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Bayesian Synthesis of a Pathogen Growth Model

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Ross. Synthesizing. Algorithm. Bayesian Synthesis. Prior on the. Model Inputs. Stated Prior ... Ross. Synthesizing. Algorithm. Raftery. 1. Baranyi Growth Model ... – PowerPoint PPT presentation

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Title: Bayesian Synthesis of a Pathogen Growth Model


1
Bayesian Synthesis of a Pathogen Growth Model
  • Mark Powell, USDA/ORACBA, Washington, DC
  • Mark Tamplin, USDA/ARS, Wyndmoor, PA
  • Bradley Marks, Mich. St. Univ., E. Lansing, MI
  • International Association of Food Protection
  • New Orleans, LA , August 10-13, 2003

2
Bayesian Synthesis
  • Bayesian synthesis is proposed as one means of
    developing and evaluating predictive microbiology
    models.
  • Motivated by empirical example.
  • Apply Baranyi growth model to data from two
    studies on the growth of Listeria monocytogenes
    Buchanan et al. (1989) and Pin et al. (2001) -
    5ºC, pH 7, population growth after 240 h.

3
Bayesian Synthesis
Prior on the Model Inputs
Model
Observed Data on Output
Stated Prior Model Output
Synthesizing Algorithm
4
Bayesian Synthesis
Baranyi
Prior on the Model Inputs
Model
Observed Data on Output
Stated Prior Model Output
Synthesizing Algorithm
5
Bayesian Synthesis
Baranyi
FAO
Prior on the Model Inputs
Model
Observed Data on Output
Ross
Stated Prior Model Output
Synthesizing Algorithm
6
Bayesian Synthesis
Baranyi
FAO
Prior on the Model Inputs
Model
Observed Data on Output
Ross
Stated Prior Model Output
Buchanan
Synthesizing Algorithm
7
Bayesian Synthesis
Baranyi
FAO
Prior on the Model Inputs
Model
Observed Data on Output
Ross
Pin
Stated Prior Model Output
Buchanan
Synthesizing Algorithm
8
Bayesian Synthesis
Baranyi
FAO
Prior on the Model Inputs
Model
Observed Data on Output
Ross
Pin
Stated Prior Model Output
Buchanan
Synthesizing Algorithm
Raftery
9
1. Baranyi Growth Model
  • Originally introduced by Baranyi and Roberts
    (1994). Parameters have an intuitive biological
    interpretation.

10
2. Prior on Inputs
  • y0 uniform(2,4)
  • ymax lognormal(9,1)
  • mu lognormal(0.0239, 0.0239)
  • FAO 1999, representative GT 29 h for L.
    monocytogenes at 5C, 7pH)
  • tlag (116, 94)
  • Ross (1999), distribution for tlag has peak _at_ 4-6
    GT, 95th percentile _at_ 10-15 GT.
  • Draw thousands of independent samples from these
    distributions, run the combinations through
    Baranyi model to obtain ...

11
Implied Prior on Output
Implied Prior on Output g240 normal(1.3422,
1.2631)
12
3. Stated Prior on OutputBuchanan et al (1989)
Stated Prior on Output g240 normal(3.9362,
0.9770)
13
4. Observed Data on OutputPin (2001)
16 Trials g240 mean 3.2592 stdev 0.6876
14
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15
5. Bayesian Synthesis Algorithm
  • Compute density of the 5,000 model predictions on
    the implied prior
  • Compute density of 5,000 model predictions on the
    stated prior
  • Compute the likelihood of the 5,000 model
    predictions given the observed data
  • Compute importance sampling weights
  • Sample values from the joint input and implied
    output distribution with probabilities
    proportional to the sampling weights

16
Importance Sampling Weights
Note if stated density implied density, then
the sampling weights are just the likelihood of
the model predictions, given the observed data
17
Importance Sampling
18
Importance Sampling
19
Importance Sampling
20
Importance Sampling
21
Importance Sampling
22
Importance Sampling
23
Results Posterior Distribution for Baranyi Model
Parameters
24
Results Posterior Distribution for Predicted
Growth
25
Thanks
  • Questions?
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