Bayesian Markov Chain Monte Carlo Methods Research Articles

Ensemble learning methods of inference for spatially stratified infectious disease systems.

Individual level models are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information accounting for population heterogeneity and are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. However, Bayesian MCMC methods of inference are computationally expensive for large data sets. This issue becomes more severe when applied to infectious disease data collected from spatially heterogeneous populations, as the number of covariates increases. In addition, summary statistics over the global population may not capture the true spatio-temporal dynamics of disease transmission. In this study we propose to use ensemble learning methods to predict epidemic generating models instead of time consuming Bayesian MCMC method. We apply these methods to infer disease transmission dynamics over spatially clustered populations, considering the clusters as natural strata instead of a global population. We compare the performance of two tree-based ensemble learning techniques: random forest and gradient boosting. These methods are applied to the 2001 foot-and-mouth disease epidemic in the U.K. and evaluated using simulated data from a clustered population. It is shown that the spatially clustered data can help to predict epidemic generating models more accurately than the global data.

Multi-population mortality modelling: a Bayesian hierarchical approach

AbstractModelling mortality co-movements for multiple populations has significant implications for mortality/longevity risk management. This paper assumes that multiple populations are heterogeneous sub-populations randomly drawn from a hypothetical super-population. Those heterogeneous sub-populations may exhibit various patterns of mortality dynamics across different age groups. We propose a hierarchical structure of these age patterns to ensure the model stability and use a Vector Error Correction Model (VECM) to fit the co-movements over time. Especially, a structural analysis based on the VECM is implemented to investigate potential interdependence among mortality dynamics of the examined populations. An efficient Bayesian Markov Chain Monte-Carlo method is also developed to estimate the unknown parameters to address the computational complexity. Our empirical application to the mortality data collected for the Group of Seven nations demonstrates the efficacy of our approach.

DIGS: deep inference of galaxy spectra with neural posterior estimation

With the advent of billion-galaxy surveys with complex data, the need of the hour is to efficiently model galaxy spectral energy distributions (SEDs) with robust uncertainty quantification. The combination of simulation-based inference (SBI) and amortized neural posterior estimation (NPE) has been successfully used to analyse simulated and real galaxy photometry both precisely and efficiently. In this work, we utilise this combination and build on existing literature to analyse simulated noisy galaxy spectra. Here, we demonstrate a proof-of-concept study of spectra that is (a) an efficient analysis of galaxy SEDs and inference of galaxy parameters with physically interpretable uncertainties; and (b) amortized calculations of posterior distributions of said galaxy parameters at the modest cost of a few galaxy fits with Markov chain Monte Carlo (MCMC) methods. We utilise the SED generator and inference framework Prospector to generate simulated spectra, and train a dataset of 2 × 106 spectra (corresponding to a five-parameter SED model) with NPE. We show that SBI—with its combination of fast and amortized posterior estimations—is capable of inferring accurate galaxy stellar masses and metallicities. Our uncertainty constraints are comparable to or moderately weaker than traditional inverse-modelling with Bayesian MCMC methods (e.g. 0.17 and 0.26 dex in stellar mass and metallicity for a given galaxy, respectively). We also find that our inference framework conducts rapid SED inference (0.9–1.2 × 105 galaxy spectra via SBI/NPE at the cost of 1 MCMC-based fit). With this work, we set the stage for further work that focuses of SED fitting of galaxy spectra with SBI, in the era of JWST galaxy survey programs and the wide-field Roman Space Telescope spectroscopic surveys.

A comparison of Bayesian Markov chain Monte Carlo methods in a multilevel scenario

Multilevel modeling is a modern approach to deal with hierarchical or a nested data structure which can assess the variability between clusters. Bayesian Markov Chain Monte Carlo (MCMC) methods of estimations are advanced methods applicable for estimating multilevel models. However, these estimation methods are not as yet tested to identify its’ performances as well as the properties associated with these estimation methods. This study targets to conduct a comparison of Bayesian MCMC methods which are developed for multilevel models where the response is normally distributed. The comparison is based upon extensive simulations and an application to a real-life dataset. The performance of Gibbs sampling (GS) and Metropolis Hastings (MH) methods are compared using a simulation study and additionally the factors which can affect the performance of both MCMC methods are identified. Practicality of these methods in real world scenario is confirmed through the application of MCMC method to a dataset. In the simulations though the Metropolis Hastings (MH) shows slightly better performance than Gibbs, there is no evidence to indicate that significant differences exist between these methods except for small samples where MH is superior. The results from the example are not as clear as from the simulations.

