Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

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Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Statistical Analysis with Missing Data

Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western

Handbook of Markov Chain Monte Carlo

A detailed review of the education sector in Australia as in the data provided by the 2006 edition of the OECD's annual publication, 'Education at a Glance' is presented. While the data has shown that in almost all OECD countries educational attainment levels are on the rise, with countries showing impressive gains in university qualifications, it also reveals that a large of share of young people still do not complete secondary school, which remains a baseline for successful entry into the labour market.

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Education at a Glance

SUMMARY We propose a recursive algorithm as a more useful alternative to the Brook expansion for the joint distribution of a vector of random variables when the original formulation is in terms of the corresponding full conditional distributions, as occurs for Markov random fields. Usually, in practical applications, the computational load will still be excessive but then the algorithm can be used to obtain the componentwise full conditionals of a system after marginalising over some variables or the joint distribution of subsets of the variables, conditioned on values of the remainder, which is required for block Gibbs sampling. As an illustrative example, we apply the algorithm in the simplest nontrivial setting of hidden Markov chains. More important, we demonstrate how it applies to Markov random fields on regular lattices and to perfect block Gibbs sampling for binary systems.

A recursive algorithm for Markov random fields

For a collection of two-way tables, where subjects are cross-classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables, we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other, positive dependence and stronger positive dependence. The approach is based on parameterizing bivariate conditional distributions with global logits and global log-odds ratios, and we provide a general framework for handling models defined by equality and inequality constraints on these parameters. In this way, such models as marginal homogeneity, proportional odds among row or columns margins, and Plackett distribution may be treated together with various models defined by inequality constraints on the same parameters, such as, for instance, those implied by...

Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins

MultiLCIRT: An R package for multidimensional latent class item response models

Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata

We propose a generalization of the Multipletry Metropolis (MTM) algorithm of Liu et al. (2000), which is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights that may be arbitrary chosen. In particular, for Bayesian estimation we also introduce a method based on weights depending on a quadratic approximation of the posterior distribution. The resulting algorithm cannot be reformulated as an MTM algorithm and leads to a comparable gain of e‐ciency with a lower computational efiort. We also outline the extension of the proposed strategy, and then of the MTM strategy, to Bayesian model selection, casting it in a Reversible Jump framework. The approach is illustrated by real examples.

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Francesco Bartolucci

Papers

A recursive algorithm for Markov random fields

Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins

MultiLCIRT: An R package for multidimensional latent class item response models

Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata

A generalization of the Multiple-try Metropolis algorithm for Bayesian estimation and model selection