A new class of multivariate skew distributions with applications to Bayesian regression models

Sahu, Sujit K.; Dey, Dipak K.; Branco, Márcia D.

doi:10.1002/cjs.10023

Cited by 92 publications

(261 citation statements)

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“…sGML model. Sahu et al (2003) modified the standard Gaussian process in order to accommodate skew patterns by the inclusion of a single additional parameter (Λ). This extra parameter accounts for right-(Λ < 0) and left-tail over-expression (Λ > 0), as well as for symmetric Gaussian patterns (Λ = 0).…”

Section: Methodsmentioning

confidence: 99%

“…Lack of sire information was accommodated into A by defining appropriate yearly within-flock genetic groups of unknown parents (Westell et al, 1988). The p(y|b,p,a,σ e 2 ,Λ) term was skew-Gaussian (Sahu et al, 2003;Varona et al, 2008), pðyjb;p;a;σ 2 e ;ΛÞ…”

Section: Methodsmentioning

confidence: 99%

“…Both the generalization of Gaussian models to non-symmetrical patterns and the implementation of non-linear models on the basis of skew parametric distributions have been suggested in previous studies Casellas and Bach, 2012;García et al, 2014). The main objective of this research was to evaluate two main parameterizations for the analysis of AFL in the Ripollesa sheep breed, the skew-Gaussian mixed linear model (sGML, Sahu et al, 2003) and the piecewise Weibull proportional hazards model (Casellas, 2007). In addition, environmental and genetic sources of variation were characterized in order to provide guidelines to shepherds to optimize flock management and to decide whether AFL can be considered as a reliable selection objective in current breeding schemes or not.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the formula h 2 = σ a 2 /[σ a 2 + σ p 2 + σ e 2 + Λ 2 (1-2/π)] can be applied to the sGML model (Sahu et al, 2003;Varona et al, 2008). (Kaplan and Meier, 1958; black dots).…”

mentioning

confidence: 99%

“…Shorter AFL intervals must be obtained by selecting those individuals with large and positive (model sGML) or large and negative (model PWPH3) predicted breeding values. Moreover, their magnitude can also differ because the sGML model assumes an additive structure for systematic and random effects (Sahu et al, 2003), whereas PHPW models rely on an exponential parameterization (Cox, 1972). Within the context of the Ripollesa data set, departures in terms of predicted breeding values from sGML and PWPH3 are shown in Figure 3; as expected, the plot suggests a negative correlation of −0.636, even higher if only sires were considered (−0.694), and departures increased for genetic background predisposing to longer AFL.…”

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confidence: 99%

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Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Casellas

2016

Animal

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Age at first lambing (AFL) plays a key role on the reproductive performance of sheep flocks, although there are no genetic selection programs accounting for this trait in the sheep industry. This could be due to the non-Gaussian distribution pattern of AFL data, which must be properly accounted for by the analytical model. In this manuscript, two different parameterizations were implemented to analyze AFL in the Ripollesa sheep breed, that is, the skew-Gaussian mixed linear model (sGML) and the piecewise Weibull proportional hazards model (PWPH). Data were available from 10 235 ewes born between 1972 and 2013 in 14 purebred Ripollesa flocks located in the north-east region of Spain. On average, ewes gave their first lambing short after their first year and a half of life (590.9 days), and within-flock averages ranged between 523.4 days and 696.6 days. Model fit was compared using the deviance information criterion (DIC; the smaller the DIC statistic, the better the model fit). Model sGML was clearly penalized (DIC = 200 059), whereas model PWPH provided smaller estimates and reached the minimum DIC when one cut point was added to the initial Weibull model (DIC = 132 545). The pure Weibull baseline and parameterizations with two or more cut points were discarded due to larger DIC estimates (>134 200). The only systematic effect influencing AFL was the season of birth, where summer-and fall-born ewes showed a remarkable shortening of their AFL, whereas neither birth type nor birth weight had a relevant impact on this reproductive trait. On the other hand, heritability on the original scale derived from model PWPH was high, with a model estimate place at 0.114 and its highest posterior density region ranging from 0.079 and 0.143. As conclusion, Gaussian-related mixed linear models should be avoided when analyzing AFL, whereas model PWPH must be viewed as better alternative with superior goodness of fit; moreover, the additive genetic background underlying this reproductive trait supports its inclusion into current genetic selection programs given its economic importance.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Casellas

2016

Animal

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Stochastic optimization for allocation problems with shortfall risk constraints

Casarin

Billio

2007

Appl Stoch Models Bus & Ind

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SUMMARYOne of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk-level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student-t distribution where each marginal can have different degrees of freedom. The stochastic optimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student-t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student-t with common degrees of freedom. Thus, the proposed simulation-based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified.

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Bayesian analysis for nonlinear regression model under skewed errors, with application in growth curves

Cruz

Branco

2009

Biometrical J

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We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

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A new class of multivariate skew distributions with applications to Bayesian regression models

Cited by 92 publications

References 4 publications

Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Stochastic optimization for allocation problems with shortfall risk constraints

Bayesian analysis for nonlinear regression model under skewed errors, with application in growth curves

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