The effect of human mobility restrictions on the COVID-19 transmission network in China.

COVID-19 poses a severe threat worldwide. This study analyzes its propagation and evaluates statistically the effect of mobility restriction policies on the spread of the disease. We apply a variation of the stochastic Susceptible-Infectious-Recovered model to describe the temporal-spatial evolution of the disease across 33 provincial regions in China, where the disease was first identified. We employ Bayesian Markov Chain Monte-Carlo methods to estimate the model and to characterize a dynamic transmission network, which enables us to evaluate the effectiveness of various local and national policies. The spread of the disease in China was predominantly driven by community transmission within regions, which dropped substantially after local governments imposed various lockdown policies. Further, Hubei was only the epicenter of the early epidemic stage. Secondary epicenters, such as Beijing and Guangdong, had already become established by late January 2020. The transmission from these epicenters substantially declined following the introduction of mobility restrictions across regions. The spatial transmission network is able to differentiate the effect of the local lockdown policies and the cross-region mobility restrictions. We conclude that both are important policy tools for curbing the disease transmission. The coordination between central and local governments is important in suppressing the spread of infectious diseases.

Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

Uncertainty Quantification of Water Level Predictions from Radar‐based Areal Rainfall Using an Adaptive MCMC Algorithm

This study proposes an approach for the uncertainty quantification at each stage of a single hydrological process of water level predictions based on different sources of mean areal precipitation (MAP) forecasts by using an adaptive Bayesian Markov chain Monte Carlo (MCMC) approach. The MAP forecasts are derived from the McGill Algorithm for Precipitation Nowcasting by Lagrangian Extrapolation (MAPLE) system and a long short-term memory (LSTM) network. The predicted water levels at two stations in the Gangnam catchment, Seoul, South Korea, are processed with a coupled 1D/2D urban hydrological model (1D/2D-UHM) forced by MAPLE MAP forecasts and LSTM-corrected MAP forecasts of five heavy rainfall events. The proposed Bayesian approach using the delayed rejection and adaptive Metropolis (DRAM) algorithm was compared with the Metropolis-Hastings (MH) algorithm in the uncertainty estimation of Weibull distribution parameters. The uncertainty contributions of the stages and sources in the related process were analyzed, including quantitative precipitation estimation (QPE) inputs, MAP inputs and 1D/2D-UHM. The results indicate that the uncertainty contribution of the MAPLE MAP forecasting is the highest in the 3-hour forecasting time. The uncertainty contribution of the QPE input for MAPLE MAP forecasting is the smallest and that of two sources, including the LSTM-corrected MAP source, and MAP and the coupled model is more significant than that of the QPE input. This research showed that the adaptive Bayesian MCMC method using the DRAM algorithm might be a robust option in quantitative uncertainty analyses of a single hydrological process, especially for urban flood management.

A network meta-analysis of direct factor Xa inhibitors for the treatment of cancer-associated venous thromboembolism.

Treatment of cancer-associated venous thromboembolism (CAVTE) remains challenging. The aim of this study was to assess the outcomes of direct acting oral anticoagulants (DOAs) for the treatment of CAVTE. A network meta-analysis of randomized clinical trials comparing DOAs (Apixaban, Rivaroxaban, and Edoxaban) versus Dalteparin for the treatment of CAVTE was performed. Outcomes of interest included, VTE recurrence, all-cause mortality, event-free survival, major bleeding, and clinically relevant non-major bleeding (CRNMB). Analysis was based on a random effects model and Bayesian Markov-chain Monte Carlo method was used for indirect comparisons. Four RCTs involving 2894 patients were included. Overall certainty of evidence was moderate regarding all outcomes. DOAs exhibited lower risk of VTE (RR 0.62; 95% CI 0.44, 0.87; P = 0.007), similar risk of major bleeding (RR 1.33; 95% CI 0.84, 2.11; P = 0.23), and higher risk of CRNMB (RR 1.66, 95% CI 1.08, 2.56; P = 0.02), compared with Dalteparin. Risk of all-cause mortality and event-free survival were similar between groups with RR 0.99 (95% CI 0.84, 1.16) and RR 1.03 (95% CI 0.94, 1.13), respectively. Apixaban ranked first for recurrent VTE (42.4%) and major bleeding (62.3%) and Dalteparin ranked first for CRNMB (54.7%). Rivaroxaban ranked best considering all-cause mortality (58.7%); Apixaban ranked best for event-free survival (83.6%). DOAs presented a reduced risk of recurrent VTE with similar risk of major bleeding compared to Dalteparin. However, a higher risk of CRNMB is expected when this cohort of patients are treated with DOAs instead of Dalteparin.

