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MCSA 06/07 L07. BBNs and mechanistic models. Andrea Castelletti. Politecnico di Milano. Didactic map. BBNS. The model of the lake. Discretization of the variables. Conditional Probability Tables. Bayesian belief networks (BBNs). The aggregated probability on each column must be 1:

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bbns and mechanistic models
MCSA 06/07

L07

BBNs and mechanistic models

Andrea Castelletti

Politecnico di Milano

bayesian belief networks bbns
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.
bayesian belief networks bbns2
Bayesian belief networks (BBNs)

State transition

function

pros and cons of bbns
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)

didactic map1
Didactic map
  • Mechanistic
mechanistic models relationships between
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
mechanistic model
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.

mechanistic models parameters
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.

mechanistic models parameters1
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.

stochastic mechanistic models
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.

remarks
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.

readings
Readings

IPWRM.Theory Ch. 4

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