Quantitative Trait Loci (QTL) Related References

• Model Fitting
• Model Selection
• Markov chain & Markov chain Monte Carlo
• Code Writing

Model Fitting

• Beran R (2003) The impact of the bootstrap on statistical algorithms and theory. Statist Sci 18: 175-184. [doi:10.1214/ss/1063994972]
• Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc B 39: 1-38. [Paper]
• Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J Roy Statist Soc B 41: 190-195. [Paper]
• Kohn R, Smith M, Chan D (2001) Nonparametric regression using linear combinations of basis functions. Statist and Comput 11: 313-322. [doi:10.1023/A:1011916902934]
• Manly BFJ (1997) Randomization, Bootstrap and Monte Carlo Methods in Biology, 2nd ed, Chapman & Hall/CRC Press. [Abstract]
• Meng XL, Rubin DB (1993) Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80: 267-268. [doi:10.1093/biomet/80.2.267]
• Nott DJ, Kuk AYC, Duc H (2002) Efficent sampling schemes for Bayesian MARS models with many predictors.
• Titterington DM, Smith AFM, Markov UE (1985) Statistical Analysis of Finite Mixture Distributions. Wiley, New York.

Model Selection

• Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Statist Math 21: 243-247. [Paper]
• Breiman L, Freedman D (1983) How many variables should be entered in a regression? J Amer Statist Assoc 78: 131-136. [doi:10.2307/2287119]
• Chipman H (2006) Prior distributions for Bayesian analysis of screening experiments. Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics, Dean A, Lewis SM, Editors: 235-267. [Paper]
• Chipman HA, George EI, McCulloch RE (2001) The practical implementation of Bayesian model selection. IMS Lecture Notes: Model Selection 38. [Paper]
• Clyde M, George EI (2004) Model uncertainty. Statist Sci 19: 81-94. [doi:10.1214/088342304000000035]
• Dellaportas P, Forster JJ, Ntzoufras I (2000) Bayesian variable selection using the Gibbs sampler. Generalized Linear Models: A Bayesian Perspective, Dey DK, Ghosh S, Mallick B, eds. New York: Marcel Dekker, 271-286. [Paper]
• Efron B (1986) Why isn't everyone a Bayesian? Amer Statist 40: 1-5. [Paper]
• Gelman A (2004) Exploratory data analysis for complex models. J Comp Graph Statist 13: 755-779. [doi:10.1198/106186004X11435]
• Gelman A (2005) Analysis of variance--why it is more important than ever. Ann Statist 33: 1-53. [doi:10.1214/009053604000001147]
• Gelman A (2008) Objections to Bayesian statistics (with discussion). Bayesian Analysis 3: 445-450. [doi:10.1214/08-BA318 | Discussion]
• Gelman A, Van Mechelen I, Verbeke G, Heitjan DF, Meulders M (2005) Multiple imputation for model checking: completed-data plots with missing and latent data. Biometrics 61: 74-85. [doi:10.1111/j.0006-341X.2005.031010.x]
• Ghosh D, Chen W, Raghunathan T (2006) The false discovery rate: a variable selection perspective. J Statist Plan Infer 136: 2668-2684 [doi:10.1016/j.jspi.2004.10.024]
• Lu F, Keles S, Wright S, Wahba G (2005) Framework for kernel regularization with application to protein clustering. PNAS 102: 12332-12337. [Paper]
• McLachlan GJ, Basford KE (1988) Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York.
• Miller AJ (1990) Subset Selection in Regression. Chapman and Hall, London.
• Ntzoufras I (1999) Aspects of Bayesian model and variable selection using MCMC. Dept Statistics, Athens U of Economics and Business. [Paper]
• Schwarz G (1978) Estimating the dimension of a model. Ann Statist 6: 461-464. [Paper]
• Shibata R (1981) An optimal selection of regression variables. Biometrika 68: 45-54. [doi:10.1093/biomet/68.1.45]
• Shibata R (1984) Approximate efficiency of a selection procedure for the number of regression variables. Biometrika 71: 43-49. [doi:10.1093/biomet/71.1.43]
• Yang X, Belin TR, Boscardin WJ (2005) Imputation and variable selection in linear regression models with missing covariates. Biometrics 61: 498-506. [doi:10.1111/j.1541-0420.2005.00317.x]
• Zhang D, Lin X (2003) Hypothesis testing in semiparametric additive mixed models. Biostatistics 4: 57-74. [Paper]

Markov chain & Markov chain Monte Carlo

• Baum LE, Petrie T, Soules G, Weiss N (1970) A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann Math Stat 41: 164-171. [Paper]
• Carlin BP, Chib S (1995) Bayesian model choice via Markov chain Monte Carlo. J Roy Statist Soc B57: 473-484. [Paper]
• Cowles MK, Carlin BP (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J Amer Statist Assoc 91: 883-904. [doi:10.2307/2291683]
• Gelfand AE, Hills SE, Racine-Poon A, Smith AFM (1990) Illustration of Bayesian inference in normal data models using Gibbs sampling. J Amer Statist Assoc 85: 972-985. [doi:10.2307/2289594]
• Godsill SJ (2001) On the relationship between Markov chain Monte Carlo methods for model uncertainty. J Comp Graph Statist 10: 230-248. [Paper]
• Green PJ (1995) Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika 82: 711-732. [doi:10.1093/biomet/82.4.711]
• Ishwaran H, Rao JS (2005) Spike and slab variable selection: Frequentist and Bayesian strategies. Ann Statist 33: 730-773. [doi:10.1214/009053604000001147]
• Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77: 257-286. [Paper]
• Richardson S, Green PJ (1997) On Bayesian analysis of mixtures with an unknown number of components. J Roy Stat Soc B 59: 731-792. [Paper]
• Rosenthal JS (2007) AMCMC: An R interface for adaptive MCMC. Comp Statist Data Anal 51: 5467-5470. [doi:10.1016/j.csda.2007.02.021]

Code Writing

• Cook SR, Gelman A, Rubin DB (2006) Validation of software for Bayesian models using posterior quantiles. J Comp Graph Statist 15: 675-692. [doi:10.1198/106186006X136976 | Software]
• Gentleman R, Temple Lang D (2007) Statistical Analyses and Reproducible Research J Comp Graph Statist 16: 1-23. [Paper]
• Kerman J, Gelman A (2004) Fully Bayesian computing. [Paper]
• Ntzoufras I (2002) Gibbs variable selection using BUGS. J Statist Soft 7: 7. [Paper | Software]
• Sturtz S, Ligges U, Gelman A (2005) R2WinBUGS: A package for running WinBUGS from R. J Statist Soft 12: 3. [Paper]