Literature Bayesian Statistics

A necessarily subjective and incomplete list of textbooks and papers that are interesting in the context of learning Bayesian statistics, compiled with input from Joe Chipperfield and Jörn Pagel for our summer schools on Bayesian statistics.

Textbooks

Basic introductions

Kéry, M. (2010) Introduction to WinBUGS for Ecologists. Academic Press.
Kruschke, J. F. (2010) Doing Bayesian Data Analysis: A Tutorial with R and BUGS. Academic Press.
McCarthy, M. A. (2007) Bayesian methods for ecology. Cambridge University Press.

Comprehensive

Lunn D. et al. (2012) The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman and Hall/CRC.
Gelman, A.; Carlin, J. B.; Stern, H. S. & Rubin, D. B. (2003) Bayesian Data Analysis. Chapman & Hall, London.

Hierarchical

Kéry, M. and Schaub, M. (2011) Bayesian population analysis using WinBUGS. Academic Press.
Banerjee, S. et al. (2009) Hierarchical Modeling and Anallysis for Spatial Data. Chapman and Hall/CRC.
Clark, J. S. and Gelfand, A. E. (2006) Hierarchical Modelling for the Environmental Sciences. Oxford University Press.

Articles

Foundations of Bayesian statistics, Bayes vs. Frequentists

Efron, B. (2013) A 250-year argument: Belief, behavior, and the bootstrap Bulletin Of The American Mathematical Society, 50, 129-146
Gelman, A. & Robert, C. P. (2010) ”Not only defended but also applied”: The perceived absurdity of Bayesian inference ArXiv e-prints
Fisher, R. A. (1922) On the mathematical foundations of theoretical statistics Philos. T. Roy. Soc. A., 222, 309-368
Kass, R. (2011) Statistical inference: The big picture Stat. Sci., 26, 1-9
Jaynes, E. (1976) Confidence intervals vs. Bayesian intervals Foundations of probability theory, statistical inference, and statistical theories of science, 2, 175-257.

Bayes in Ecology

Hobbs, N. T. & Hilborn, R. (2006) Alternatives to statistical hypothesis testing in ecology: A guide to self teaching Ecol. Appl., 16, 5-19
Ellison, A. M. (2004) Bayesian inference in ecology Ecol. Lett., 7, 509-520

Prior choice

Kass, R. E. & Wasserman, L. (1996) The selection of prior distributions by formal rules. J. Am. Stat. Assoc., 91, 1343-1370

MCMC sampling

Andrieu, C.; de Freitas, N.; Doucet, A. & Jordan, M. I. (2003) An introduction to MCMC for machine learning Mach. Learning, 50, 5-43
Andrieu, C. & Thoms, J. (2008) A tutorial on adaptive MCMC Stat. Comput., 18, 343-373.

Bayesian Model Selection

Kass, R. E. & Raftery, A. E. (1995) Bayes Factors J. Am. Stat. Assoc., 90, 773-795

Hierarchical Models

Wikle, C. K. (2003) Hierarchical Bayesian models for predicting the spread of ecological processes Ecology, 84, 1382-1394
Clark, J. S. (2003) Uncertainty and variability in demography and population growth: A hierarchical approach Ecology, 84, 1370-1381
Clark, J. S. & Gelfand, A. E. (2006) A future for models and data in environmental science. Trends in Ecology & Evolution, 21, 375-380
Cressie, N.; Calder, C. A.; Clark, J. S.; Hoef, J. M. V. & Wikle, C. K. (2009) Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling Ecol. Appl., 19, 553-570
Marion, G.; McInerny, G. J.; Pagel, J.; Catterall, S.; Cook, A. R.; Hartig, F. & O’Hara, R. B. (2012) Parameter and uncertainty estimation for process-oriented population and distribution models: data, statistics and the niche J. Biogeogr., 39, 2225–2239
Cook, A.; Marion, G.; Butler, A. & Gibson, G. (2007) Bayesian Inference for the Spatio-Temporal Invasion of Alien Species Bull. Math. Biol., 69, 2005-2025
Pagel, J. & Schurr, F. M. (2011) Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics Global Ecol. Biogeogr.

Approximate Bayesian

Beaumont, M. A. (2010) Approximate Bayesian computation in evolution and ecology Annu. Rev. Ecol. Evol. Syst., 41, 379-406
Csilléry, K.; Blum, M. G. B.; Gaggiotti, O. E. & François, O. (2010) Approximate Bayesian Computation (ABC) in practice Trends in Ecology & Evolution, 25, 410-418
Hartig, F.; Calabrese, J. M.; Reineking, B.; Wiegand, T. & Huth, A. (2011) Statistical inference for stochastic simulation models – theory and application Ecol. Lett., 14, 816-827
Jabot, F. & Chave, J. (2009) Inferring the parameters of the neutral theory of biodiversity using phylogenetic information and implications for tropical forests Ecol. Lett., 12, 239-248

Comprehensive list at http://approximatebayesiancomputational.wordpress.com/

Fitting (stochastic) process-based models

Van Oijen, M.; Rougier, J. & Smith, R. (2005) Bayesian calibration of process-based forest models: bridging the gap between models and data Tree Physiol., 25, 915-927
Hartig, F.; Dyke, J.; Hickler, T.; Higgins, S. I.; O’Hara, R. B.; Scheiter, S. & Huth, A. (2012) Connecting dynamic vegetation models to data – an inverse perspective J. Biogeogr., 39, 2240-2252.

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