BBNs and mechanistic models

1. MCSA 06/07 L07 BBNs and mechanistic models Andrea Castelletti Politecnico di Milano

2. Didactic map • BBNS

3. The model of the lake

4. Discretization of the variables

5. Conditional Probability Tables

6. Bayesian belief networks (BBNs) • The aggregated probability on each column must be 1: • Each variable can only take values in each discretization set • And at least one value must always occur.

7. Bayesian belief networks (BBNs)

8. Bayesian belief networks (BBN) .9

9. Bayesian belief networks (BBN) .9

10. Bayesian belief networks (BBNs) State transition function

11. cons –not particularly suited for describing deterministic relationships among the variables, e.g. is the sum of & cons –not particularly suited when the number of points on the discretization grid of the variable is rather big, e.g. Lake Maggiore the CPT describing the state transiton includes 1 350 000 000 elements Pros and cons of BBNs pros –very useful when there are not quantitative, well structured theories (e.g. social systems)

12. Didactic map • Mechanistic

13. from Physics Mass balance equation from Hydraulics: free regime storage discharge function Release function From bathymetry e.g. if we assume a cylindric lake Mechanistic models: relationships between

14. state transitions output transformation Mechanistic model The model is call mechanistic (or conceptual) model because It is based on the conceptualization of the internal mechanis of the natural process.

15. state transition Parameters: variables that specify the particular features of a system. Very often parameters are state variables not yet at the equilibrium or whose value change very slowly in time with respect to the dominant system mode. output transformation Mechanistic models: parameters The value of parameters has to be estimated using data.

16. state transition output transformation Mechanistic models: parameters Do these models provide the same representation of reality as a BBN? NOT!! BBNs are intrinsically uncertain, while in this model uncertainty in in the input but for a given et+1 the model is a deterministic one. The value of parameters has to be estimated using data.

17. Error due to the simplifications on the release:process error Level measurement errors: output error Stochastic mechanistic models The mechanistic model we defined so far is based on the hidden hypothesis that storage and level measures are not error-biased? Is this acceptable? Now the mechanistic model is providing the same uncertain description as the BBM.

18. Remarks • With BBNs measurement and process errors are implicitly embedded in the model. • Errors have to be explicitly considered in mechanistic models. • The structure of model is never satisfactory in a definite way. • Conceptually, stochastic models should be preferred over deterministic models. However, this does not imply that deterministic models are less accurate or precise. The accuracy of a model is not only the result of its structure, but also of the way the model has been calibrated.

19. Readings IPWRM.Theory Ch. 4