## Benefits of a Bayesian Approach for Synthesizing Multiple Sources of Evidence and Uncertainty Linked by a Deterministic Model (1993)

Citations: | 7 - 6 self |

### BibTeX

@MISC{Givens93benefitsof,

author = {Geof H. Givens and Adrian E. Raftery and Judith E. Zeh},

title = {Benefits of a Bayesian Approach for Synthesizing Multiple Sources of Evidence and Uncertainty Linked by a Deterministic Model},

year = {1993}

}

### OpenURL

### Abstract

A Bayesian synthesis approach has been proposed by Raftery, Givens, and Zeh (1992) for making inferences from a deterministic model with many inputs and outputs. The approach was applied to population dynamics models for bowhead whales. The approach consists of establishing a joint prior, or pre-model distribution, on the model inputs and outputs for which there exists evidence independent of the model. The restriction of this distribution to a subspace defined by the model mapping then constitutes a post-model distribution, from which inferences are drawn. We briefly review a methodology for implementing the Bayesian synthesis approach, and then consider in detail the potential uses of the results and the strengths and weaknesses of the approach compared to past methodologies. 1 Introduction Complex deterministic models reflect scientists' simplified conceptions of natural mechanisms about which they have incomplete understanding. Such a model depends on a set of input para...

### Citations

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49 | Inference from a deterministic population dynamics model for bowhead whales - Raftery, Givens, et al. - 1995 |

40 |
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Citation Context ...mparison, as discussed in Section 4. 5.2 Numerical Methods For extremely complex models, the large number of runs required may not be computationally feasible. In this case, Gauss-Hermite quadrature (=-=Naylor and Smith, 1982-=-) could lead to successful calculation of the necessary integral. The choice of grid points is a topic for investigation, as a simple product rule would not reduce the required model runs because of t... |

16 | A Bayesian framework and importance sampling methods for synthesizing multiple sources of evidence and uncertainties linked by a complex mechanistic model - Givens - 1993 |

16 | Bowhead whale, Balaena mysticetus, population size estimated from acoustic and visual census data collected near
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(Show Context)
Citation Context ...ates of outputs like the recent population size and age structure which may or may not be consistent with independent assessment work via aerial, visual, and acoustical counts (Raftery and Zeh, 1991; =-=Raftery and Zeh, 1993-=-; Zeh, George, Raftery and Carroll, 1991), photogrammetry 2 Inputs calf, juvenile, and adult mortality rates (possibly age-specific) ages of recruitment, sexual maturity, and senescence calving interv... |

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Citation Context ...ctory produced by the model, but the best values of these parameters are unknown. Independently of any modeling, researchers can provide information about these input parameters from whaling records (=-=Breiwick et al., 1984-=-, Table 1 and footnotes; Braund, Marquette and Bockstoce, 1988; IWC, 1992), carbon isotope analysis (Schell, Saupe and Haubenstock, 1989; Withrow, Burke, Jones and Brooks, 1991), photoidentification a... |

8 | A reweighting approach for sensitivity analysis within the Bayesian synthesis framework for population assessment modeling. Rep. int - Givens, Raftery, et al. - 1994 |

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Citation Context ...rone, Rugh, Withrow and Fraker, 1992), examination of specimens (George, Philo, Suydam, Tarpley and Albert, 1992; Nerini, Braham, Marquette and Rugh, 1984), and interspecific comparisons (Best, 1991; =-=Fowler, 1988). This information -=-provides evidence about the "true" trajectory, but the uncertainty about these inputs renders the "true" trajectory uncertain, even if the PDM exactly modeled bowhead dynamics. Fur... |

6 |
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Citation Context ...jectories provide estimates of outputs like the recent population size and age structure which may or may not be consistent with independent assessment work via aerial, visual, and acoustical counts (=-=Raftery and Zeh, 1991-=-; Raftery and Zeh, 1993; Zeh, George, Raftery and Carroll, 1991), photogrammetry 2 Inputs calf, juvenile, and adult mortality rates (possibly age-specific) ages of recruitment, sexual maturity, and se... |

