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.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

Chinese Basic Pension Substitution Rate: A Monte Carlo Demonstration of the Individual Account Model

At the end of 2005, the State Council of China passed ”The Decision on adjusting the Individual Account of Basic Pension System”, which adjusted the individual account in the 1997 basic pension system. In this essay, we will analyze the adjustment above, and use Life Annuity Actuarial Theory to establish the basic pension substitution rate model. Monte Carlo simulation is also used to prove the rationality of the model. Some suggestions are put forward associated with the substitution rate according to the current policy.

Comparison of Two Methods for Caluculating the Partition Functions of Various Spatial Statistical Models

Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate the normalizing constant by Markov chain Monte Carlo methods are compared by simulation experiments for an Ising model, a Gaussian Markov field model and a pairwise interaction point field model.

A Bayesian framework for learning shared and individual subspaces from multiple data sources

This paper presents a novel Bayesian formulation to exploit shared structures across multiple data sources, constructing foundations for effective mining and retrieval across disparate domains. We jointly analyze diverse data sources using a unifying piece of metadata (textual tags). We propose a method based on Bayesian Probabilistic Matrix Factorization (BPMF) which is able to explicitly model the partial knowledge common to the datasets using shared subspaces and the knowledge specific to each dataset using individual subspaces. For the proposed model, we derive an efficient algorithm for learning the joint factorization based on Gibbs sampling. The effectiveness of the model is demonstrated by social media retrieval tasks across single and multiple media. The proposed solution is applicable to a wider context, providing a formal framework suitable for exploiting individual as well as mutual knowledge present across heterogeneous data sources of many kinds.

A bayesian nonparametric joint factor model for learning shared and individual subspaces from multiple data sources

Joint analysis of multiple data sources is becoming increasingly popular in transfer learning, multi-task learning and cross-domain data mining. One promising approach to model the data jointly is through learning the shared and individual factor subspaces. However, performance of this approach depends on the subspace dimensionalities and the level of sharing needs to be specified a priori. To this end, we propose a nonparametric joint factor analysis framework for modeling multiple related data sources. Our model utilizes the hierarchical beta process as a nonparametric prior to automatically infer the number of shared and individual factors. For posterior inference, we provide a Gibbs sampling scheme using auxiliary variables. The effectiveness of the proposed framework is validated through its application on two real world problems - transfer learning in text and image retrieval.

Disease mapping and regression with count data in the presence of overdispersion and spatial autocorrelation: a Bayesian model averaging approach

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

Continuous discovery of co-location contexts from Bluetooth data

The discovery of contexts is important for context-aware applications in pervasive computing. This is a challenging problem because of the stream nature of data, the complexity and changing nature of contexts. We propose a Bayesian nonparametric model for the detection of co-location contexts from Bluetooth signals. By using an Indian buffet process as the prior distribution, the model can discover the number of contexts automatically. We introduce a novel fixed-lag particle filter that processes data incrementally. This sampling scheme is especially suitable for pervasive computing as the computational requirements remain constant in spite of growing data. We examine our model on a synthetic dataset and two real world datasets. To verify the discovered contexts, we compare them to the communities detected by the Louvain method, showing a strong correlation between the results of the two methods. Fixed-lag particle filter is compared with Gibbs sampling in terms of the normalized factorization error that shows a close performance between the two inference methods. As fixed-lag particle filter processes a small chunk of data when it comes and does not need to be restarted, its execution time is significantly shorter than that of Gibbs sampling.

Data clustering using side information dependent Chinese restaurant processes

Side information, or auxiliary information associated with documents or image content, provides hints for clustering. We propose a new model, side information dependent Chinese restaurant process, which exploits side information in a Bayesian nonparametric model to improve data clustering. We introduce side information into the framework of distance dependent Chinese restaurant process using a robust decay function to handle noisy side information. The threshold parameter of the decay function is updated automatically in the Gibbs sampling process. A fast inference algorithm is proposed. We evaluate our approach on four datasets: Cora, 20 Newsgroups, NUS-WIDE and one medical dataset. Types of side information explored in this paper include citations, authors, tags, keywords and auxiliary clinical information. The comparison with the state-of-the-art approaches based on standard performance measures (NMI, F1) clearly shows the superiority of our approach.

Small-variance asymptotics for bayesian nonparametric models with constraints

The users often have additional knowledge when Bayesian nonparametric models (BNP) are employed, e.g. for clustering there may be prior knowledge that some of the data instances should be in the same cluster (must-link constraint) or in different clusters (cannot-link constraint), and similarly for topic modeling some words should be grouped together or separately because of an underlying semantic. This can be achieved by imposing appropriate sampling probabilities based on such constraints. However, the traditional inference technique of BNP models via Gibbs sampling is time consuming and is not scalable for large data. Variational approximations are faster but many times they do not offer good solutions. Addressing this we present a small-variance asymptotic analysis of the MAP estimates of BNP models with constraints. We derive the objective function for Dirichlet process mixture model with constraints and devise a simple and efficient K-means type algorithm. We further extend the small-variance analysis to hierarchical BNP models with constraints and devise a similar simple objective function. Experiments on synthetic and real data sets demonstrate the efficiency and effectiveness of our algorithms.