Parameter Estimation of Extreme Rainfall Distribution in Johor using Bayesian Markov Chain Monte Carlo

Heavy rainfall and the associated floods occur frequently in the Malaysia and have caused huge economic losses as well as massive impact on agriculture and people. As a consequence, it is necessary to understand the distribution of extreme rainfall in order to improve the managements in a country. Thus, the aim of this paper is to determine the best method to estimate parameters of Generalized Extreme Value (GEV) distribution that represent the annual maximum series (AMS) data of daily rainfall by using method of moments (MOM), maximum likelihood estimators (MLE) and Bayesian Markov Chain Monte Carlo (MCMC). The daily precipitation rainfall amount of 12 rain gauge stations in Johor from year 1975 to 2008 were used and the AMS data of each year were fitted with GEV distribution. Based on goodness-of-fit tests, namely Relative Root Mean Square Error (RRMSE) and Relative Absolute Square Error (RASE), the performances of three parameters of GEV distribution estimated by MOM, MLE and Bayesian MCMC were compared for each station. The results indicated that Bayesian MCMC method was performed better than MOM and MLE method in estimating the parameters of GEV distribution.

Uncertainty assessment of extreme flood estimation in the Dongting Lake basin, China

Abstract In this paper, we study uncertainty in estimating extreme floods of the Dongting Lake basin, China. We used three methods, including the Delta, profile likelihood function (PLF), and the Bayesian Markov chain Monte Carlo (MCMC) methods, to calculate confidence intervals of parameters of the generalized extreme value (GEV) distribution and quantiles of extreme floods. The annual maximum flow (AMF) data from four hydrologic stations were selected. Our results show that AMF data from Taoyuan and Xiangtan stations followed the Weibull class distribution, while the data from Shimen and Taojiang stations followed the Fréchet class distribution. The three methods show similar confidence intervals of design floods for short return periods. However, there are large differences between results of the Delta and the other two methods for long return periods. Both PLF and Bayesian MCMC methods have similar confidence intervals to reflect the uncertainty of design floods. However, because the PLF method is quite burdensome in computation, the Bayesian MCMC method is more suitable for practical use.

Parallel Markov chain Monte Carlo for Bayesian hierarchical models with big data, in two stages

ABSTRACTDue to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.

Frequency Analysis and Uncertainty Assessment of Annual Maximum Flood Series Using Bayesian MCMC Method

The calculation of flood quantiles and its uncertainty estimation are important subjects of hydraulic engineering planning and water resources management. In this study, the Bayesian theory is used to implement frequency analysis and uncertainty assessment of annual maximum flood series, the Generalized Extreme Value (GEV) distribution is considered as the flood frequency distribution line type, and the Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm is used to evaluate the GEV distribution parameters, then the posterior distributions of flood flow quantiles are used to calculate the point estimations and interval estimations of flood design values under different return periods. The results show that the fitting effect of the Bayesian MCMC method is the same as the maximum likelihood estimation (MLE), but the Bayesian MCMC more superior when the uncertainties were considered. Compared with the traditional methods of flood frequency analysis, the proposed Bayesian MCMC method provides not only the design flood estimated values, but also the confidence intervals of the estimated values. In addition, the lengths between upper confidence limits and estimated values are greater than the lower confidence limits and estimated values, this asymmetry is more realistic than the traditional methods such as the delta method, thus improve the reliability of flood frequency analysis.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

Abstract C32: Native American genetic ancestry is protective against prostate cancer in African Americans and European Americans

