Wesley L. Crouse ◽  
Samir N.P. Kelada ◽  
William Valdar
Keyword(s):  
Dirichlet Process ◽  
Bayesian Regression ◽  
Allelic Series ◽  
Posterior Inference ◽  
True Number ◽  
Tests Of Association ◽  
Selection Framework ◽  
Effect Estimation ◽  
Functional Alleles ◽  
Fully Bayesian

ABSTRACTMultiparental populations (MPPs) are experimental populations in which the genome of every individual is a mosaic of known founder haplotypes. These populations are useful for detecting quantitative trait loci (QTL) because tests of association can leverage inferred founder haplotype descent. It is difficult, however, to determine how haplotypes at a locus group into distinct functional alleles, termed the allelic series. The allelic series is important because it provides information about the number of causal variants at a QTL and their combined effects. In this study, we introduce a fully-Bayesian model selection framework for inferring the allelic series. This framework accounts for sources of uncertainty found in typical MPPs, including the number and composition of functional alleles. Our prior distribution for the allelic series is based on the Chinese restaurant process, a relative of the Dirichlet process, and we leverage its connection to the coalescent to introduce additional prior information about haplotype relatedness via a phylogenetic tree. We evaluate our approach via simulation and apply it to QTL from two MPPs: the Collaborative Cross (CC) and the Drosophila Synthetic Population Resource (DSPR). We find that, although posterior inference of the exact allelic series is often uncertain, we are able to distinguish biallelic QTL from more complex multiallelic cases. Additionally, our allele-based approach improves haplotype effect estimation when the true number of functional alleles is small. Our method, Tree-Based Inference of Multiallelism via Bayesian Regression (TIMBR), provides new insight into the genetic architecture of QTL in MPPs.

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.

scholarly journals Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

2021 ◽  
Author(s):  
Chong Zhong ◽  
Zhihua Ma ◽  
Junshan Shen ◽  
Catherine Liu
Keyword(s):  
Survival Analysis ◽  
Dirichlet Process ◽  
Survival Function ◽  
Frailty Model ◽  
Survival Models ◽  
Bayesian Paradigm ◽  
Posterior Sampling ◽  
Posterior Inference ◽  
Shared Frailty Model ◽  
Shared Frailty

Bayesian paradigm takes advantage of well-fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through a Bayesian analysis of survival modeling for multivariate survival outcomes with the complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of the ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis, and Stan relaxes the posterior inference.

scholarly journals Dynamic degree-corrected blockmodels for social networks: A nonparametric approach

2018 ◽  
Vol 19 (4) ◽  
pp. 386-411
Author(s):  
Linda SL Tan ◽  
Maria De Iorio
Keyword(s):  
Social Networks ◽  
Dirichlet Process ◽  
Dynamic Networks ◽  
Static Model ◽  
Probit Regression ◽  
Dirichlet Process Prior ◽  
Nonparametric Approach ◽  
Mcmc Algorithms ◽  
Posterior Inference ◽  
Stochastic Blockmodel

A nonparametric approach to the modelling of social networks using degree-corrected stochastic blockmodels is proposed. The model for static network consists of a stochastic blockmodel using a probit regression formulation, and popularity parameters are incorporated to account for degree heterogeneity. We specify a Dirichlet process prior to detect community structure as well as to induce clustering in the popularity parameters. This approach is flexible yet parsimonious as it allows the appropriate number of communities and popularity clusters to be determined automatically by the data. We further discuss and implement extensions of the static model to dynamic networks. In a Bayesian framework, we perform posterior inference through MCMC algorithms. The models are illustrated using several real-world benchmark social networks.

scholarly journals Bayesian Autoregressive Frailty Models for Inference in Recurrent Events

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Marta Tallarita ◽  
Maria De Iorio ◽  
Alessandra Guglielmi ◽  
James Malone-Lee
Keyword(s):  
Dirichlet Process ◽  
Recurrent Events ◽  
Parametric Models ◽  
Recurrent Event ◽  
Event Time ◽  
Mcmc Algorithms ◽  
Posterior Inference ◽  
Gap Times ◽  
Tract Infections ◽  
Time Varying Covariates

AbstractWe propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.

scholarly journals Spiked Dirichlet Process Priors for Gaussian Process Models

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Terrance Savitsky ◽  
Marina Vannucci
Keyword(s):  
Gaussian Process ◽  
Dirichlet Process ◽  
Continuous Distribution ◽  
Bayesian Variable Selection ◽  
Process Models ◽  
Model Based Clustering ◽  
Posterior Sampling ◽  
Posterior Inference ◽  
Gaussian Process Models ◽  
Prior Models

We expand a framework for Bayesian variable selection for Gaussian process (GP) models by employing spiked Dirichlet process (DP) prior constructions over set partitions containing covariates. Our approach results in a nonparametric treatment of the distribution of the covariance parameters of the GP covariance matrix that in turn induces a clustering of the covariates. We evaluate two prior constructions: the first one employs a mixture of a point-mass and a continuous distribution as the centering distribution for the DP prior, therefore, clustering all covariates. The second one employs a mixture of a spike and a DP prior with a continuous distribution as the centering distribution, which induces clustering of the selected covariates only. DP models borrow information across covariates through model-based clustering. Our simulation results, in particular, show a reduction in posterior sampling variability and, in turn, enhanced prediction performances. In our model formulations, we accomplish posterior inference by employing novel combinations and extensions of existing algorithms for inference with DP prior models and compare performances under the two prior constructions.

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