Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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%.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

Sustainable bioenergy: a framework for decision makers

Includes bibliography

The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Body condition score of Nellore beef cows: a heritable measure to improve the selection of reproductive and maternal traits

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Can the red palm mite threaten the Amazon vegetation?

The red palm mite Raoiella indica Hirst (Tenuipalpidae) was first reported in the New World in 2004, dispersing quickly and widely while adopting new plant species as hosts. Since then, it has caused severe damage in this region, especially to coconut (Cocos nucifera L.). It was first found in Brazil in 2009, in the northern Amazonian state of Roraima. In the present study, native and introduced plants were sampled between March 2010 and February 2011 in sites of the 15 Roraima municipalities, to estimate its distribution and the associated mite fauna. In addition, monthly samples were taken from a coconut plantation in Mucajai throughout the same period, for an initial appraisal of the levels R. indica could reach. It was found in 10 municipalities, on 19 plant species of four families. Six species are reported for the first time as hosts. Among the associated predators, 89.1% were Phytoseiidae, most commonly Amblyseius largoensis (Muma), Iphiseiodes zuluagai Denmark & Muma and Euseius concordis (Chant). The highest densities of R. indica, 1.5 and 0.35 mites/cm2 of leaflet (approx total of 331 and 77 mites/leaflet), were reached respectively in March 2010 and February 2011. The highest density of phytoseiids on coconut (0.009 mites/cm2 or about 2 mites/leaflet) was reached in November 2010. The average densities of R. indica recorded for Roraima were comparable to those reported for countries in which the mite is reportedly economically damaging. The dispersal of R. indica through the Amazon forest may result in damage to cultivated and native palms, and plants of other families, if the projected increase in both the frequency and the severity of drought events occurs. Parts of the Amazon have undergone periods of low rainfall, a condition that appears to favour the biology of this mite. Its eventual arrival to northeastern Brazil may result in heavy economic and ecological losses.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Modelling biogeochemical cycles in forest ecosystems: a Bayesian approach

Forest models are tools for explaining and predicting the dynamics of forest ecosystems. They simulate forest behavior by integrating information on the underlying processes in trees, soil and atmosphere. Bayesian calibration is the application of probability theory to parameter estimation. It is a method, applicable to all models, that quantifies output uncertainty and identifies key parameters and variables. This study aims at testing the Bayesian procedure for calibration to different types of forest models, to evaluate their performances and the uncertainties associated with them. In particular,we aimed at 1) applying a Bayesian framework to calibrate forest models and test their performances in different biomes and different environmental conditions, 2) identifying and solve structure-related issues in simple models, and 3) identifying the advantages of additional information made available when calibrating forest models with a Bayesian approach. We applied the Bayesian framework to calibrate the Prelued model on eight Italian eddy-covariance sites in Chapter 2. The ability of Prelued to reproduce the estimated Gross Primary Productivity (GPP) was tested over contrasting natural vegetation types that represented a wide range of climatic and environmental conditions. The issues related to Prelued's multiplicative structure were the main topic of Chapter 3: several different MCMC-based procedures were applied within a Bayesian framework to calibrate the model, and their performances were compared. A more complex model was applied in Chapter 4, focusing on the application of the physiology-based model HYDRALL to the forest ecosystem of Lavarone (IT) to evaluate the importance of additional information in the calibration procedure and their impact on model performances, model uncertainties, and parameter estimation. Overall, the Bayesian technique proved to be an excellent and versatile tool to successfully calibrate forest models of different structure and complexity, on different kind and number of variables and with a different number of parameters involved.

Benchmarking in the SWISSspine registry: results of 52 Dynardi lumbar total disc replacements compared with the data pool of 431 other lumbar disc prostheses

The SWISSspine registry is the first mandatory registry of its kind in the history of Swiss orthopaedics and it follows the principle of "coverage with evidence development". Its goal is the generation of evidence for a decision by the Swiss federal office of health about reimbursement of the concerned technologies and treatments by the basic health insurance of Switzerland. Recently, developed and clinically implemented, the Dynardi total disc arthroplasty (TDA) accounted for 10% of the implanted lumbar TDAs in the registry. We compared the outcomes of patients treated with Dynardi to those of the recipients of the other TDAs in the registry. Between March 2005 and October 2009, 483 patients with single-level TDA were documented in the registry. The 52 patients with a single Dynardi lumbar disc prosthesis implanted by two surgeons (CE and OS) were compared to the 431 patients who received one of the other prostheses. Data were collected in a prospective, observational multicenter mode. Surgery, implant, 3-month, 1-year, and 2-year follow-up forms as well as comorbidity, NASS and EQ-5D questionnaires were collected. For statistical analyses, the Wilcoxon signed-rank test and chi-square test were used. Multivariate regression analyses were also performed. Significant and clinically relevant reduction of low back pain and leg pain as well as improvement in quality of life was seen in both groups (P < 0.001 postop vs. preop). There were no inter-group differences regarding postoperative pain levels, intraoperative and follow-up complications or revision procedures with a new hospitalization. However, significantly more Dynardi patients achieved a minimum clinically relevant low back pain alleviation of 18 VAS points and a quality of life improvement of 0.25 EQ-5D points. The patients with Dynardi prosthesis showed a similar outcome to patients receiving the other TDAs in terms of postoperative low back and leg pain, complications, and revision procedures. A higher likelihood for achieving a minimum clinically relevant improvement of low back pain and quality of life in Dynardi patients was observed. This difference might be due to the large number of surgeons using other TDAs compared to only two surgeons using the Dynardi TDA, with corresponding variations in patient selection, patient-physician interaction and other factors, which cannot be assessed in a registry study.