Bayesian updating in natural hazard risk assessment

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1 International Forum on Engineering Decision Making, Third IFED Forum, Shoal Bay, Australia, December /23 Bayesian updating in natural hazard risk assessment Mathias Graf, Kazuyoshi Nishijima, Michael H. Faber, ETH Zurich

2 Overview 2/23 Approach for conditioning/updating g probabilistic models utilized in the risk management of natural hazards Investigate how the uncertainties have to be included Investigate how an efficient and consistent use of data that become available after the models are installed can be used to reduce the uncertainties

3 Natural hazard risk model 3/23

4 Natural hazard risk model as a Bayesian 4/23 probabilistic network Taking basis in a Bayesian probabilistic representation and Bayesian updating scheme

5 Examples overview 5/23 Three examples considering i the updating of fragility models Example I: statistical uncertainty involved in the estimation of the hazard indices Example II: model uncertainty Example III: reducing model uncertainty by using observed indicators

6 Examples: Bayesian probabilistic network 6/23 E = occurrence of a typhoon S i = wind speed (hazard index) P i = failure probability of the structure Θ characterizes the fragility model F i = state of the structure

7 Examples: Bayesian probabilistic network 7/23 The structures considered in the examples are assumed to have identical probabilistic characteristics in regard to the resistance to strong wind.

8 Examples: Procedure 8/23 Representation through a Bayesian probabilistic network Simulating a dataset Update Bayesian probabilistic network with dataset Investigate convergence rate and values of fragility model parameters

9 Examples: WinBUGS 9/23 WinBUGS is used for the Bayesian probabilistic network representation for the updating of the models Markov Chain Monte Carlo (MCMC) algorithm for the updating

10 Example I 10/23 Example I Standard approach disregarding the uncertainties involved in the estimation of the hazard indices. Proposed approach considering the uncertainties involved in the estimation of the hazard indices.

11 Example I: Bayesian probabilistic network 11/23 S ~ LN ( λ, ξ ) i s, i S p i F i ln S i a =Φ b = failure or survival

12 Example I: Simulating dataset 12/23 Parameter λsi, ξ S Value ln(10), ln(20),..., ln(250) 0.2 a ln b

13 Example I: Simulating dataset 13/23 Proposed Standard Ideal (control) S i S ~ LN ( λ, ξ ) S = λ S = real wind speed S i i s, i S i s, i i F i Are known (obtained from dataset simulation)

14 Example I: Prior distribution of a and b 14/23 Parameter Distribution mean Standard deviation a Normal b Gamma

15 Example I: convergence of parameter a 15/23 proposed standard ideal

16 Example I: convergence of parameter b 16/23 proposed standard ideal

17 Example I: Fragility curve estimated for 17/23 different ξ S

18 Example II: Bayesian probabilistic network 18/23 Introducing model uncertainty ε V i = ε S i ε ~ ( λ, ξ ) LN ε ε λ = ε 0

19 Example II: Simulating dataset 19/23 Datasets 1 Datasets 2 Number of 1 1,2,,n Typhoons ξ 2 2 Vi, ξ S ξε 2 2 S ε = + = = ξ + ξ = ρ = ξ ξ ε 2 2 S + ξε = 0.5

20 Example II: Results 20/23 Mean value of the posterior distribution ib tion of parameter a after updating with datasets with different values of the parameter ρ (left) and with datasets with samples from different number of typhoons (right).

21 Example III: Bayesian probabilistic network 21/23 and dataset Using measured wind speeds from meteorological stations to condition model uncertainty λ s,i ξ s V i F i Conditioning of ε Updating

22 Example III: convergence of parameter a 22/23 and b

23 Conclusions 23/23 The suggested approach - takes an integral approach to the representation of knowledge in the assessment of portfolio losses - facilitates that model uncertainties are accounted for consistently in the risk assessment - facilitates for easy updating of risks and hazard indices when new information after hazard events can be observed

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