%0 Book Section %1 carlin_elements_2006 %A Carlin, Bradley P. %A Clark, James S %A Gelfand, Alan E %B Hierarchical Modelling for the Environmental Sciences: Statistical Methods and Applications %C New York, NY %D 2006 %E Clark, James S. %E Gelfand, Alan E. %I Oxford University Press %K Bayesian bayesian inference, kriging, review %P 3--24 %T Elements of hierarchical Bayesian inference %X Serious investigation of ecological processes is challenging due to the complex nature of these processes and the lack of sufficient data to see them well. Hence, acknowledging our limitations, we turn to stochastic modeling as a means to capture the uncertainty in inference about the process. Since typically, such processes involve components at different levels, stages, and scales, it is natural to frame our modeling in the context of hierarchical models. In turn, since such models introduce unknowns, for example, parameters or latent processes, we need to incorporate the uncertainty associated with these unknowns in order to achieve a better overall assessment of uncertainty. This encourages us to cast the models under the Bayesian framework. The objective of this first chapter is to provide an introduction to the tools for Bayesian hierarchical modeling. Indeed, we acknowledge that the required material here is substantial, that we are only opening the proverbial Pandora’s box, and that readers will have to invest sufficient time to climb the learning curve, to achieve comfort with the technology. To that end, we have supplied a rich reference list. And, we emphasize that the reward is substantial. The ability to let the problem and, more generally, the science drive the modeling rather than forcing the analysis to fit a standard technique, is wonderfully liberating and considerably enhances the way one approaches the understanding of complex systems. The tools we discuss here include the Bayesian inference paradigm, hierarchical modeling and, more generally, directed graphical models, model comparison, and Bayesian computation. Though the development of each is, of necessity brief, we provide exemplification and as noted above, direction to further resources. %@ 978-0-19-856966-4

@incollection{carlin_elements_2006, abstract = {Serious investigation of ecological processes is challenging due to the complex nature of these processes and the lack of sufficient data to see them well. Hence, acknowledging our limitations, we turn to stochastic modeling as a means to capture the uncertainty in inference about the process. Since typically, such processes involve components at different levels, stages, and scales, it is natural to frame our modeling in the context of hierarchical models. In turn, since such models introduce unknowns, for example, parameters or latent processes, we need to incorporate the uncertainty associated with these unknowns in order to achieve a better overall assessment of uncertainty. This encourages us to cast the models under the Bayesian framework. The objective of this first chapter is to provide an introduction to the tools for Bayesian hierarchical modeling. Indeed, we acknowledge that the required material here is substantial, that we are only opening the proverbial Pandora’s box, and that readers will have to invest sufficient time to climb the learning curve, to achieve comfort with the technology. To that end, we have supplied a rich reference list. And, we emphasize that the reward is substantial. The ability to let the problem and, more generally, the science drive the modeling rather than forcing the analysis to fit a standard technique, is wonderfully liberating and considerably enhances the way one approaches the understanding of complex systems. The tools we discuss here include the Bayesian inference paradigm, hierarchical modeling and, more generally, directed graphical models, model comparison, and Bayesian computation. Though the development of each is, of necessity brief, we provide exemplification and as noted above, direction to further resources.}, added-at = {2017-01-09T13:57:26.000+0100}, address = {New York, NY}, author = {Carlin, Bradley P. and Clark, James S and Gelfand, Alan E}, biburl = {https://www.bibsonomy.org/bibtex/272dcdc44682c8ba80d5faf50023e620d/yourwelcome}, booktitle = {Hierarchical {Modelling} for the {Environmental} {Sciences}: {Statistical} {Methods} and {Applications}}, editor = {Clark, James S. and Gelfand, Alan E.}, interhash = {c28064d88ca9ba3f5830346267284151}, intrahash = {72dcdc44682c8ba80d5faf50023e620d}, isbn = {978-0-19-856966-4}, keywords = {Bayesian bayesian inference, kriging, review}, note = 205, pages = {3--24}, publisher = {Oxford University Press}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Elements of hierarchical {Bayesian} inference}, year = 2006 }