Significance tests in climate science

A large fraction of papers in the climate literature includes erroneous uses of significance tests. A Bayesian analysis is presented to highlight the meaning of significance tests and why typical misuse occurs. The significance statistic is not a quantitative measure of how confident we can be of the ‘reality’ of a given result. It is concluded that a significance test very rarely provides useful quantitative information.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

DENSITY PROFILE, VELOCITY ANISOTROPY, AND LINE-OF-SIGHT EXTERNAL CONVERGENCE OF SLACS GRAVITATIONAL LENSES

Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are used to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of these two estimates inside models with up to three degrees of freedom with respect to the lens density profile, stellar velocity anisotropy, and line-of-sight (LOS) external convergence, which incorporates the effect of the large-scale structure on strong lensing. A Bayesian analysis is employed to estimate the model parameters, evaluate their significance, and compare models. We find that the data favor Jaffe`s light profile over Hernquist`s, but that any particular choice between these two does not change the qualitative conclusions with respect to the features of the system that we investigate. The density profile is compatible with an isothermal, being sightly steeper and having an uncertainty in the logarithmic slope of the order of 5% in models that take into account a prior ignorance on anisotropy and external convergence. We identify a considerable degeneracy between the density profile slope and the anisotropy parameter, which largely increases the uncertainties in the estimates of these parameters, but we encounter no evidence in favor of an anisotropic velocity distribution on average for the whole sample. An LOS external convergence following a prior probability distribution given by cosmology has a small effect on the estimation of the lens density profile, but can increase the dispersion of its value by nearly 40%.

Population genetic structure and dispersal in white-lipped peccaries (Tayassu pecari) from the Brazilian Pantanal

In many mammals social organization promotes genetic structuring, which can be influenced by the dispersal pattern of the species. We analyzed the population genetic structure and dispersal of white-lipped peccaries (Tayassu pecan) from the Pantanal, Brazil. We genotyped 100 individuals at 7 microsatellite loci from 2 adjacent locations with no obvious geographic barrier between them. We found a significant but low F(ST) value, and the Bayesian analysis indicated a unique cluster. No significant differences were observed between mean assignment indices of resident males and females from both locations, and the probability of being born at the location sampled of > 30% of the individuals analyzed was lower than average. Mean relatedness between resident female, male, and opposite-sex pairs was not statistically different in both locations. These results suggest a low degree of genetic differentiation between the locations analyzed, and dispersal by both sexes (contrary to the predicted male-biased dispersal of most mammalian species).

Independent fusions and recent origins of sex chromosomes in the evolution and diversification of glass knife fishes (Eigenmannia)

The genus Eigenmannia comprises several species groups that display a surprising variety of diploid chromosome numbers and sex-determining systems. In this study, hypotheses regarding phylogenetic relationships and karyotype evolution were investigated using a combination of molecular and cytogenetic methods. Phylogenetic relationships were analyzed for 11 cytotypes based on sequences from five mitochondrial DNA regions. Parsimony-based character mapping of sex chromosomes confirms previous suggestions of multiple origins of sex chromosomes. Molecular cytogenetic analyses involved chromosome painting using probes derived from whole sex chromosomes from two taxa that were hybridized to metaphases of their respective sister cytotypes. These analyses showed that a multiple XY system evolved recently (<7 mya) by fusion. Furthermore, one of the chromosomes that fused to form the neo-Y chromosome is fused independently to another chromosome in the sister cytotype. This may constitute an efficient post-mating barrier and might imply a direct function of sex chromosomes in the speciation processes in Eigenmannia. The other chromosomal sex-determination system investigated is shown to have differentiated by an accumulation of heterochromatin on the X chromosome. This has occurred in the past 0.6 my, and is the most recent chromosomal sex-determining system described to date. These results show that the evolution of sex-determining systems can proceed very rapidly. Heredity (2011) 106, 391-400; doi:10.1038/hdy.2010.82; published online 23 June 2010

The timing of Neotropical speciation dynamics: A reconstruction of Myiopagis flycatcher diversification using phylogenetic and paleogeographic data

Neotropical forests have brought forth a large proportion of the world`s terrestrial biodiversity, but the underlying evolutionary mechanisms and their timing require further elucidation. Despite insights gained from phylogenetic studies, uncertainties about molecular clock rates have hindered efforts to determine the timing of diversification processes. Moreover, most molecular research has been detached from the extensive body of data on Neotropical geology and paleogeography. We here examine phylogenetic relationships and the timing of speciation events in a Neotropical flycatcher genus (Myiopagis) by using calibrations from modern geologic data in conjunction with a number of recently developed DNA sequence dating algorithms and by comparing these estimates with those based on a range of previously proposed molecular clock rates. We present a well-supported hypothesis of systematic relationships within the genus. Our age estimates of Myiopagis speciation events based on paleogeographic data are in close agreement with nodal ages derived from a ""traditional"" avian mitochondrial 2%/My clock, while contradicting other clock rates. Our comparative approach corroborates the consistency of the traditional avian mitochondrial clock rate of 2%/My for tyrant-flycatchers. Nevertheless, our results argue against the indiscriminate use of molecular clock rates in evolutionary research and advocate the verification of the appropriateness of the traditional clock rate by means of independent calibrations in individual studies. (C) 2009 Elsevier Inc. All rights reserved.

Determinants of Accelerated Small Intestinal Transit in Alcohol-Related Chronic Pancreatitis

Patients with chronic pancreatitis may have abnormal gastrointestinal transit, but the factors underlying these abnormalities are poorly understood. Gastrointestinal transit was assessed, in 40 male outpatients with alcohol-related chronic pancreatitis and 18 controls, by scintigraphy after a liquid meal labeled with (99m)technetium-phytate. Blood and urinary glucose, fecal fat excretion, nutritional status, and cardiovascular autonomic function were determined in all patients. The influence of diabetes mellitus, malabsorption, malnutrition, and autonomic neuropathy on abnormal gastrointestinal transit was assessed by univariate analysis and Bayesian multiple regression analysis. Accelerated gastrointestinal transit was found in 11 patients who showed abnormally rapid arrival of the meal marker to the cecum. Univariate and Bayesian analysis showed that diabetes mellitus and autonomic neuropathy had significant influences on rapid transit, which was not associated with either malabsorption or malnutrition. In conclusion, rapid gastrointestinal transit in patients with alcohol-related chronic pancreatitis is related to diabetes mellitus and autonomic neuropathy.

Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different ofrailtyo models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

Heteroscedastic Nonlinear Regression Models

In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

Predator-prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator-prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.