A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Baysian Model Averaging, Learning and Model Selection

Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth's model of price determination.

Trade, firm selection, and innovation: the competition channel

The availability of rich firm-level data sets has recently led researchers to uncover new evidence on the effects of trade liberalization. First, trade openness forces the least productive firms to exit the market. Secondly, it induces surviving firms to increase their innovation efforts and thirdly, it increases the degree of product market competition. In this paper we propose a model aimed at providing a coherent interpretation of these findings. We introducing firm heterogeneity into an innovation-driven growth model, where incumbent firms operating in oligopolistic industries perform cost-reducing innovations. In this framework, trade liberalization leads to higher product market competition, lower markups and higher quantity produced. These changes in markups and quantities, in turn, promote innovation and productivity growth through a direct competition effect, based on the increase in the size of the market, and a selection effect, produced by the reallocation of resources towards more productive firms. Calibrated to match US aggregate and firm-level statistics, the model predicts that a 10 percent reduction in variable trade costs reduces markups by 1:15 percent, firm surviving probabilities by 1 percent, and induces an increase in productivity growth of about 13 percent. More than 90 percent of the trade-induced growth increase can be attributed to the selection effect.

Identifying genetic signatures of selection in a non-model species, alpine gentian (Gentiana nivalis L.), using a landscape genetic approach

It is generally accepted that most plant populations are locally adapted. Yet, understanding how environmental forces give rise to adaptive genetic variation is a challenge in conservation genetics and crucial to the preservation of species under rapidly changing climatic conditions. Environmental variation, phylogeographic history, and population demographic processes all contribute to spatially structured genetic variation, however few current models attempt to separate these confounding effects. To illustrate the benefits of using a spatially-explicit model for identifying potentially adaptive loci, we compared outlier locus detection methods with a recently-developed landscape genetic approach. We analyzed 157 loci from samples of the alpine herb Gentiana nivalis collected across the European Alps. Principle coordinates of neighbor matrices (PCNM), eigenvectors that quantify multi-scale spatial variation present in a data set, were incorporated into a landscape genetic approach relating AFLP frequencies with 23 environmental variables. Four major findings emerged. 1) Fifteen loci were significantly correlated with at least one predictor variable (R (adj) (2) > 0.5). 2) Models including PCNM variables identified eight more potentially adaptive loci than models run without spatial variables. 3) When compared to outlier detection methods, the landscape genetic approach detected four of the same loci plus 11 additional loci. 4) Temperature, precipitation, and solar radiation were the three major environmental factors driving potentially adaptive genetic variation in G. nivalis. Techniques presented in this paper offer an efficient method for identifying potentially adaptive genetic variation and associated environmental forces of selection, providing an important step forward for the conservation of non-model species under global change.

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.

Missing value imputation in longitudinal measures of alcohol consumption

Attrition in longitudinal studies can lead to biased results. The study is motivated by the unexpected observation that alcohol consumption decreased despite increased availability, which may be due to sample attrition of heavy drinkers. Several imputation methods have been proposed, but rarely compared in longitudinal studies of alcohol consumption. The imputation of consumption level measurements is computationally particularly challenging due to alcohol consumption being a semi-continuous variable (dichotomous drinking status and continuous volume among drinkers), and the non-normality of data in the continuous part. Data come from a longitudinal study in Denmark with four waves (2003-2006) and 1771 individuals at baseline. Five techniques for missing data are compared: Last value carried forward (LVCF) was used as a single, and Hotdeck, Heckman modelling, multivariate imputation by chained equations (MICE), and a Bayesian approach as multiple imputation methods. Predictive mean matching was used to account for non-normality, where instead of imputing regression estimates, "real" observed values from similar cases are imputed. Methods were also compared by means of a simulated dataset. The simulation showed that the Bayesian approach yielded the most unbiased estimates for imputation. The finding of no increase in consumption levels despite a higher availability remained unaltered. Copyright (C) 2011 John Wiley & Sons, Ltd.