Hierarchical Bayesian nonparametric models for knowledge discovery from electronic medical records

Electronic Medical Record (EMR) has established itself as a valuable resource for large scale analysis of health data. A hospital EMR dataset typically consists of medical records of hospitalized patients. A medical record contains diagnostic information (diagnosis codes), procedures performed (procedure codes) and admission details. Traditional topic models, such as latent Dirichlet allocation (LDA) and hierarchical Dirichlet process (HDP), can be employed to discover disease topics from EMR data by treating patients as documents and diagnosis codes as words. This topic modeling helps to understand the constitution of patient diseases and offers a tool for better planning of treatment. In this paper, we propose a novel and flexible hierarchical Bayesian nonparametric model, the word distance dependent Chinese restaurant franchise (wddCRF), which incorporates word-to-word distances to discover semantically-coherent disease topics. We are motivated by the fact that diagnosis codes are connected in the form of ICD-10 tree structure which presents semantic relationships between codes. We exploit a decay function to incorporate distances between words at the bottom level of wddCRF. Efficient inference is derived for the wddCRF by using MCMC technique. Furthermore, since procedure codes are often correlated with diagnosis codes, we develop the correspondence wddCRF (Corr-wddCRF) to explore conditional relationships of procedure codes for a given disease pattern. Efficient collapsed Gibbs sampling is derived for the Corr-wddCRF. We evaluate the proposed models on two real-world medical datasets - PolyVascular disease and Acute Myocardial Infarction disease. We demonstrate that the Corr-wddCRF model discovers more coherent topics than the Corr-HDP. We also use disease topic proportions as new features and show that using features from the Corr-wddCRF outperforms the baselines on 14-days readmission prediction. Beside these, the prediction for procedure codes based on the Corr-wddCRF also shows considerable accuracy.

Price discovery using a regime-sensitive cointegration approach

This work proposes a method to examine variations in the cointegration relation between preferred and common stocks in the Brazilian stock market via Markovian regime switches. It aims on contributing for future works in "pairs trading" and, more specifically, to price discovery, given that, conditional on the state, the system is assumed stationary. This implies there exists a (conditional) moving average representation from which measures of "information share" (IS) could be extracted. For identification purposes, the Markov error correction model is estimated within a Bayesian MCMC framework. Inference and capability of detecting regime changes are shown using a Montecarlo experiment. I also highlight the necessity of modeling financial effects of high frequency data for reliable inference.

Estimativa de parâmetros genéticos da habilidade de permanência aos 48, 60 e 72 meses de idade em vacas da raça Caracu

Objetivou-se estimar a herdabilidade da característica habilidade de permanência (HP) em um rebanho de bovinos da raça Caracu visando sua utilização como critério de seleção. A característica em estudo foi definida como a probabilidade de a vaca estar presente no rebanho aos 48 (HP48), aos 60 (HP60) e aos 72 (HP72) meses, desde que possuíssem registros de pelo menos duas lactações nas específicas idades. Observações binárias, com zero (0 = fracasso) e um (1 = sucesso) foram designadas aos animais. Para análise da HP, foram utilizados dados de 5.487, 4.947 e 4.308 animais aos 48, 60 e 72 meses, respectivamente. Os componentes de variância e as herdabilidades foram estimados mediante inferência Bayesiana, via amostragem de Gibbs, pelo programa MTGSAM - threshold, utilizando-se um modelo touro. Foram utilizadas como variáveis explanatórias grupo de contemporâneos, classe de produção de leite na primeira lactação, classe de idade ao primeiro parto e sua interação. As análises forneceram estimativas médias de herdabilidade iguais a 0,28 ± 0,07 para HP48, 0,27 ± 0,07 para HP60 e 0,23 ± 0,07 para HP72. Os resultados evidenciaram que a característica HP apresentou variação aditiva em todas as idades estudadas e, portanto, pode ser empregada como critério de seleção para longevidade produtiva.

Testicular traits as selection criteria for young Nellore bulls

The objective of this study was to evaluate the possible use of biometric testicular traits as selection criteria for young Nellore bulls using Bayesian inference to estimate heritability coefficients and genetic correlations. Multitrait analysis was performed including 17,211 records of scrotal circumference obtained during andrological assessment (SCAND) and 15,313 records of testicular volume and shape. In addition, 50,809 records of scrotal circumference at 18 mo (SC18), used as an anchor trait, were analyzed. The (co) variance components and breeding values were estimated by Gibbs sampling using the Gibbs2F90 program under an animal model that included contemporary groups as fixed effects, age of the animal as a linear covariate, and direct additive genetic effects as random effects. Heritabilities of 0.42, 0.43, 0.31, 0.20, 0.04, 0.16, 0.15, and 0.10 were obtained for SC18, SCAND, testicular volume, testicular shape, minor defects, major defects, total defects, and satisfactory andrological evaluation, respectively. The genetic correlations between SC18 and the other traits were 0.84 (SCAND), 0.75 (testicular shape), 0.44 (testicular volume), -0.23 (minor defects), -0.16 (major defects), -0.24 (total defects), and 0.56 (satisfactory andrological evaluation). Genetic correlations of 0.94 and 0.52 were obtained between SCAND and testicular volume and shape, respectively, and of 0.52 between testicular volume and testicular shape. In addition to favorable genetic parameter estimates, SC18 was found to be the most advantageous testicular trait due to its easy measurement before andrological assessment of the animals, even though the utilization of biometric testicular traits as selection criteria was also found to be possible. In conclusion, SC18 and biometric testicular traits can be adopted as a selection criterion to improve the fertility of young Nellore bulls.