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Fitting Mathematical Models to Data Adapting Likelihood Based Inference Meaningful Modeling of Epidemiologic Data, 2010 AIMS, Muizenberg, South Africa.

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Presentation on theme: "Fitting Mathematical Models to Data Adapting Likelihood Based Inference Meaningful Modeling of Epidemiologic Data, 2010 AIMS, Muizenberg, South Africa."— Presentation transcript:

1 Fitting Mathematical Models to Data Adapting Likelihood Based Inference Meaningful Modeling of Epidemiologic Data, 2010 AIMS, Muizenberg, South Africa Steve Bellan MPH Epidemiology Department of Environmental Science, Policy & Management University of California at Berkeley

2 This presentation is made available through a Creative Commons Attribution- Noncommercial license. Details of the license and permitted uses are available at http://creativecommons.org/licenses/by-nc/3.0/ © 2010 Steve Bellan and the Meaningful Modeling of Epidemiological Data Clinichttp://creativecommons.org/licenses/by-nc/3.0/ Title: Fitting Mathematical Models of to Data Attribution: Steve Bellan, Clinic on the Meaningful Modeling of Epidemiological Data Source URL: http://lalashan.mcmaster.ca/theobio/mmed/index.php/http://lalashan.mcmaster.ca/theobio/mmed/index.php/ For further information please contact Steve Bellan (sbellan@berkeley.edu).

3 Fitting Dynamic Models to Data Adapt our dynamic models in a probabilistic framework so we can ask: What is the probability that a model would have generated the observed data? What is the likelihood of a model given the data?

4 Likelihood of parameters (given data)

5 Likelihood of parameters (given data) Distribution Binomial Distribution

6 Likelihood of parameters (given data) Distribution Normal Distribution

7 Likelihood of parameters (given data) Distribution Exponential Distribution

8 Likelihood of parameters (given data) Distribution Poisson Distribution

9 Likelihood of parameters (given data) Distribution Binomial Distribution Stochastic Component of Model

10 Likelihood of parameters (given data) Data Distribution HIV in Harare

11 Likelihood of parameters (given data) Data Distribution Expectation of distributional parameters, given model Stochastic Component of Model

12 Likelihood of parameters (given data) Data Distribution Expectation of distributional parameters, given model Model S I Stochastic Component of Model Deterministic Component of Model

13 Likelihood of parameters (given data) Data Distribution Expectation of distributional parameters, given model Model S I Stochastic Component of Model Deterministic Component of Model Parameters (some fixed and others to be fitted)

14 Parameters (some fixed and others to be fitted) Likelihood of parameters (given data) Data Distribution Expectation of distributional parameter(s), given model Time series prevalence Time series cases Model S I

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