Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data.Many of the issues that are discussed with reference to the statistical analysis of compositionaldata have a natural counterpart in the construction of a Bayesian statistical model for categoricaldata.This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986)in his seminal book on compositional data. Particular emphasis is put on the problem of whatparameterization to use

Industrial Location and Space: New Insights

This paper tries to resolve some of the main shortcomings in the empirical literature of location decisions for new plants, i.e. spatial effects and overdispersion. Spatial effects are omnipresent, being a source of overdispersion in the data as well as a factor shaping the functional relationship between the variables that explain a firm’s location decisions. Using Count Data models, empirical researchers have dealt with overdispersion and excess zeros by developments of the Poisson regression model. This study aims to take this a step further, by adopting Bayesian methods and models in order to tackle the excess of zeros, spatial and non-spatial overdispersion and spatial dependence simultaneously. Data for Catalonia is used and location determinants are analysed to that end. The results show that spatial effects are determinant. Additionally, overdispersion is descomposed into an unstructured iid effect and a spatially structured effect. Keywords: Bayesian Analysis, Spatial Models, Firm Location. JEL Classification: C11, C21, R30.

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Cancer mortality inequalities in urban areas: a Bayesian small area analysis in Spanish cities [correcció]

After publication of this work in 'International Journal of Health Geographics' on 13 january 2011 was wrong. The map of Barcelona in Figure two (figure 1 here) was reversed. The final correct Figure is presented here

Cancer mortality inequalities in urban areas: a Bayesian small area analysis in Spanish cities

Intra-urban inequalities in mortality have been infrequently analysed in European contexts. The aim of the present study was to analyse patterns of cancer mortality and their relationship with socioeconomic deprivation in small areas in 11 Spanish cities

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

What explains the Great Moderation in the US? A structural analysis

This paper investigates what has caused output and inflation volatility to fall in the USusing a small scale structural model using Bayesian techniques and rolling samples. Thereare instabilities in the posterior of the parameters describing the private sector, the policyrule and the standard deviation of the shocks. Results are robust to the specification ofthe policy rule. Changes in the parameters describing the private sector are the largest,but those of the policy rule and the covariance matrix of the shocks explain the changes most.

Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

Application of Multi-SNP Approaches Bayesian LASSO and AUC-RF to Detect Main Effects of Inflammatory-Gene Variants Associated with Bladder Cancer Risk

The relationship between inflammation and cancer is well established in several tumor types, including bladder cancer. We performed an association study between 886 inflammatory-gene variants and bladder cancer risk in 1,047 cases and 988 controls from the Spanish Bladder Cancer (SBC)/EPICURO Study. A preliminary exploration with the widely used univariate logistic regression approach did not identify any significant SNP after correcting for multiple testing. We further applied two more comprehensive methods to capture the complexity of bladder cancer genetic susceptibility: Bayesian Threshold LASSO (BTL), a regularized regression method, and AUC-Random Forest, a machine-learning algorithm. Both approaches explore the joint effect of markers. BTL analysis identified a signature of 37 SNPs in 34 genes showing an association with bladder cancer. AUC-RF detected an optimal predictive subset of 56 SNPs. 13 SNPs were identified by both methods in the total population. Using resources from the Texas Bladder Cancer study we were able to replicate 30% of the SNPs assessed. The associations between inflammatory SNPs and bladder cancer were reexamined among non-smokers to eliminate the effect of tobacco, one of the strongest and most prevalent environmental risk factor for this tumor. A 9 SNP-signature was detected by BTL. Here we report, for the first time, a set of SNP in inflammatory genes jointly associated with bladder cancer risk. These results highlight the importance of the complex structure of genetic susceptibility associated with cancer risk.

An integrative computational analysis provides evidence for FBN1-associated network deregulation in trisomy 21

Although approximately 50% of Down Syndrome (DS) patients have heart abnormalities, they exhibit an overprotection against cardiac abnormalities related with the connective tissue, for example a lower risk of coronary artery disease. A recent study reported a case of a person affected by DS who carried mutations in FBN1, the gene causative for a connective tissue disorder called Marfan Syndrome (MFS). The fact that the person did not have any cardiac alterations suggested compensation effects due to DS. This observation is supported by a previous DS meta-analysis at the molecular level where we have found an overall upregulation of FBN1 (which is usually downregulated in MFS). Additionally, that result was cross-validated with independent expression data from DS heart tissue. The aim of this work is to elucidate the role of FBN1 in DS and to establish a molecular link to MFS and MFS-related syndromes using a computational approach. To reach that, we conducted different analytical approaches over two DS studies (our previous meta-analysis and independent expression data from DS heart tissue) and revealed expression alterations in the FBN1 interaction network, in FBN1 co-expressed genes and FBN1-related pathways. After merging the significant results from different datasets with a Bayesian approach, we prioritized 85 genes that were able to distinguish control from DS cases. We further found evidence for several of these genes (47%), such as FBN1, DCN, and COL1A2, being dysregulated in MFS and MFS-related diseases. Consequently, we further encourage the scientific community to take into account FBN1 and its related network for the study of DS cardiovascular characteristics.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.