Sex allocation and sex-dependent selection for body size in Trypoxylon rogenhoferi Kohl (Hymenoptera, Sphecidae)

Two populations of the wasp Trypoxylon rogenhoferi Kohl, 1884 from São Carlos and Luís Antônio, State of São Paulo, Brazil, were observed and sampled from May 1999 to February 2001 using trap-nests. This mass-provisioning wasp was used to test some aspects of optimal sex allocation theory. Both populations fit all the predictions of the models of Green and Brockmann and Grafen. Maternal provisions determined the size of each offspring, and females allocated well-stocked brood cells to daughters, the sex that benefits most being large. This strategy resulted in a difference in size between the sexes. In São Carlos, female weight at emergence was 1.18 times that of males, in Luís Antônio this value was 1.13. The brood cell volume was correlated with both wing length and weight at emergence in both sexes, and the chance that a given brood cell contained a male offspring decreased with increased brood cell volume. In T. rogenhoferi female body size was related to fitness. Larger females were able to collect more mass of spiders per day, the spiders they captured were heavier, and they provisioned more brood cells per day. They also produced larger daughters. For males, no relationship between body size and fitness was found, but the data were scarce. Since the patterns of provisioning were variable among different females in both study sites, it is possible that the females not follow a unique strategy for sex allocation. The sex ratio and/or investment ratio in the São Carlos population was female-biased and in Luís Antônio, male-biased. In spite of the influence of trap-nests diameters on male production in Luís Antônio, there is some evidence that in São Carlos population the local availability of prey and/or lower rate of parasitism may be major forces in determining the observed sex ratio, but further studies are necessary to verify such hypothesis.

PyRate: a new program to estimate speciation and extinction rates from incomplete fossil data

Despite the advancement of phylogenetic methods to estimate speciation and extinction rates, their power can be limited under variable rates, in particular for clades with high extinction rates and small number of extant species. Fossil data can provide a powerful alternative source of information to investigate diversification processes. Here, we present PyRate, a computer program to estimate speciation and extinction rates and their temporal dynamics from fossil occurrence data. The rates are inferred in a Bayesian framework and are comparable to those estimated from phylogenetic trees. We describe how PyRate can be used to explore different models of diversification. In addition to the diversification rates, it provides estimates of the parameters of the preservation process (fossilization and sampling) and the times of speciation and extinction of each species in the data set. Moreover, we develop a new birth-death model to correlate the variation of speciation/extinction rates with changes of a continuous trait. Finally, we demonstrate the use of Bayes factors for model selection and show how the posterior estimates of a PyRate analysis can be used to generate calibration densities for Bayesian molecular clock analysis. PyRate is an open-source command-line Python program available at http://sourceforge.net/projects/pyrate/.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Therapeutic Drug Monitoring (TDM) of Imatinib: Effectiveness of Bayesian dose adjustment for CML patients enrolled in the Imatinib Concentration Monitoring (I-COME) study

Introduction: As imatinib pharmacokinetics are highly variable, plasma levels differ largely between patients under the same dosage. Retrospective studies in chronic myeloid leukemia (CML) patients showed significant correlations between low levels and suboptimal response, as well as between high levels and poor tolerability. Monitoring of trough plasma levels, targeting 1000 μg/L and above, is thus increasingly advised. Our study was launched to assess prospectively the clinical usefulness of systematic imatinib TDM in CML patients. This preliminary analysis addresses the appropriateness of the dosage adjustment approach applied in this study, which targets the recommended trough level and allows an interval of 4-24 h after last drug intake for blood sampling. Methods: Blood samples from the first 15 patients undergoing 1st TDM were obtained 1.5-25 h after last dose. Imatinib plasma levels were measured by LC-MS/MS and the concentrations were extrapolated to trough based on a Bayesian approach using a population pharmacokinetic model. Trough levels were predicted to differ significantly from the target in 12 patients (10 <750 μg/L; 2 >1500 μg/L along with poor tolerance) and individual dose adjustments were proposed. 8 patients underwent a 2nd TDM cycle. Trough levels of 1st and 2nd TDM were compared, the sample drawn 1.5 h after last dose (during distribution phase) was excluded from the analysis. Results: Individual dose adjustments were applied in 6 patients. Observed concentrations extrapolated to trough ranged from 360 to 1832 μg/L (median 725; mean 810, CV 52%) on 1st TDM and from 720 to 1187 μg/L (median 950; mean 940, CV 18%) on 2nd TDM cycle. Conclusions: These preliminary results suggest that TDM of imatinib using a Bayesian interpretation is able to target the recommended trough level of 1000 μg/L and to reduce the considerable differences in trough level exposure between patients (with CV decreasing from 52% to 18%). While this may simplify blood collection in daily practice, as samples do not have to be drawn exactly at trough, the largest possible interval to last drug intake yet remains preferable to avoid sampling during distribution phase leading to biased extrapolation. This encourages the evaluation of the clinical benefit of a routine TDM intervention in CML patients, which the randomized Swiss I-COME trial aims to.

