Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.

The Poisson-exponential distribution: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Elicitation of multivariate prior distributions: A nonparametric Bayesian approach

In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(.) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(.), instead we use nonparametric Bayesian inference, modelling f(.) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D with which to update his/her prior beliefs to obtain the posterior distribution for f(.). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given. (C) 2010 Elsevier B.V. All rights reserved.

A Bayesian approach for constructing genetic maps when markers are miscoded

The advent of molecular markers has created opportunities for a better understanding of quantitative inheritance and for developing novel strategies for genetic improvement of agricultural species, using information on quantitative trait loci (QTL). A QTL analysis relies on accurate genetic marker maps. At present, most statistical methods used for map construction ignore the fact that molecular data may be read with error. Often, however, there is ambiguity about some marker genotypes. A Bayesian MCMC approach for inferences about a genetic marker map when random miscoding of genotypes occurs is presented, and simulated and real data sets are analyzed. The results suggest that unless there is strong reason to believe that genotypes are ascertained without error, the proposed approach provides more reliable inference on the genetic map.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

A Bayesian approach to estimate the accuracy of in-house ELISA assay to measure rabies antibodies from compulsory vaccinated dogs and cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Bayesian view of the Higgs sector with higher dimensional operators

We investigate the possibilities of New Physics affecting the Standard Model (SM) Higgs sector. An effective Lagrangian with dimension-six operators is used to capture the effect of New Physics. We carry out a global Bayesian inference analysis, considering the recent LHC data set including all available correlations, as well as results from Tevatron. Trilinear gauge boson couplings and electroweak precision observables are also taken into account. The case of weak bosons tensorial couplings is closely examined and NLO QCD corrections are taken into account in the deviations we predict. We consider two scenarios, one where the coefficients of all the dimension-six operators are essentially unconstrained, and one where a certain subset is loop suppressed. In both scenarios, we find that large deviations from some of the SM Higgs couplings can still be present, assuming New Physics arising at 3 TeV. In particular, we find that a significantly reduced coupling of the Higgs to the top quark is possible and slightly favored by searches on Higgs production in association with top quark pairs. The total width of the Higgs boson is only weakly constrained and can vary between 0.7 and 2.7 times the Standard Model value within 95% Bayesian credible interval (BCI). We also observe sizeable effects induced by New Physics contributions to tensorial couplings. In particular, the Higgs boson decay width into Zγ can be enhanced by up to a factor 12 within 95% BCI. © 2013 SISSA.

New strategies for planning and performance evaluation of wireless networks: case studies based on the cross-layer approach

The use of wireless local area networks, called WLANs, as well as the proliferation of the use of multimedia applications have grown rapidly in recent years. Some factors affect the quality of service (QoS) received by the user and interference is one of them. This work presents strategies for planning and performance evaluation through an empirical study of the QoS parameters of a voice over Internet Protocol (VoIP) application in an interference network, as well as the relevance in the design of wireless networks to determine the coverage area of an access point, taking into account several parameters such as power, jitter, packet loss, delay, and PMOS. Another strategy is based on a hybrid approach that considers measuring and Bayesian inference applied to wireless networks, taking into consideration QoS parameters. The models take into account a cross layer vision of networks, correlating aspects of the physical environment, on the signal propagation (power or distance) with aspects of VoIP applications (e.g., jitter and packet loss). Case studies were carried out for two indoor environments and two outdoor environments, one of them displaying main characteristics of the Amazon region (e.g., densely arboreous environments). This last test bed was carried out in a real system because the Government of the State of Pará has a digital inclusion program called NAVEGAPARÁ.

Phylogenetic study of Class Armophorea (Alveolata, Ciliophora) based on 18S-rDNA data

The 18S rDNA phylogeny of Class Armophorea, a group of anaerobic ciliates, is proposed based on an analysis of 44 sequences (out of 195) retrieved from the NCBI/GenBank database. Emphasis was placed on the use of two nucleotide alignment criteria that involved variation in the gap-opening and gap-extension parameters and the use of rRNA secondary structure to orientate multiple-alignment. A sensitivity analysis of 76 data sets was run to assess the effect of variations in indel parameters on tree topologies. Bayesian inference, maximum likelihood and maximum parsimony phylogenetic analyses were used to explore how different analytic frameworks influenced the resulting hypotheses. A sensitivity analysis revealed that the relationships among higher taxa of the Intramacronucleata were dependent upon how indels were determined during multiple-alignment of nucleotides. The phylogenetic analyses rejected the monophyly of the Armophorea most of the time and consistently indicated that the Metopidae and Nyctotheridae were related to the Litostomatea. There was no consensus on the placement of the Caenomorphidae, which could be a sister group of the Metopidae + Nyctorheridae, or could have diverged at the base of the Spirotrichea branch or the Intramacronucleata tree.

