Evaluation of an average numerator relationship matrix model and a Bayesian hierarchical model for growth traits in Nellore cattle with uncertain paternity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Genetic parameters for buffalo milk yield and milk quality traits using Bayesian inference

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimação de parâmetros genéticos em caprinos leiteiros por meio de análise de regressão aleatória utilizando-se a Amostragem de Gibbs

Modelos de regressão aleatória foram utilizados neste estudo para estimar parâmetros genéticos da produção de leite no dia do controle (PLDC) em caprinos leiteiros da raça Alpina, por meio da metodologia Bayesiana. As estimativas geradas foram comparadas às obtidas com análise de regressão aleatória, utilizando-se o REML. As herdabilidades encontradas pela análise Bayesiana variaram de 0,18 a 0,37, enquanto, pelo REML, variaram de 0,09 a 0,32. As correlações genéticas entre dias de controle próximos se aproximaram da unidade, decrescendo gradualmente conforme a distância entre os dias de controle aumentou. Os resultados obtidos indicam que: a estrutura de covariâncias da PLDC em caprinos ao longo da lactação pode ser modelada adequadamente por meio da regressão aleatória; a predição de ganhos genéticos e a seleção de animais geneticamente superiores é viável ao longo de toda a trajetória da lactação; os resultados gerados pelas análises de regressão aleatória utilizando-se a Amostragem de Gibbs e o REML foram semelhantes, embora as estimativas das variâncias genéticas e das herdabilidades tenham sido levemente superiores na análise Bayesiana, utilizando-se a Amostragem de Gibbs.

Genetic parameters of total milk yield and factors describing the shape of lactation curve in dairy buffaloes

The objective of this study was to apply factor analysis to describe lactation curves in dairy buffaloes in order to estimate the phenotypic and genetic association between common latent factors and cumulative milk yield. A total of 31 257 monthly test-day milk yield records from buffaloes belonging to herds located in the state of São Paulo were used to estimate two common latent factors, which were then analysed in a multi-trait animal model for estimating genetic parameters. Estimates of (co)variance components for the two common latent factors and cumulated 270-d milk yield were obtained by Bayesian inference using a multiple trait animal model. Contemporary group, number of milkings per day (two levels) and age of buffalo cow at calving (linear and quadratic) as covariate were included in the model as fixed effects. The additive genetic, permanent environmental and residual effects were included as random effects. The first common latent factor (F1) was associated with persistency of lactation and the second common latent factor (F2) with the level of production in early lactation. Heritability estimates for Fl and F2 were 0.12 and 0.07, respectively. Genetic correlation estimates between El and F2 with cumulative milk yield were positive and moderate (0.63 and 0.52). Multivariate statistics employing factor analysis allowed the extraction of two variables (latent factors) that described the shape of the lactation curve. It is expected that the response to selection to increase lactation persistency is higher than the response obtained from selecting animals to increase lactation peak. Selection for higher total milk yield would result in a favourable correlated response to increase the level of production in early lactation and the lactation persistency.

Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Associação genética de escores de conformação com características de crescimento em bovinos da raça Angus

O objetivo deste trabalho foi determinar a associação genética entre escores visuais de conformação e as características de ganho de peso médio diário e de velocidade de crescimento em bovinos da raça Angus à desmama e ao sobreano. Os componentes de covariância foram estimados por modelo animal de análise tetracaracterística, com uso do método de inferência bayesiana, tendo-se assumido o modelo linear para: ganho de peso médio diário do nascimento à desmama (GMD) e da desmama ao sobreano (GMS); e velocidade de ganho de peso do nascimento à desmama (VD) e da desmama ao sobreano (VS). Um modelo não linear (de limiar) foi utilizado para os escores de conformação à desmama (CD) e ao sobreano (CS). As médias a posteriori, para a herdabilidade direta, foram: 0,12±0,023 (CD), 0,15±0,020 (GMD), 0,15±0,024 (VD), 0,17±0,020 (CS), 0,17±0,023(GMS), e 0,17±0,023 (VS). A correlação genética variou de -0,09±0,11 a 0,60±0,06, entre os escores CD e CS e as características de ganho médio diário de peso e velocidade de ganho de peso. A correlação entre CD e CS foi 0,52±0,089. A seleção direta para escores visuais de conformação, ganho médio diário e velocidade de ganho responde de forma lenta à seleção, tanto à desmama como ao sobreano.

Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.

Comparação entre análises para permanência no rebanho de vacas Nelore utilizando modelo linear e modelo de limiar

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Study of stayability in Nellore cows using a threshold model

