The primary difficulty with MCMC algorithms, however, is the issue of mixing — that is,ensuring that the algorithm does not get 'stuck' in local maxima. Various solutions have been developed to deal with this problem. One of the simplest involves running several copies of the MCMC algorithm in parallel and starting from different points, with pairs of copies switching states from time-to-time⁵⁶. Allowing copies to swap places occasionally means that the parameter space can be explored more efficiently. Other schemes involve augmenting the 'state–space' of the process: we add another variable to the space of parameters in such a way that it is easier for the algorithm to accept new states. For example, a useful idea is to add a 'temperature' to the process. In practice, this might involve mixing a 'hot' chain, which takes more frequent jumps, and a 'cool' chain, in which jumps are rarer. The addition of temperature allows the process to explore the parameter space with less risk of getting stuck; however, this greater efficiency occurs at the cost of the requirement for a more complicated algorithm. In some settings, a single process is run; in others, multiple parallel chains are used^48,⁵⁷. Owing to the additional complexity involved, these schemes have yet to be widely embraced within the genetics community.

2011年6月5日星期日

Bayesian analysis for species distribution modelling

http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2010.00077.x/full

Fine-scale environmental variation in species distribution modelling: regression dilution, latent variables and neighbourly advice

2011年5月30日星期一

advantages of Mixed model/Bayesian/MCMCglmm - gathered from relevant references

1.
Phylogenetic mixed models have mainly been applied to traits which are assumed to be normally distributed (for exceptions, see Felsenstein, 2005; Naya et al., 2006). Generalized linear mixed models extend the linear mixed model to non-Gaussian responses, although model fitting has proved more difficult because the likelihood cannot be obtained in closed form. MCMC techniques solve this
problem by breaking the high-dimensional joint distribution into a series of lower dimensional conditional distributions which are easier to sample from. By repeatedly sampling from these conditional distributions it is possible to very accurately approximate the complete joint distribution, and thereby extract things of interest (often marginal distributions).

Hadfield, J. D., & Nakagawa, S. (2010). General quantitative genetic methods for comparative biology: Phylogenies, taxonomies and multi-trait models for continuous and categorical characters. Journal of Evolutionary Biology, 23(3), 494-508.

2.
The major reason for the popularity of mixed modelling is probably its ability to account for statistical non-independence of data by having random effects as well as fixed effects (the name ‘mixed-effects’ originated from combining these two types of effects) (McCulloch and Searle, 2002). It is difficult to think of an example of any dataset where the data points would be truly independent from one another.

http://www.sciencedirect.com/science/article/pii/S0149763410001028

3.
An important advantage of the mixed model approach relates to the statistical inferences drawn from non-normal data. To date, in neurosciences, non-parametric (NP) tests such as Mann-Whitney and Kruskal–Wallis tests have been often used to deal with small samples sizes, where normality cannot be tested, or with truly non-normally distributed data (Janusonis, 2009)

4.
To test for a genetic change in the population, we used Bayesian methods. Use of Bayesian methods allows the time trends to be estimated directly instead of requiring statistics to be based on the best linear unbiased predictions (BLUPs) from a linear model, which incurs problems in terms of error propagation (Ovaskainen et al., 2008; Hadfield, 2010).

J . EVOL. BI O L . 23 ( 2 0 1 0 ) 935–944
http://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2010.01959.x/abstract

5.

Our dataset allowed us to estimate the variance in offspring sex ratio, both at ca 6 days post-hatching and at independence from parental care, and to test how much of the observed variation in sex ratio was accounted for by additive genetic variance as opposed to environmental/non-additive genetic and sampling variance.

Variance components were estimated by fitting a generalized animal model. An animal model is a specific type of mixed model that explicitly takes into account the resemblance among all relatives. It models an individual's phenotype as a function of a number of fixed and random effects, including a random additive genetic ‘animal’ effect. The variance–covariance structure of the latter is proportional to the pairwise coefficients of relatedness among all individuals in the pedigree. Thereby an animal model allows us to fully exploit all pedigree data, and to simultaneously account for a number of potentially confounding environmental effects [32–34]. Fitting an animal model, or any mixed model for that matter, with non-Gaussian traits using (restricted) maximum-likelihood techniques is challenging. Hence, we used Bayesian Markov chain Monte Carlo (MCMC) techniques implemented in the R package MCMCglmm [30,35]

Disentangling the effect of genes, the environment and chance on sex ratio variation in a wild bird population

http://rspb.royalsocietypublishing.org/content/early/2011/02/17/rspb.2010.2763.full

2011年5月23日星期一

priors for a multi-response model in MCMCglmm

http://finzi.psych.upenn.edu/R-sig-mixed-models/2010q4/004590.html

modeling nested predictor in MCMCglmm - a nice explanation

http://finzi.psych.upenn.edu/R-sig-mixed-models/2010q3/004437.html

If every nest has a unique identifier then MCMCglmm should give the  
same answer (up to Monte Carlo error) for random ~ pairID + nest and  
random ~ pairID + pairID:nest,

zero inflation model for MCMCglmm - here a nice reference

http://finzi.psych.upenn.edu/R-sig-mixed-models/2009q3/002619.html

2011年5月18日星期三

R based Computational tools for Bayesian analysis

The increasing number of R-oriented Bayesian computational tools such as MCMCpack, MCMCglmm, DPpackage, R-INLA, spBayes, have made BUGS less and less crucial for day to day Bayesian computation. Honestly, I cannot figure out a single analysis that BUGS can do but at least one of the above mentioned packages cannot.

R-INLA

From a quick look at the web site, R-INLA seems to be able to carry out bayesian analysis without the actual MCMC sampling. This makes it possible to quickly try various different model specifications without hours of waiting time. This package looks very interesting and definitely deserves more attention.

http://sgsong.blogspot.com/search/label/Bayesian

2011年4月23日星期六

Bayesian inference in ecology

Ellison, A.M. (2004) Bayesian inference in ecology. Ecology Letters, 7, 509–520.

Direct Link:

2011年4月18日星期一

two books of introductory bayesian statistics

As recommended by this blogger.
http://telliott99.blogspot.com/search/label/bayes

(1) a book by Dennis Lindley entitled Understanding Uncertainty

(2) further understanding of Bayesian methods is William Bolstad, Introduction to Bayesian Statistics.

2011年4月13日星期三

spatial bayesian modeling - Andrew Finley

see him for spBayes package, and spatial Bayesian modeling.

http://blue.for.msu.edu/index.html

there are tutorials:
http://blue.for.msu.edu/courses.html

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