Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs

2006 ◽  
Vol 36 (5) ◽  
pp. 1276-1285 ◽  
Author(s):  
Eduardo P Cappa ◽  
Rodolfo JC Cantet
Keyword(s):  
Variance Components ◽  
Data Augmentation ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Multivariate Normal ◽  
Multiple Trait ◽  
Individual Tree ◽  
Tree Models ◽  
Fully Bayesian ◽  
Reml Estimation

In forest genetics, restricted maximum likelihood (REML) estimation of (co)variance components from normal multiple-trait individual-tree models is affected by the absence of observations in any trait and individual. Missing records affect the form of the distribution of REML estimates of genetics parameters, or of functions of them, and the estimating equations are computationally involved when several traits are analysed. An alternative to REML estimation is a fully Bayesian approach through Markov chain Monte Carlo. The present research describes the use of the full conjugate Gibbs algorithm proposed by Cantet et al. (R.J.C. Cantet, A.N. Birchmeier, and J.P. Steibel. 2004. Genet. Sel. Evol. 36: 49–64) to estimate (co)variance components in multiple-trait individual-tree models. This algorithm converges faster to the marginal posterior densities of the parameters than regular data augmentation from multivariate normal data with missing records. An expression to calculate the deviance information criterion for the selection of linear parameters in normal multiple-trait models is also given. The developments are illustrated by means of data from different crosses of two species of Pinus.

scholarly journals Multiple-trait model through Bayesian inference applied to Jatropha curcas breeding for bioenergy

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247775
Author(s):  
Marco Antônio Peixoto ◽  
Jeniffer Santana Pinto Coelho Evangelista ◽  
Igor Ferreira Coelho ◽  
Rodrigo Silva Alves ◽  
Bruno Gâlveas Laviola ◽  
...  
Keyword(s):  
Jatropha Curcas ◽  
Repeated Measures ◽  
Bayesian Model ◽  
Genetic Parameters ◽  
Genetic Correlations ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Monte Carlo Algorithm ◽  
Multiple Trait ◽  
Trait Model

Multiple-trait model tends to be the best alternative for the analysis of repeated measures, since they consider the genetic and residual correlations between measures and improve the selective accuracy. Thus, the objective of this study was to propose a multiple-trait Bayesian model for repeated measures analysis in Jatropha curcas breeding for bioenergy. To this end, the grain yield trait of 730 individuals of 73 half-sib families was evaluated over six harvests. The Markov Chain Monte Carlo algorithm was used to estimate genetic parameters and genetic values. Genetic correlation between pairs of measures were estimated and four selective intensities (27.4%, 20.5%, 13.7%, and 6.9%) were used to compute the selection gains. The full model was selected based on deviance information criterion. Genetic correlations of low (ρg ≤ 0.33), moderate (0.34 ≤ ρg ≤ 0.66), and high magnitude (ρg ≥ 0.67) were observed between pairs of harvests. Bayesian analyses provide robust inference of genetic parameters and genetic values, with high selective accuracies. In summary, the multiple-trait Bayesian model allowed the reliable selection of superior Jatropha curcas progenies. Therefore, we recommend this model to genetic evaluation of Jatropha curcas genotypes, and its generalization, in other perennials.

scholarly journals Spatial analysis of distribution of dengue cases in Espírito Santo, Brazil, in 2010: use of Bayesian model

2014 ◽  
Vol 17 (suppl 2) ◽  
pp. 150-159 ◽  
Author(s):  
Taizi Honorato ◽  
Priscila Pagung de Aquino Lapa ◽  
Carolina Maia Martins Sales ◽  
Barbara Reis-Santos ◽  
Ricardo Tristão-Sá ◽  
...  
Keyword(s):  
Spatial Analysis ◽  
Spatial Regression ◽  
Health Sector ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Thematic Maps ◽  
Espírito Santo ◽  
Fully Bayesian ◽  
Espirito Santo ◽  
The Relationship