Abstract Prostate cancer (PCa) incidence and mortality varies by racial/ethnic groups in the U.S. African American (AA) men have a 60% higher incidence and twice the mortality rate of European America (EA) men, while Hispanic Americans and Native Americans have lower incidence rates than EA men. Several genetic admixture studies have examined the role of west African ancestry on prostate cancer risk in AA men, however the influence of Native American ancestry on PCa risk has not been explored. Here we evaluated the relationship between individual genetic ancestry proportions and the likelihood of PCa diagnosis and aggressiveness. Methods: We recruited 40-79 year old men who were undergoing prostate biopsy or routine PSA screening at outpatient urology clinics in Chicago, IL. Blood was drawn at the time of enrollment for genotyping of 105 ancestry informative markers. West African, European, and Native American genetic ancestry was estimated using the Bayesian Markov Chain-Monte Carlo method implemented in the program STRUCTURE. Unconditional binary logistic regression models were used to estimate odds ratios for the likelihood of PCa diagnosis and for the likelihood of having high-risk PCa relative to controls, adjusting for age and family history of PCa. Results: In AAs, NAA ranged from 0.4% to 28.8%. Mean NAA was 4.6% in AA cases, while controls had mean NAA of 6.6%. NAA ranged from 0.5% to 17.4% in EAs. Mean NAA was 5.1% in cases and 6.8% in controls. NAA was negatively associated with PCa diagnosis. AA men in the highest quartile of NAA had significantly reduced odds of PCa diagnosis compared to men in the lowest quartile of NAA (OR 0.47, 95% C.I.: 0.29-0.77). Similarly, EA men in the highest quartile of NAA had significantly reduced odds of PCa diagnosis compared men in the lowest NAA quartile (OR 0.36, 95% C.I.: 0.21-0.61). Additional adjustment of body mass index, education, smoking, alcohol use, and marital status did not change the results. NAA was also negatively associated with diagnosis of high risk PCa in EAs (P=0.04) and also trending in the same direction in AAs however not significant. Conclusions: Our study reveals that NAA is protective against PCa diagnosis and high-risk PCa. Hispanic Americans and Native Americans have lower PCa incidence rates than AAs and EAs, and the identification of inherited genetic or environmental factors that are associated with high NAA may improve PCa risk prediction and/or help to develop prevention strategies. Citation Format: Adam Murphy, Ken Batai, Ebony Shah, Rick A. Kittles. Native American genetic ancestry is protective against prostate cancer in African Americans and European Americans. [abstract]. In: Proceedings of the Eighth AACR Conference on The Science of Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; Nov 13-16, 2015; Atlanta, GA. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2016;25(3 Suppl):Abstract nr C32.

Genetic ancestry and odds of prostate cancer diagnosis in African American and European American men.

86 Background: Although ethnic differences in disease incidence among African American (AA) men may reflect differences in screening behaviors and behavioral and socioeconomic factors, genetic ancestry may be a factor. This study will investigate the association between West African and Native American genetic ancestry and PCa diagnosis. Methods: We enrolled 40-79 year-old men who were undergoing prostate biopsy or routine PSA screening at outpatient urology clinics in Chicago, IL. Blood was drawn at the time of enrollment for the genotyping of 105 ancestry informative markers. West African (WAA), European (EA), and Native American (NAA) genetic ancestry was estimated using the Bayesian Markov Chain-Monte Carlo method implemented in the program STRUCTURE. Univariate analysis was performed by Wilcoxon rank-sum test for continuous variables. Unconditional binary logistic regression models were used to estimate odds ratios for the likelihood of PCa diagnosis and for the odds of having high-risk PCa relative to controls, adjusting for age, body mass index (BMI), alcohol-use, and family history of PCa. Results: 857 men were enrolled; 34.5 % were diagnosed with PCa, 50.9 % were controls and 14.6 % were men with negative prostate biopsies. AAs comprised 27% of the sample. The median was 63 years (IQR 57 – 68). Among AA men, the median genetic WAA proportion was 0.78 (IQR 0.69 – 0.83) and NAA was 0.04 (IQR 0.02 – 0.09). There was no significant difference in genetic WAA among AA men with and without PCa diagnosis (p = 0.54); however, genetic NAA was significantly lower among PCa cases (median 0.034 vs 0.057,p = 0.03) compared to controls. Among EA men, the media NAA was 0.067 (IQR (0.03 – 0.10). Similarly among EA men, genetic NAA was significantly lower among cancer cases (0.04 vs. 0.08, p < 0.001). On logistic regression, WAA ≥ 88% was associated with increased odds of PCa in AA men (OR 2.6 95% CI 1.1 – 6.7). In both AAs (OR 0.5, 95% CI 0.2 – 1.1) and EAs (OR 0.3, 95 % 0.2 – 0.6), men in the highest genetic NAA quintile had a decreased risk of PCa on logistic regression compared to men in the lowest quintile. Conclusions: Our study reveals that NAA is protective against PCa diagnosis among all men. Additionally, AA men with a high degree of WAA demonstrate an increased risk of PCa. Future work will focus on determining the association of known prostate cancer risk SNPs such as the 8q24 regions and genetic ancestry.

