Modeling
Assessment and Updating of Predictive Models
Predictive models are usually constructed based on simplifying assumptions, and sometimes on a purely heuristic basis when underlying phenomenon is not well understood.
PredictionProbe has developed a proprietary framework for the analysis of uncertainties and model assessment using Bayesian Updating Rule. The process of model assessment amounts to estimating the unobservable model parameters z based on a set of measurements xi, and yi, i=1,…..m of the observable model variables.
Following the Bayesian paradigm, we express our lack of precise knowledge about z by assigning it a probability distribution to z. The Bayesian Updating Rule allows us to combine previous information about z with information obtained from observed data to arrive at a new distribution.
There are three important steps in constructing predictive mathematical model using Bayesian Updating Rule. These steps include:1) selection of prior distribution, 2) formulation of the likelihood function, and 3) computation of the posterior distribution.
The prior distribution often incorporates subjective information, whereas the likelihood function incorporates the objective information contained in the observed data. Mathematically, the likelihood function describes the probability of observing the data for a given value of the model parameters z. The formulation of z for each problem is unique and is the main challenge in Bayesian Updating. The posterior distribution combines the information gained from the new set of data with the prior information on the parameters.
The prior distribution for the observable random variables, x, can initially be identified using a combination of the maximum likelihood method, statistical tests, and probability plotting.