POOR PERFORMANCE OF BOOTSTRAP CONFIDENCE INTERVALS FOR THE LOCATION OF A QUANTITATIVE TRAIT LOUCS

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTLs) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTLs are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the non-parametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals are poorly behaved and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.

Análise Bayesiana para a distribuição Exponencial-Logarítmica

Pós-graduação em Matematica Aplicada e Computacional - FCT

Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6×10²⁰ protons on target

We report on measurements of neutrino oscillation using data from the T2K long-baseline neutrino experiment collected between 2010 and 2013. In an analysis of muon neutrino disappearance alone, we find the following estimates and 68% confidence intervals for the two possible mass hierarchies: Normal Hierarchy: sin²θ₂₃= 0.514+0.055−0.056 and ∆m²_32 = (2.51 ± 0.10) × 10⁻³ eV²/c⁴ Inverted Hierarchy: sin²θ₂₃= 0.511 ± 0.055 and ∆m²_13 = (2.48 ± 0.10) × 10⁻³ eV²/c⁴ The analysis accounts for multi-nucleon mechanisms in neutrino interactions which were found to introduce negligible bias. We describe our first analyses that combine measurements of muon neutrino disappearance and electron neutrino appearance to estimate four oscillation parameters, |∆m^2|, sin²θ₂₃, sin²θ₁₃, δCP , and the mass hierarchy. Frequentist and Bayesian intervals are presented for combinations of these parameters, with and without including recent reactor measurements. At 90% confidence level and including reactor measurements, we exclude the region δCP = [0.15, 0.83]π for normal hierarchy and δCP = [−0.08, 1.09]π for inverted hierarchy. The T2K and reactor data weakly favor the normal hierarchy with a Bayes Factor of 2.2. The most probable values and 68% 1D credible intervals for the other oscillation parameters, when reactor data are included, are: sin²θ₂₃= 0.528+0.055−0.038 and |∆m²_32| = (2.51 ± 0.11) × 10⁻³ eV²/c⁴.

An ecological and comparative analysis of parasites in juvenile Mugil liza (Pisces, Mugilidae) from two sites in Samborombón bay, Argentina

ABSTRACT Mugil liza Valenciennes, 1836 is an economically important food fish and has been recommended for aquaculture in South America. A total of 278 fishes were collected in the spring and summer of 2009 and 2010. These fish were sorted into sample groups according to their size class. We used Bayesian statistics and 95% credible intervals for each parameter tested were calculated. Fish studied harbored a total of 15 different species of parasites. Diversity of parasite species found on Mugil liza was greatest at the S.R.C. collection site, but evidenced a lower species richness than at A.R. site. The 1st size fishes of both sites evidenced greater parasite diversity than either 2nd or 3rd size fish. Differences observed could be explained by the different use of habitat types at the two sites or differential susceptibility to infection by parasites. The dominance of D. fastigatainfluenced observed results of lower community diversity indexes. New works elucidating different parasite life cycles within juvenile and adults ofM. liza in Argentina, promise to be important for determining the risk of the parasitism by zoonotic metacercariae A. (P.) longa and use of this fish as food and an economic resource, and the possible use of mullet parasites in other promising fields as indicators of biodiversity, and/ or water contamination.

Bayesian genetic parameters for body weight and survival of Nile tilapia farmed in Brazil

The objective of this study was to estimate genetic parameters for survival and weight of Nile tilapia (Oreochromis niloticus), farmed in cages and ponds in Brazil, and to predict genetic gain under different scenarios. Survival was recorded as a binary response (dead or alive), during harvest time in the 2008 grow-out period. Genetic parameters were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. The breeding population consisted of 2,912 individual fish, which were analyzed together with the pedigree of 5,394 fish. The heritabilities estimates, with 95% posterior credible intervals, for tagging weight, harvest weight and survival were 0.17 (0.09-0.27), 0.21 (0.12-0.32) and 0.32 (0.22-0.44), respectively. Credible intervals show a 95% probability that the true genetic correlations were in a favourable direction. The selection for weight has a positive impact on survival. Estimated genetic gain was high when selecting for harvest weight (5.07%), and indirect gain for tagging weight (2.17%) and survival (2.03%) were also considerable.

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.

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.

Approche bayésienne de la construction d'intervalles de crédibilité simultanés à partir de courbes simulées

Ce mémoire porte sur la simulation d'intervalles de crédibilité simultanés dans un contexte bayésien. Dans un premier temps, nous nous intéresserons à des données de précipitations et des fonctions basées sur ces données : la fonction de répartition empirique et la période de retour, une fonction non linéaire de la fonction de répartition. Nous exposerons différentes méthodes déjà connues pour obtenir des intervalles de confiance simultanés sur ces fonctions à l'aide d'une base polynomiale et nous présenterons une méthode de simulation d'intervalles de crédibilité simultanés. Nous nous placerons ensuite dans un contexte bayésien en explorant différents modèles de densité a priori. Pour le modèle le plus complexe, nous aurons besoin d'utiliser la simulation Monte-Carlo pour obtenir les intervalles de crédibilité simultanés a posteriori. Finalement, nous utiliserons une base non linéaire faisant appel à la transformation angulaire et aux splines monotones pour obtenir un intervalle de crédibilité simultané valide pour la période de retour.

How well do regional or national Breeding Bird Survey data predict songbird population trends at an intact boreal site?