Interactions between real economic and financial sides of the US economy in a regime-switching environment

This objective of this study is to examine the linkages between real (economic) and financial variables in the United States in a regime-switching environment that accounts explicitly for high volatility in the stock market and high stress in financial markets. Since the linearity test shows that the linear model should be rejected, we employ the Markov-switching VECM to examine the same objective using the Bayesian Markov-chain Monte Carlo method. The regime-dependent impulse response function (RDIRF) highlights the increasing importance of the financial sector of the economy during stress periods. The responses and their fluctuations are significantly greater in the high-volatility regime than in the low-volatility regime.

Realized population change for long‐term monitoring: California spotted owl case study

ABSTRACTThe annual rate of population change (λt) is a good metric for evaluating population performance because it summarizes survival and recruitment rates and can be used for open populations. Another measure of population performance, realized population change (Δt) is an encompassing metric of population trend over a period of time; it is the ratio of population size at an end time period relative to the initial population size. Our first goal was to compare mean λ and Δt as summaries of population change over time. Our second goal was to evaluate different methods for estimating these parameters; specifically we wished to compare the value of estimates from fixed effects models, random effects estimates from mixed effects models, and Bayesian Markov chain Monte Carlo (MCMC) methods. Our final goal was to evaluate the use of the posterior distribution of Δt as a means for estimating the probability of population decline retrospectively. To meet these goals, we used California spotted owl (Strix occidentalis occidentalis) data collected on 3 study areas from 1990 to 2011 as a case study. The estimated MCMC median λs for 2 of the study areas were 0.986 and 0.993, indicating declining populations, whereas median λ was 1.014 for the third study area, indicating an increasing population. For 2 of the study areas, estimated MCMC median Δts over the 18‐year monitoring period were 0.78 and 0.89, suggesting 21% and 11% declines in population size, whereas the third study area was 1.22 suggesting a 22% increase. Results from Δt analyses highlight that small differences in mean λ from 1.0 (stationary) can result in large differences in population size over a longer time period; these temporal effects are better depicted by Δt. Fixed effects, random effects, and MCMC estimates of mean and median λ and of Δt were similar (≤9% relative difference). The estimate of temporal process variance was larger for MCMC than the random effects estimates. Results from a Bayesian approach using MCMC simulations indicated that the probabilities of a ≥15% decline over 18 years were 0.69, 0.40, and 0.04 for the 3 study areas, whereas the probabilities the populations were stationary or increasing were 0.07, 0.22, and 0.82. For retrospective analyses of monitored populations, using Bayesian MCMC methods to generate a posterior distribution of Δt is a valuable conservation and management tool for robustly estimating probabilities of specified declines of interest. © 2013 The Wildlife Society.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

An introduction to generalized linear models—third edition

- Introduces GLMs in a way that enables readers to understand the unifying structure that underpins them. - Discusses common concepts and principles of advanced GLMs, including nominal and ordinal regression, survival analysis, and longitudinal analysis. - Connects Bayesian analysis and MCMC methods to fit GLMs. - Contains numerous examples from business, medicine, engineering, and the social sciences. - Provides the example code for R, Stata, and WinBUGS to encourage implementation of the methods. - Offers the data sets and solutions to the exercises online. Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

Bayesian multimodel inference for geostatistical regression models.

The problem of simultaneous covariate selection and parameter inference for spatial regression models is considered. Previous research has shown that failure to take spatial correlation into account can influence the outcome of standard model selection methods. A Markov chain Monte Carlo (MCMC) method is investigated for the calculation of parameter estimates and posterior model probabilities for spatial regression models. The method can accommodate normal and non-normal response data and a large number of covariates. Thus the method is very flexible and can be used to fit spatial linear models, spatial linear mixed models, and spatial generalized linear mixed models (GLMMs). The Bayesian MCMC method also allows a priori unequal weighting of covariates, which is not possible with many model selection methods such as Akaike's information criterion (AIC). The proposed method is demonstrated on two data sets. The first is the whiptail lizard data set which has been previously analyzed by other researchers investigating model selection methods. Our results confirmed the previous analysis suggesting that sandy soil and ant abundance were strongly associated with lizard abundance. The second data set concerned pollution tolerant fish abundance in relation to several environmental factors. Results indicate that abundance is positively related to Strahler stream order and a habitat quality index. Abundance is negatively related to percent watershed disturbance.