Bayesian inference for deterministic simulation models for environmental assessment [microform]
- Bib ID:
- 3284219
- Format:
- Book and Microform
- Author:
- Bates, Samantha Colleen
- Description:
- 106 p.
- ISBN:
- 0493336702
- Summary:
-
In this thesis, Bayesian methodology is used to make inference from deterministic models, particularly those in environmental assessment, while accounting for uncertainty in the model inputs. Suppose we have a deterministic simulation model which maps inputs to outputs. Available expert knowledge about the values of the inputs and observed data on inputs and outputs, are represented by prior distributions and likelihoods respectively. Inference about the outputs can be made from their marginal posterior distribution. Often, the analytical form of this posterior is intractable and obtaining an exact sample from it can be difficult or impossible. One method to obtain a sample approximately from this posterior, is to use the sampling importance resampling (SIR) algorithm (Rubin 1988). This method yields posterior distributions which represent uncertainty in the inputs and outputs. This methodology is extended to sequential multicompartment models.
Further, we are able to determine by inspection which set of observed data reduces the uncertainty. In applications where the posterior distribution of interest is highly dependent, perhaps concentrated close to a ridge in a high-dimensional space, SIR may be an inefficient sampling method. Markov chain Monte Carlo (MCMC) is an alternative method for sampling from posterior distributions but the MCMC output in these ridgelike situations, will tend to be highly correlated. We present an MCMC method which at each iteration proposes a value for the model inputs from a multivariate normal centered at the current value. The covariance matrix is estimated using the nearest neighbors of the current value in a pilot data set. While this proposal distribution adapts to the shape of the (unknown) posterior region, it does not suffer the problems of some adaptive methods in that the proposal distribution is fixed for a given input value.
We present simulated and real examples where this nearest neighbors MCMC method outperforms SIR and generic MCMC methods. Two tools to assess deterministic models in a Bayesian framework are presented. The first measures the discrepancy between model inputs and outputs and observed values related to each, and investigates the source of this discrepancy. The second may serve as a pre-analysis indicator of model inadequacy.
- Notes:
-
- (UnM)AAI3022810
- Source: Dissertation Abstracts International, Volume: 62-08, Section: B, page: 3678.
- Chair: Adrian E. Raftery.
- Thesis (Ph.D.)--University of Washington, 2001.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Statistics
- Other authors/contributors:
- University of Washington
- Copyright:
-
In Copyright
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 2001
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