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4 |
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Citation Context ...arting condition, deterministic PDM's for bowhead whales project a population size and age structure through time, producing a trajectory (e.g. de la Mare, 1989; Breiwick, Eberhardt and Braham, 1984; =-=Allen, 1980-=-). Table 1 displays variables which might be inputs or outputs of a bowhead PDM. Different PDM's may have different inputs and outputs, and inputs for one model may be outputs of another. A successful... |

4 | Growth rates of bowhead whales as determined from low-level aerial photogrammetry. Rep. int - Koski, Davis, et al. - 1992 |

3 |
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Citation Context ...is, Koski, Crone, Rugh, Withrow and Fraker, 1992), examination of specimens (George, Philo, Suydam, Tarpley and Albert, 1992; Nerini, Braham, Marquette and Rugh, 1984), and interspecific comparisons (=-=Best, 1991; Fowler, 1988). Thi-=-s information provides evidence about the "true" trajectory, but the uncertainty about these inputs renders the "true" trajectory uncertain, even if the PDM exactly modeled bowhead... |

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3 |
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Citation Context ...lid statistical inference about model inputs and outputs. 2.2 The HITTER--FITTER Approach Many inferences from whale PDM's are now made using versions of the HITTER--FITTER program (de la Mare, 1989; =-=Punt and Butterworth, 1991-=-). Here, estimates are obtained by forcing the trajectory to pass through a certain point at a certain time (HITTER), or to minimize some measure of distance between the model trajectory and a number ... |

2 |
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Citation Context ...evidence. It is common to see uncertainty about model inputs expressed in a table, where a small number of model outputs are displayed for multiple runs of the model, each with different inputs (e.g. =-=Eberhardt and Breiwick, 1992-=-, Table 3; IWC, 1988, p. 116; Breiwick et al., 1984, Table 3). The tabled runs typically reflect only a few values of a few of the input parameters, with all other variables fixed. Scientists may peru... |

2 | Calving intervals of bowhead whales: an analysis of photographic data - Miller, Davis, et al. - 1992 |

2 |
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(Show Context)
Citation Context ...; OE). From this sample of (`; OE) values, the corresponding sample of / values can be calculated. The simplest way to obtain such a sample is via the Sampling, Importance Resampling (SIR) algorithm (=-=Rubin 1987-=-, 1988). A simple version of the SIR algorithm may be used when the pre-model distribution is specified as p(`; OE) = p(`)p(OE), as it is for the bowheads 5 in RGZ. This means that the evidence about ... |

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1 |
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(Show Context)
Citation Context ...t dominates the results. However, this is easy to detect and is simply remedied by increasing the number of draws; we are also working on automatic remedies that are more efficient but not as simple (=-=Givens 1992, 1993). B-=-y contrast, it can be hard for a user to know whether FITTER has converged to a local or a global maximum. 5. Oscillatory trajectories: The parameter values identified as "reasonable" by the... |

1 |
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(Show Context)
Citation Context ...ng maximized, and can lead to the HITTER--FITTER program converging to local rather than global maxima of the likelihood function, to unreliable estimates and to negatively biased variance estimates (=-=Punt and Butterworth, 1992-=-). Punt and Butterworth (1992) have proposed a possible solution to avoid many of these difficulties. The Bayesian synthesis framework involves no maximization, and so avoids the problems with maximiz... |

1 | Maximum net productivity level estimation for the Northern fur seal (Callorhinus ursinus) population of St - Ragen - 1992 |

1 |
Length frequency of bowhead whales from spring aerial photogrammetric surveys in
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(Show Context)
Citation Context ...988; IWC, 1992), carbon isotope analysis (Schell, Saupe and Haubenstock, 1989; Withrow, Burke, Jones and Brooks, 1991), photoidentification and photogrammetry (Koski, Davis, Miller and Withrow, 1992; =-=Withrow and Angliss, 1992-=-; Miller, Davis, Koski, Crone, Rugh, Withrow and Fraker, 1992), examination of specimens (George, Philo, Suydam, Tarpley and Albert, 1992; Nerini, Braham, Marquette and Rugh, 1984), and interspecific ... |

1 | Variation in ffi C carbon isotope ratios in bowhead whale baleen plates used to estimate age. Rep. int - Withrow, Burke, et al. - 1992 |