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A point process approach for spatial stochastic modeling of thunderstorm cells

Kriesche B., Hess R., Schmidt V.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

471--496

In this paper we consider two different approaches for spatial stochastic modeling of thunderstorms. Thunderstorm cells are represented using germ-grain models from stochastic geometry, which are based on Cox or doubly-stochastic cluster processes. We present methods for the operational fitting of model parameters based on available point probabilities and thunderstorm records of past periods. Furthermore, we derive formulas for the computation of point and area probabilities according to the proposed germ-grain models. We also introduce a conditional simulation algorithm in order to increase the model’s ability to precisely predict thunderstorm events. A systematic comparison of area probabilities, which are estimated from the proposed models, and thunderstorm records conclude the paper.

A note on impotance sampling simulation for germ-grain model

Palmowski Z.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

293--304

In this paper we demonstrate how to use the importance sampling method to simulate rare events in a germ-grain model. We analyze conditions under which two germ-grain models are mutually absolutely continuous. We also find the likelihood set process. We apply these results in simulating the probability that the radius of the occupied component of the origin in continuous percolation is greater than some R. This method is based on the reduction of the variance of estimator.