16  Summary and Conclusions

16.1 Further readings

16.1.1 Textbooks

16.1.1.1 Basic for Ecologists

  • 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.
  • Korner-Nievergelt, F.; Roth, T.; von Felten, S.; Almasi, B. & Korner-Nievergelt, P. (2015) Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan.

16.1.1.2 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.

16.1.1.3 Hierarchical

  • Kéry, M. and Schaub, M. (2011) Bayesian population analysis using WinBUGS. Academic Press.
  • Kéry, M. & Royle, J. A.(2016) Applied Hierarchical Modeling in Ecology: Analysis of distribution, abundance and species richness in R and BUGS: Volume 1: Prelude and Static Models
  • 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.

16.1.1.4 Classics

  • Jaynes, E. T. (2003) Probability theory: the logic of science. Cambridge university press.

16.1.2 Important articles

16.1.2.1 Reviews / opinion papers on Bayesian methods 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

16.1.2.2 Prior choice

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

16.1.2.3 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.

16.1.2.4 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.

16.1.2.5 Summaries of the posterior

http://www.sumsar.net/blog/2014/10/probable-points-and-credible-intervals-part-one/

16.1.3 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.

16.1.4 Bayesian Model selection

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

https://radfordneal.wordpress.com/2008/08/17/the-harmonic-mean-of-the-likelihood-worst-monte-carlo-method-ever/

http://www.biomedcentral.com/1471-2105/14/85

http://hedibert.org/bayes-factor-computing-marginal-likelihoods-savage-dickey-ratio-reversible-jump-mcmc-bayesian-model-averaging-and-deviance-information-criterion/

16.1.5 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
  • 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
  • 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.