Phylogeny of cissus (vitaceae) focusing on south american species

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

Influence of genotype-environment interaction on the classification of Nellore bulls in Southern Brazil

The aim of this study was to assess the occurrence of genotype-environment interaction, as well as its effects on the magnitude of genetic parameters and the classification of Nellore breeding bulls for the trait adjusted weight at 205 days (W205) on Southern Brazil. The components of (co)variance were estimated by Bayesian inference, using a linear-linear animal model in a bi-trait analysis. The proposed model for the analyses considers as random the direct additive genetic and maternal effects and residual effects, and as fixed effects the contemporary groups, sex, season of birth and weighing, and calving age as covariable (linear and quadratic effects). The a posteriori mean estimates of the direct heritabilities for W205 in the three States varied from 0.24 in Paraná (PR) to 0.34 in Santa Catarina (SC). The estimates of maternal heritability varied from 0.23 in SC and Rio Grande do Sul (RS) to 0.28 in PR. The a posteriori mean distributions of the genetic correlation varied from 0.52 between SC and RS, to 0.84 between PR and RS, suggesting that the best breeding bulls in SC are not the same as in RS.

Phylogeny of Lundia (Bignoniaceae) based on ndhF and PepC sequences

The circumscription of genera belonging to tribe Bignonieae (Bignoniaceae) has traditionally been complex, with only a few genera having stable circumscriptions in the various classification systems proposed for the tribe. The genus Lundia, for instance, is well characterized by a series of morphological synapomorphies and its circumscription has remained quite stable throughout its history. Despite the stable circumscription of Lundia, the circumscription of species within the genus has remained problematic. This study aims to reconstruct the phylogeny of Lundia in order to refine species circumscriptions, gain a better understanding of relationships between taxa, and identify potential morphological synapomorphies for species and major clades. We sampled 26 accessions representing 13 species of Lundia, and 5 outgroups, and reconstructed the phylogeny of the genus using a chloroplast (ndhF) and a nuclear marker (PepC). Data derived from sequences of the individual loci were analyzed using parsimony and Bayesian inference, and the combined molecular dataset was analyzed with Bayesian methods. The monophyly of Lundia nitidula, a species with a particularly complex circumscription, was tested using Shimodaira-Hasegawa (SH) test and the approximately unbiased test for phylogenetic tree selection (AU test). In addition, 40 morphological characters were mapped onto the tree that resulted from the analysis of the combined molecular dataset in order to identify morphological synapomorphies of individual species and major clades. Lundia and most species currently recognized within the genus were strongly supported as monophyletic in all analyses. One species, Lundia nitidula, was not resolved as monophyletic, but the monophyly of this species was not rejected by the AU and SH tests. Lundia sect. Eriolundia is resolved as paraphyletic in all analyses, while Lundia sect. Eulundia is monophyletic and supported by the same morphological characters traditionally used to circumscribe this section. The phylogeny of Lundia contributed important information for a better circumscription of species and served as basis the taxonomic revision of the genus.

Study of using marker assisted selection on a beef cattle breeding program by model comparison

A data set of a commercial Nellore beef cattle selection program was used to compare breeding models that assumed or not markers effects to estimate the breeding values, when a reduced number of animals have phenotypic, genotypic and pedigree information available. This herd complete data set was composed of 83,404 animals measured for weaning weight (WW), post-weaning gain (PWG), scrotal circumference (SC) and muscle score (MS), corresponding to 116,652 animals in the relationship matrix. Single trait analyses were performed by MTDFREML software to estimate fixed and random effects solutions using this complete data. The additive effects estimated were assumed as the reference breeding values for those animals. The individual observed phenotype of each trait was adjusted for fixed and random effects solutions, except for direct additive effects. The adjusted phenotype composed of the additive and residual parts of observed phenotype was used as dependent variable for models' comparison. Among all measured animals of this herd, only 3160 animals were genotyped for 106 SNP markers. Three models were compared in terms of changes on animals' rank, global fit and predictive ability. Model 1 included only polygenic effects, model 2 included only markers effects and model 3 included both polygenic and markers effects. Bayesian inference via Markov chain Monte Carlo methods performed by TM software was used to analyze the data for model comparison. Two different priors were adopted for markers effects in models 2 and 3, the first prior assumed was a uniform distribution (U) and, as a second prior, was assumed that markers effects were distributed as normal (N). Higher rank correlation coefficients were observed for models 3_U and 3_N, indicating a greater similarity of these models animals' rank and the rank based on the reference breeding values. Model 3_N presented a better global fit, as demonstrated by its low DIC. The best models in terms of predictive ability were models 1 and 3_N. Differences due prior assumed to markers effects in models 2 and 3 could be attributed to the better ability of normal prior in handle with collinear effects. The models 2_U and 2_N presented the worst performance, indicating that this small set of markers should not be used to genetically evaluate animals with no data, since its predictive ability is restricted. In conclusion, model 3_N presented a slight superiority when a reduce number of animals have phenotypic, genotypic and pedigree information. It could be attributed to the variation retained by markers and polygenic effects assumed together and the normal prior assumed to markers effects, that deals better with the collinearity between markers. (C) 2012 Elsevier B.V. All rights reserved.

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.