基于Gibbs抽样的分层贝叶斯模型在火灾发生次数统计推断中的应用

Application of Hierarchical Bayesian Model Based on Gibbs Sampling in Statistical Inference of Fire Occurrences

摘要: Gibbs抽样是MCMC抽样算法中应用最广泛的方法之一，其核心思想是对高维参数进行后验推断时，通过参数向量的分量的条件分布族来构造Markov链，使其不变分布为目标分布。本文利用Gibbs抽样方法结合分层贝叶斯模型，对我国各地区火灾发生次数进行了回测，结果显示，相比于传统的poisson分布刻画方法，基于Gibbs抽样的分层贝叶斯方法充分利用了历史信息使结果更具可信度。

Abstract: Gibbs sampling method is the most widely used method in MCMC algorithm. The basic idea of Gibbs sampling is to construct the Markov chain by the conditional distribution family of the components of the parameter vector when the high-dimensional parameters are posteriorly inferred, so that its invariant distribution is the target distribution. This topic is based on the method to determine the parameters of the model, which can be based on existing information to estimate the number of years, the number of fire occurred in the region and the estimated confidence interval of the parameters.