A study to monitor boreal songbird trends was initiated in 1998 in a relatively undisturbed and remote part of the boreal forest in the Northwest Territories, Canada. Eight years of point count data were collected over the 14 years of the study, 1998-2011. Trends were estimated for 50 bird species using generalized linear mixed-effects models, with random effects to account for temporal (repeat sampling within years) and spatial (stations within stands) autocorrelation and variability associated with multiple observers. We tested whether regional and national Breeding Bird Survey (BBS) trends could, on average, predict trends in our study area. Significant increases in our study area outnumbered decreases by 12 species to 6, an opposite pattern compared to Alberta (6 versus 15, respectively) and Canada (9 versus 20). Twenty-two species with relatively precise trend estimates (precision to detect > 30% decline in 10 years; observed SE ≤ 3.7%/year) showed nonsignificant trends, similar to Alberta (24) and Canada (20). Precision-weighted trends for a sample of 19 species with both reliable trends at our site and small portions of their range covered by BBS in Canada were, on average, more negative for Alberta (1.34% per year lower) and for Canada (1.15% per year lower) relative to Fort Liard, though 95% credible intervals still contained zero. We suggest that part of the differences could be attributable to local resource pulses (insect outbreak). However, we also suggest that the tendency for BBS route coverage to disproportionately sample more southerly, developed areas in the boreal forest could result in BBS trends that are not representative of range-wide trends for species whose range is centred farther north.

Estimating technical efficiency of Australian dairy farms using alternative frontier methodologies

Technical efficiency is estimated and examined for a cross-section of Australian dairy farms using various frontier methodologies; Bayesian and Classical stochastic frontiers, and Data Envelopment Analysis. The results indicate technical inefficiency is present in the sample data. Also identified are statistical differences between the point estimates of technical efficiency generated by the various methodologies. However, the rank of farm level technical efficiency is statistically invariant to the estimation technique employed. Finally, when confidence/credible intervals of technical efficiency are compared significant overlap is found for many of the farms' intervals for all frontier methods employed. The results indicate that the choice of estimation methodology may matter, but the explanatory power of all frontier methods is significantly weaker when interval estimate of technical efficiency is examined.

Assessing the impact on chronic disease of incorporating the societal cost of greenhouse gases into the price of food: an econometric and comparative risk assessment modelling study

Objectives To model the impact on chronic disease of a tax on UK food and drink that internalises the wider costs to society of greenhouse gas (GHG) emissions and to estimate the potential revenue. Design An econometric and comparative risk assessment modelling study. Setting The UK. Participants The UK adult population. Interventions Two tax scenarios are modelled: (A) a tax of £2.72/tonne carbon dioxide equivalents (tCO2e)/100 g product applied to all food and drink groups with above average GHG emissions. (B) As with scenario (A) but food groups with emissions below average are subsidised to create a tax neutral scenario. Outcome measures Primary outcomes are change in UK population mortality from chronic diseases following the implementation of each taxation strategy, the change in the UK GHG emissions and the predicted revenue. Secondary outcomes are the changes to the micronutrient composition of the UK diet. Results Scenario (A) results in 7770 (95% credible intervals 7150 to 8390) deaths averted and a reduction in GHG emissions of 18 683 (14 665to 22 889) ktCO2e/year. Estimated annual revenue is £2.02 (£1.98 to £2.06) billion. Scenario (B) results in 2685 (1966 to 3402) extra deaths and a reduction in GHG emissions of 15 228 (11 245to 19 492) ktCO2e/year. Conclusions Incorporating the societal cost of GHG into the price of foods could save 7770 lives in the UK each year, reduce food-related GHG emissions and generate substantial tax revenue. The revenue neutral scenario (B) demonstrates that sustainability and health goals are not always aligned. Future work should focus on investigating the health impact by population subgroup and on designing fiscal strategies to promote both sustainable and healthy diets.

Calibration and evaluation of individual-based models using Approximate Bayesian Computation

This paper investigates the feasibility of using approximate Bayesian computation (ABC) to calibrate and evaluate complex individual-based models (IBMs). As ABC evolves, various versions are emerging, but here we only explore the most accessible version, rejection-ABC. Rejection-ABC involves running models a large number of times, with parameters drawn randomly from their prior distributions, and then retaining the simulations closest to the observations. Although well-established in some fields, whether ABC will work with ecological IBMs is still uncertain. Rejection-ABC was applied to an existing 14-parameter earthworm energy budget IBM for which the available data consist of body mass growth and cocoon production in four experiments. ABC was able to narrow the posterior distributions of seven parameters, estimating credible intervals for each. ABC’s accepted values produced slightly better fits than literature values do. The accuracy of the analysis was assessed using cross-validation and coverage, currently the best available tests. Of the seven unnarrowed parameters, ABC revealed that three were correlated with other parameters, while the remaining four were found to be not estimable given the data available. It is often desirable to compare models to see whether all component modules are necessary. Here we used ABC model selection to compare the full model with a simplified version which removed the earthworm’s movement and much of the energy budget. We are able to show that inclusion of the energy budget is necessary for a good fit to the data. We show how our methodology can inform future modelling cycles, and briefly discuss how more advanced versions of ABC may be applicable to IBMs. We conclude that ABC has the potential to represent uncertainty in model structure, parameters and predictions, and to embed the often complex process of optimizing an IBM’s structure and parameters within an established statistical framework, thereby making the process more transparent and objective.

Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.