1) Gelman A.(2006) Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, 1, Number 3, pp. 515–533 Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. The authors use an example to illustrate serious problems with the inverse-gamma family of “noninformative” prior distributions. They suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-t family. 2) Craiu R.V. and Meng, Xiao Li (2011) Perfection within Reach: Exact MCMC Sampling, Handbook of Markov Chain Monte Carlo The authors present the general scheme of coupling from the past, and the state of the art of perfect sampling or exact sampling algorithms, so named because such algorithms use Markov chains and yet obtain genuine i.i.d. draws— hence perfect or exact — from their limit distritibution within a ?nite numbers of iterations. 3) Hobert J.P., Roy V. and Robert C.P. (2011) Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling, Statistical Science DA (Gibbs) algorithms often suffer from slow convergence. Over the last decade, a great deal of effort has gone into modifying the DA algorithm to speed convergence. The authors study a widely used DA algorithm for the exploration of posterior densities associated with Bayesian mixture models (Diebolt and Robert,1994). In particular, they compare this mixture DA algorithm with an alternative algorithm proposed by Fruhwirth-Schnatter (2001) that is based on random label switching. The article is very technical, you should focus only on the practical aspects. 4) Sherlock, Chris and Fearnhead, Paul and Roberts, Gareth O. (2010) The random walk Metropolis: linking theory and practice through a case study. Statistical Science, 25 (2). pp. 172-190. The random walk Metropolis (RWM) is one of the most common Markov Chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important practical implications have been derived. This article draws together a selection of new and existing key results and concepts and describes their implications. The impact of each new idea on algorithm efficiency is demonstrated for the practical example of the Markov modulated Poisson process (MMPP). 5) H. Rue, S. Martino, and N. Chopin. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society B, 71, 2009 The authors consider approximate Bayesian inference in structured additive regressions models where there is a latent Gaussian field, controlled by a few hyperparameters and with 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. This has been one of the most remarkable papers in the past 2-3 years; however, it's a bit technical; just try to grasp the main ideas from a practical standpoint and leave technicalities aside for the most. 6) Liutkus, A., Badeau R. and Richard G. (2011) Gaussian Processes for Underdetermined Source Separation, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 7. Gaussian process (GP) models are very popular for machine learning and regression and they are widely used to account for spatial or temporal relationships between multivariate random variables. In this paper, the authors propose a general formulationof underdetermined source separation as a problem involving GP regression. 7) Banerjee, S., A.E. Gelfand, A.O. Finley, and H. Sang. (2008) Gaussian Predictive Process Models for Large Spatial Datasets. Journal of the Royal Statistical Society Series B, 70:825–848. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, this paper works with predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. 8) Stingo, F.C., Vannucci, M. and Downey, G. (2010). Bayesian Wavelet-based Curve Classification via Discriminant Analysis with Markov Random Tree Priors. Statistica Sinica, accepted. Discriminant analysis is an effective tool for the classification of experimental units into groups. Here we present a typical example from chemometrics that deals with the classification of different types of food into species via near infrared spectroscopy. We take a nonparametric approach by modeling the functional predictors via wavelet transforms and then apply discriminant analysis in the wavelet domain. We introduce latent binary indicators for the selection of the discriminatory wavelet coefficients and propose prior formulations that use Markov random tree (MRT) priors to map scale-location connections among wavelets coefficients. We show performances on our case study on food authenticity. 9) Huerta, G. (2010). Bayesian Wavelet Shrinkage. Comp Stat 2010, 2, 668. Bayesian wavelet-shrinkage methods are defined through a prior distribution on the space of wavelet coefficients after a Discrete Wavelet Transformation (DWT) has been applied to the data. Posterior summaries of the wavelet coefficients establish a Bayes shrinkage rule. After the Bayes shrinkage is performed, an Inverse DWT can be used to recover the signal that generated the observations. This article reviews some of the main approaches for Bayesian wavelet shrinkage that span both smooth and multivariate types of shrinkage. 10) Hongxiao Zhu, Philip J. Brown, and Jeffrey S. Morris (2011). Robust, Adaptive Functional Regression in Functional Mixed Model Framework, Journal of the American Statistical Association, to appear. Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between function correlation induced by the experimental design.