Abstract
This chapter summarizes the main elements of Bayesian probability theory to help reconcile dynamic environmental system models with observations, including prediction in space (interpolation), prediction in time (forecasting), assimilation of data, and inference of the model parameters. Special attention is given to the treatment of parameter uncertainty (first-order approximations and Bayesian intervals), the prior distribution, the formulation of the likelihood function (using first-principles), the marginal likelihood, and sampling techniques used to estimate the posterior target distribution. This includes rejection sampling, importance sampling, and recent developments in Markov chain Monte Carlo simulation to sample efficiently complex and/or high-dimensional target distri- butions, including limits of acceptability. We illustrate the application of Bayes’ theorem and inference using three illustrative examples involving the flow and storage of water in the surface and subsurface. At least some level of calibration of these models is required to match their output with observations of system behavior and response. Algorithmic recipes of the different methods are provided to simplify implementation and use of Bayesian analysis.
Original language | English |
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Title of host publication | Handbook of Hydrometeorological Ensemble Forecasting |
Publisher | Springer Berlin Heidelberg |
Pages | 563-636 |
Number of pages | 74 |
ISBN (Electronic) | 9783642399251 |
ISBN (Print) | 9783642399244 |
DOIs | |
State | Published - Jan 1 2019 |
Externally published | Yes |
Keywords
- Bayesian analysis
- Data assimilation
- Hydrologic modeling
- Hypothesis testing
- Likelihood function
- Markov chain Monte Carlo simulation
- Monte Carlo sampling
- Posterior distribution
- Prior distribution