OBJECTIVE: To study the relationship between the risk of dengue and sociodemographic variables through the use of spatial regression models fully Bayesian in the municipalities of Espírito Santo in 2010. METHOD: This is an ecological study and exploration that used spatial analysis tools in preparing thematic maps with data obtained from SinanNet. An analysis by area, taking as unit the municipalities of the state, was performed. Thematic maps were constructed by the computer program R 2.15.00 and Deviance Information Criterion (DIC), calculated in WinBugs, Absolut and Normalized Mean Error (NMAE) were the criteria used to compare the models. RESULTS: We were able to geocode 21,933 dengue cases (rate of 623.99 cases per 100 thousand habitants) with a higher incidence in the municipalities of Vitória, Serra and Colatina; model with spatial effect with the covariates trash and income showed the best performance at DIC and Nmae criteria. CONCLUSION: It was possible to identify the relationship of dengue with factors outside the health sector and to identify areas with higher risk of disease.

Bayesian estimation of a surface to account for a spatial trend using penalized splines in an individual-tree mixed model

2007 ◽  
Vol 37 (12) ◽  
pp. 2677-2688 ◽  
Author(s):  
Eduardo P. Cappa ◽  
Rodolfo J.C. Cantet
Keyword(s):  
Spatial Variability ◽  
Large Scale ◽  
Mixed Model ◽  
Deviance Information Criterion ◽  
Covariance Structure ◽  
Information Criterion ◽  
Penalized Splines ◽  
Dispersion Parameters ◽  
Individual Tree ◽  
Breeding Values

Unaccounted for spatial variability leads to bias in estimating genetic parameters and predicting breeding values from forest genetic trials. Previous attempts to account for large-scale continuous spatial variation employed spatial coordinates in the direction of the rows (or columns). In this research, we use an individual-tree mixed model and the tensor product of B-spline bases with a proper covariance structure for the random knot effects to account for spatial variability. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. The procedure is illustrated with data from a progeny trial of Eucalyptus globulus subsp. globulus Labill. Four different models were used in the sequel. The first model included block effects and the three other models included a surface on a grid of either 8 × 8, 12 × 12, or 18 × 18 knots. The three models with B-splines displayed a sizeable lower value of the deviance information criterion than the model with blocks. Also, the mixed models fitting a surface displayed a consistent reduction in the posterior mean of σ2e, an increase in the posterior means of σ2A and h2DBH, and an increase of 66% (for parents) or 60% (for offspring) in the accuracy of breeding values.

scholarly journals Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 248
Author(s):  
Reem Aljarallah ◽  
Samer A Kharroubi
Keyword(s):  
Monte Carlo ◽  
Down Syndrome ◽  
Mental Retardation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Univariate Analysis ◽  
Deviance Information Criterion ◽  
Predictive Ability ◽  
Information Criterion ◽  
Medical Genetic

Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via R2, adjusted R2, root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with R2 (0.1145), adjusted R2 (0.114), RMSE (0.3074) and DIC (7435.98) for DS, and R2 (0.0626), adjusted R2 (0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models.

Incorporating predictions into an annual forest inventory

1996 ◽  
Vol 26 (9) ◽  
pp. 1709-1713 ◽  
Author(s):  
Paul C. Van Deusen
Keyword(s):  
Forest Inventory ◽  
Variance Components ◽  
Growth Modeling ◽  
Estimation Procedure ◽  
Regression Estimator ◽  
Forest Types ◽  
Model Estimate ◽  
Individual Tree ◽  
Time Period ◽  
The Individual

Growth modeling of forests at the individual tree and stand levels is a highly refined procedure for many forest types. A method to incorporate predictions from such models into a forest inventory system is developed. Variance components from the actual measurements and from the predicted measurements are used to estimate the variance of the combined predicted value. The only assumption required to justify this method is that the model estimate has a bias that does not change from one time period to the next. The estimation procedure proposed here can also incorporate remotely sensed information via a regression estimator.

