Bayesian analysis of skew-t multivariate null intercept measurement error model

The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001; J R Stat Soc, Ser B 65:367-389, 2003; Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

An improved estimate of leaf area index based on the histogram analysis of hemispherical photographs

Leaf area index (LAI) is a key parameter that affects the surface fluxes of energy, mass, and momentum over vegetated lands, but observational measurements are scarce, especially in remote areas with complex canopy structure. In this paper we present an indirect method to calculate the LAI based on the analyses of histograms of hemispherical photographs. The optimal threshold value (OTV), the gray-level required to separate the background (sky) and the foreground (leaves), was analytically calculated using the entropy crossover method (Sahoo, P.K., Slaaf, D.W., Albert, T.A., 1997. Threshold selection using a minimal histogram entropy difference. Optical Engineering 36(7) 1976-1981). The OTV was used to calculate the LAI using the well-known gap fraction method. This methodology was tested in two different ecosystems, including Amazon forest and pasturelands in Brazil. In general, the error between observed and calculated LAI was similar to 6%. The methodology presented is suitable for the calculation of LAI since it is responsive to sky conditions, automatic, easy to implement, faster than commercially available software, and requires less data storage. (C) 2008 Elsevier B.V. All rights reserved.

Morphometric analysis of the urethra of castrated female rats treated with tamoxifen

Objectives: The aim of this study was to evaluate the effects of tamoxifen on the weight and thickness of the urethral epithelium of castrated female rats. Methods: Forty castrated adult female Wistar-Hannover rats were randomly divided into two groups: Group I (n = 20) in which the animals received only the vehicle (propylene glycol) and Group 11 (n = 20) in which the rats received tamoxifen 250 mu g/day by gavage. After 30 days of treatment, all animals were sacrificed and the urethra was immediately removed for weighing. Next, the urethra was divided into the proximal and distal segments, which were fixed in 10% formaldehyde and submitted to routine histological techniques for morphometric study. The data were analyzed using the weighted minimum mean-square error method and Student`s t-test for two independent samples (p < 0.05). Results: There was a significant increase in the mean weight of the urethra in the rats of Group 11 compared to the control group, 32.0 +/- 2.0 mg and 22.0 +/- 1.6 mg, respectively (p < 0.001). The mean thickness of the distal urethral epithelium of the animals treated with tamoxifen was significantly greater than that of the control group, 42.8 +/- 2.0 mu m and 36.6 +/- 1.5 mu m, respectively (p < 0.001). There was no statistically significant difference between the two groups with respect to the epithelial thickness of the proximal urethra (p = 0.514). Conclusion: Treating castrated adult rats with 250 mu g/day of tamoxifen for 30 days may increase the weight of the urethra and the thickness of the distal urethral epithelium. (c) 2008 Elsevier Ireland Ltd. All rights reserved.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

Semiparametric Bayesian measurement error modeling

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients. (C) 2009 Elsevier Inc. All rights reserved.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

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.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.