The objectives of the current study were to assess the feasibility of using stayability traits to improve fertility of Nellore cows and to examine the genetic relationship among the stayabilities at different ages. Stayability was defined as whether a cow calved every year up to the age of 5 (Stay5), 6 (Stay6), or 7 (Stay7) yr of age or more, given that she was provided the opportunity to breed. Data were analyzed based on a maximum a posteriori probit threshold model to predict breeding values on the liability scale, whereas the Gibbs sampler was used to estimate variance components. The EBV were obtained using all animals included in the pedigree or bulls with at least 10 daughters with stayability observations, and average genetic trends were obtained in the liability and transformed to the probability scale. Additional analyses were performed to study the genetic relationship among stayability traits, which were compared by contrasting results in terms of EBV and the average genetic superiority as a function of the selected proportion of sires. Heritability estimates and SD were 0.25 +/- 0.02, 0.22 +/- 0.03, and 0.28 +/- 0.03 for Stay5, Stay6, and Stay7, respectively. Average genetic trends, by year, were 0.51 +/- 0.34, and 0.38% for Stay5, Stay6, and Stay7, respectively. Estimates of EBV SD, in the probability scale, for all animals included in the pedigree and for bulls with at least 10 daughters with stayability observations were 7.98 and 12.95, 6.93 and 11.38, and 8.24 and 14.30% for Stay5, Stay6, and Stay7, respectively. A reduction in the average genetic superiorities in Stay7 would be expected if the selection were based on Stay5 or Stay6. Nonetheless, the reduction in EPD, depending on selection intensity, is on average 0.74 and 1.55%, respectively. Regressions of the sires' EBV for Stay5 and Stay6 on the sires' EBV for Stay7 confirmed these results. The heritability and genetic trend estimates for all stayability traits indicate that it is possible to improve fertility with selection based on a threshold analysis of stayability. The SD of EBV for stayability traits show that there is adequate genetic variability among animals to justify inclusion of stayability as a selection criterion. The potential linear relationship among stayability traits indicates that selection for improved female traits would be more effective by having predictions on the Stay5 trait.

Abordagens freqüentista e bayesiana para avaliação genética de bovinos da raça Canchim para características de crescimento

This study aimed to: a) to compare the covariance components obtained by Restricted Maximum Likelihood (REML) and by bayesian inference (BI): b) to run genetic evaluations for weights of Canchim cattle measured at weaning (W240) and at eighteen months of age (W550), adjusted or not to 240 and 550 days of age, respectively, using the mixed model methodology with covariance components obtained by REML or by BI; and c) to compare selection decisions from genetic evaluations using observed or adjusted weights and by REML or BI. Covariance components, heritabilities and genetic correlation for W240 and W550 were estimated and the predicted breeding values were used to select 10% and 50% of the best bulls and cows, respectively. The covariance components obtained by REML were smaller than the a posteriori means obtained by Bl. Selected animals from both procedures were not the same, probably because the covariance components and genetic parameters were different. The inclusion of age of animal at weighing as a covariate in the statistical model fitted by BI did not change the selected bulls and cows.

Estudo da interação genótipo × ambiente sobre características de crescimento de bovinos de corte utilizando-se inferência bayesiana

The objective of this study was to evaluate the genotype x environment interaction for weaning and yearling weights, daily weight gain from weaning to 12 months of age and the growth performance in Canchim (5/8 Charolais + 3/8 Zebu) beef cattle estimated by a principal components analysis including those three traits. The environment was defined by season of birth (first and second semesters of the year). Genetic parameters were estimated by bayesian method with the Gibbs sampler using bivariate analyses (considering the trait in each of the two seasons as a different one) and models that included the fixed effects of year and month of birth, sex and age of cow (linear and quadratic) and the random effects of animal and residual. The results suggested that genetic evaluation and selection in Canchim beef cattle for the traits studied should consider the genotype and season of birth interaction.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Additive genetic relationships between scrotal circumference, heifer pregnancy, and stayability in Nellore cattle

Scrotal circumference data from 47,605 Nellore young bulls, measured at around 18 mo of age (SC18), were analyzed simultaneously with 27,924 heifer pregnancy (HP) and 80,831 stayability (STAY) records to estimate their additive genetic relationships. Additionally, the possibility that economically relevant traits measured directly in females could replace SC18 as a selection criterion was verified. Heifer pregnancy was defined as the observation that a heifer conceived and remained pregnant, which was assessed by rectal palpation at 60 d. Females were exposed to sires for the first time at about 14 mo of age (between 11 and 16 mo). Stayability was defined as whether or not a cow calved every year up to 5 yr of age, when the opportunity to breed was provided. A Bayesian linear-threshold-threshold analysis via Gibbs sampler was used to estimate the variance and covariance components of the multitrait model. Heritability estimates were 0.42 +/- 0.01, 0.53 +/- 0.03, and 0.10 +/- 0.01, for SC18, HP, and STAY, respectively. The genetic correlation estimates were 0.29 +/- 0.05, 0.19 +/- 0.05, and 0.64 +/- 0.07 between SC18 and HP, SC18 and STAY, and HP and STAY, respectively. The residual correlation estimate between HP and STAY was -0.08 +/- 0.03. The heritability values indicate the existence of considerable genetic variance for SC18 and HP traits. However, genetic correlations between SC18 and the female reproductive traits analyzed in the present study can only be considered moderate. The small residual correlation between HP and STAY suggests that environmental effects common to both traits are not major. The large heritability estimate for HP and the high genetic correlation between HP and STAY obtained in the present study confirm that EPD for HP can be used to select bulls for the production of precocious, fertile, and long-lived daughters. Moreover, SC18 could be incorporated in multitrait analysis to improve the prediction accuracy for HP genetic merit of young bulls.

Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.