PSXV-9 Transgenerational epigenetic variance for production and reproduction traits in maternal-line pigs

2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 258-259
Author(s):  
Jason R Graham ◽  
Jay S Johnson ◽  
Andre C Araujo ◽  
Jeremy T Howard ◽  
Luiz F Brito
Keyword(s):  
Additive Genetic Variance ◽  
Phenotypic Expression ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Pedigree Information ◽  
Relationship Matrix ◽  
Maternal Line ◽  
Genetic Heritability ◽  
Reproduction Traits ◽  
Search Approach

Abstract Modeling epigenetic factors impacting phenotypic expression of economically important traits has become a hot-topic in the field of animal breeding due to the variability in genetic expression caused by environmental stressors (e.g., heat stress). This variability may be due, in part, to in-utero epigenomic remodeling, which has been reported to be passed from parent to offspring. We aimed to estimate transgenerational epigenetic variance for various production and reproduction traits measured in a maternal-line pig population, using a Bayesian approach. The phenotypes for production [n = 10,862; i.e., weaning weight (WW), birth weight (BW) and ultrasound-backfat thickness (BF)] and reproduction [n = 5,235, i.e., number of piglets born alive (NBA) and total number of piglets born (TB)] traits from a purebred Landrace population were provided by Smithfield Premium Genetics (NC, USA). The pedigree information traced back to 10 generations. Single-trait genetic analyses were performed using mixed models that included additive genetic, common environmental, and epigenetic random effects. The Gibbs sampler algorithm based on Markov chain Monte Carlo was used to estimate the variance components. The epigenetic relationship matrix was constructed using a recursive parameter (λ) related to the transmissibility coefficient of epigenetic markers. A grid search approach was used to define the optimal λ value (λ values ranged from 0.1 to 0.5, with an interval of 0.1). The optimal λ value was determined based on the deviance information criterion, and it was used to estimate the additive and epigenetic variances. For instance, based on preliminary results, the optimal λ value estimated for TB was 0.3 with an additive genetic variance of 0.94 (0.19 PSD) and epigenetic variance of 0.67 (0.18 PSD). The additive genetic heritability was 0.076 (0.015 PSD) and the estimated epigenetic heritability was 0.053 (0.015 PSD). This preliminary result suggests that epigenetics contribute to the non-Mendelian variability in pigs.

scholarly journals Utilização da modelagem inteiramente bayesiana na detecção de padrões de variação de risco relativo de mortalidade infantil no Rio Grande do Sul, Brasil

2009 ◽  
Vol 25 (7) ◽  
pp. 1501-1510 ◽  
Author(s):  
Sérgio Kakuta Kato ◽  
Diego de Matos Vieira ◽  
Jandyra Maria Guimarães Fachel
Keyword(s):  
Deviance Information Criterion ◽  
Rio Grande ◽  
Information Criterion ◽  
Rio Grande Do Sul ◽  
Standardised Mortality Ratio ◽  
Mortality Ratio

Neste artigo são analisados os fatores possivelmente associados à mortalidade infantil nos 496 municípios do Rio Grande do Sul, Brasil, com base em dados acumuladas entre os anos de 2001 a 2004, obtidos pela análise de regressão utilizando modelagem inteiramente bayesiana como alternativa para superar a autocorrelação espacial e a instabilidade dos estimadores clássicos, como a taxa bruta e a SMR (Standardised Mortality Ratio). Foram comparadas diferentes especificações de componente espacial e covariáveis, provenientes dos blocos do Índice de Desenvolvimento Sócio-econômico da Fundação de Economia e Estatística (IDESE/FEE-2003). Verificou-se que o modelo que utiliza a estrutura espacial além da covariável educação apresenta melhor desempenho, quando comparado pelo critério DIC (Deviance Information Criterion). Comparando as estimativas das SMR com os riscos relativos obtidos pela modelagem inteiramente bayesiana, foi possível observar um ganho substancial na interpretação e na detecção de padrões de variação do risco de mortalidade infantil nos municípios do Rio Grande do Sul ao utilizar essa modelagem. A região da Serra Gaúcha destacou-se com baixo risco relativo e estimativas muito homogêneas.

