BAYESIAN ANALYSIS AND UPDATING Clause Samples
BAYESIAN ANALYSIS AND UPDATING. For the modelling of rockfall exposure, Bayesian analysis is particularly useful, as it facilitates the consistent combination of different information in a single model. This is because the probabilistic model can be updated when new information becomes available. Consider the case where rockfall exposure at a particular location is expressed by the model HV (v|θ) with uncertain parameters θ . When new information becomes available (denoted by fΘ θ z L θ z fΘ θ
BAYESIAN ANALYSIS AND UPDATING. For the modelling of rockfall exposure, Bayesian analysis is particularly useful, as it facilitates the consistent combination of different information in a single model. This is because the probabilistic model can be updated when new information becomes available. Consider the case where rockfall exposure at a particular location is expressed by the model HV (v|θ) with uncertain parameters θ . When new information becomes available (denoted by fΘ (θ z ) ∝ L (θ z ) fΘ (θ) (5.3) fΘ (θ) is the prior probabilistic model, fΘ (θ z ) is the updated model and L (θ z ) is the likelihood function, which describes the new information. The proportionality constant is obtained from the fact that integration of fΘ (θ z ) over the entire domain of θ must yield one. The likelihood function is the probability of the observed information given the parameters θ , i.e., L (θ z ) = Pr (z θ)