Postglacial recolonization at a snail's pace (Trochulus villosus): confronting competing refugia hypotheses using model selection.

The localization of Last Glacial Maximum (LGM) refugia is crucial information to understand a species' history and predict its reaction to future climate changes. However, many phylogeographical studies often lack sampling designs intensive enough to precisely localize these refugia. The hairy land snail Trochulus villosus has a small range centred on Switzerland, which could be intensively covered by sampling 455 individuals from 52 populations. Based on mitochondrial DNA sequences (COI and 16S), we identified two divergent lineages with distinct geographical distributions. Bayesian skyline plots suggested that both lineages expanded at the end of the LGM. To find where the origin populations were located, we applied the principles of ancestral character reconstruction and identified a candidate refugium for each mtDNA lineage: the French Jura and Central Switzerland, both ice-free during the LGM. Additional refugia, however, could not be excluded, as suggested by the microsatellite analysis of a population subset. Modelling the LGM niche of T. villosus, we showed that suitable climatic conditions were expected in the inferred refugia, but potentially also in the nunataks of the alpine ice shield. In a model selection approach, we compared several alternative recolonization scenarios by estimating the Akaike information criterion for their respective maximum-likelihood migration rates. The 'two refugia' scenario received by far the best support given the distribution of genetic diversity in T. villosus populations. Provided that fine-scale sampling designs and various analytical approaches are combined, it is possible to refine our necessary understanding of species responses to environmental changes.

Startegy selection during exploratory behavior: sex differences, uncertainty and risk managment

This study deals with the psychological processes underlying the selection of appropriate strategy during exploratory behavior. A new device was used to assess sexual dimorphisms in spatial abilities that do not depend on spatial rotation, map reading or directional vector extraction capacities. Moreover, it makes it possible to investigate exploratory behavior as a specific response to novelty that trades off risk and reward. Risk management under uncertainty was assessed through both spontaneous searching strategies and signal detection capacities. The results of exploratory behavior, detection capacities, and decision-making strategies seem to indicate that women's exploratory behavior is based on risk-reducing behavior while men behavior does not appear to be influenced by this variable. This difference was interpreted as a difference in information processing modifying beliefs concerning the likelihood of uncertain events, and therefore influencing risk evaluation.

Natural selection in a postglacial range expansion: the case of the colour cline in the European barn owl.

Gradients of variation-or clines-have always intrigued biologists. Classically, they have been interpreted as the outcomes of antagonistic interactions between selection and gene flow. Alternatively, clines may also establish neutrally with isolation by distance (IBD) or secondary contact between previously isolated populations. The relative importance of natural selection and these two neutral processes in the establishment of clinal variation can be tested by comparing genetic differentiation at neutral genetic markers and at the studied trait. A third neutral process, surfing of a newly arisen mutation during the colonization of a new habitat, is more difficult to test. Here, we designed a spatially explicit approximate Bayesian computation (ABC) simulation framework to evaluate whether the strong cline in the genetically based reddish coloration observed in the European barn owl (Tyto alba) arose as a by-product of a range expansion or whether selection has to be invoked to explain this colour cline, for which we have previously ruled out the actions of IBD or secondary contact. Using ABC simulations and genetic data on 390 individuals from 20 locations genotyped at 22 microsatellites loci, we first determined how barn owls colonized Europe after the last glaciation. Using these results in new simulations on the evolution of the colour phenotype, and assuming various genetic architectures for the colour trait, we demonstrate that the observed colour cline cannot be due to the surfing of a neutral mutation. Taking advantage of spatially explicit ABC, which proved to be a powerful method to disentangle the respective roles of selection and drift in range expansions, we conclude that the formation of the colour cline observed in the barn owl must be due to natural selection.

Conditional manipulation of sex ratios by ant workers: A test of kin selection theory

Variable queen mating frequencies provide a unique opportunity to study the resolution of worker-queen conflict over sex ratio in social Hymenoptera, because the conflict is maximal in colonies headed by a singly mated queen and is weak or nonexistent in colonies headed by a multiply mated queen. In the wood ant Formica exsecta, workers in colonies with a singly mated queen, but not those in colonies with a multiply mated queen, altered the sex ratio of queen-laid eggs by eliminating males to preferentially raise queens. By this conditional response to queen mating frequency, workers enhance their inclusive fitness.

Evolution: social selection for eccentricity.

The dress code of paper wasps, like that of humans, is related to their social habits: species with a flexible nest-founding strategy have highly variable black-and-yellow markings. This color polymorphism facilitates individual recognition and might have been selected to permit complex social interactions.