Understanding historical summer flounder (Paralichthys dentatus) abundance patterns through the incorporation of oceanography-dependent vital rates in Bayesian hierarchical models

2019 ◽  
Vol 76 (8) ◽  
pp. 1275-1294 ◽  
Author(s):  
Cecilia A. O’Leary ◽  
Timothy J. Miller ◽  
James T. Thorson ◽  
Janet A. Nye
Keyword(s):  
Population Dynamics ◽  
Gulf Stream ◽  
Stock Assessment ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Natural Mortality ◽  
Vital Rates ◽  
Summer Flounder ◽  
Paralichthys Dentatus ◽  
Abundance Patterns

Climate can impact fish population dynamics through changes in productivity and shifts in distribution, and both responses have been observed for many fish species. However, few studies have incorporated climate into population dynamics or stock assessment models. This study aimed to uncover how past variations in population vital rates and fishing pressure account for observed abundance variation in summer flounder (Paralichthys dentatus). The influences of the Gulf Stream Index, an index of climate variability in the Northwest Atlantic, on abundance were explored through natural mortality and stock–recruitment relationships in age-structured hierarchical Bayesian models. Posterior predictive loss and deviance information criterion indicated that out of tested models, the best estimates of summer flounder abundances resulted from the climate-dependent natural mortality model that included log-quadratic responses to the Gulf Stream Index. This climate-linked population model demonstrates the role of climate responses in observed abundance patterns and emphasizes the complexities of environmental effects on populations beyond simple correlations. This approach highlights the importance of modeling the combined effect of fishing and climate simultaneously to understand population dynamics.

scholarly journals Random regression for modeling yield genetic trajectories in Jatropha curcas breeding

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0244021
Author(s):  
Marco Antônio Peixoto ◽  
Rodrigo Silva Alves ◽  
Igor Ferreira Coelho ◽  
Jeniffer Santana Pinto Coelho Evangelista ◽  
Marcos Deon Vilela de Resende ◽  
...  
Keyword(s):  
Jatropha Curcas ◽  
Repeated Measures ◽  
Variance Components ◽  
High Reliability ◽  
Genetic Selection ◽  
Information Criterion ◽  
Random Regression ◽  
Ratio Test ◽  
Sib Families ◽  
Over Time

Random regression models (RRM) are a powerful tool to evaluate genotypic plasticity over time. However, to date, RRM remains unexplored for the analysis of repeated measures in Jatropha curcas breeding. Thus, the present work aimed to apply the random regression technique and study its possibilities for the analysis of repeated measures in Jatropha curcas breeding. To this end, the grain yield (GY) trait of 730 individuals of 73 half-sib families was evaluated over six years. Variance components were estimated by restricted maximum likelihood, genetic values were predicted by best linear unbiased prediction and RRM were fitted through Legendre polynomials. The best RRM was selected by Bayesian information criterion. According to the likelihood ratio test, there was genetic variability among the Jatropha curcas progenies; also, the plot and permanent environmental effects were statistically significant. The variance components and heritability estimates increased over time. Non-uniform trajectories were estimated for each progeny throughout the measures, and the area under the trajectories distinguished the progenies with higher performance. High accuracies were found for GY in all harvests, which indicates the high reliability of the results. Moderate to strong genetic correlation was observed across pairs of harvests. The genetic trajectories indicated the existence of genotype × measurement interaction, once the trajectories crossed, which implies a different ranking in each year. Our results suggest that RRM can be efficiently applied for genetic selection in Jatropha curcas breeding programs.

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