两两相互作用Gibbs点过程的行列式过程逼近强度
Approximation intensity for pairwise interaction Gibbs point processes using determinantal point processes
摘要：
吉布斯点过程的强度通常是模型参数的一个难处理的函数。对于排斥的两两相互作用点过程，这种强度可以表示为某些特定函数的拉普拉斯变换。Baddeley和Nair（2002）发展了泊松鞍点近似，对于基本模型，该近似包括计算关于齐次泊松点过程的拉普拉斯变换。在本文中，我们开发了一个近似，它包括在计算相同的拉普拉斯变换相对于一个特定的行列式点过程。这种新的近似是有效地实现，原来是更准确的比泊松鞍点近似，证明了一些数值例子。
英文摘要：
The intensity of a Gibbs point process is usually an intractable function of the model parameters. For repulsive pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function. Baddeley and Nair (2002) developped the Poisson-saddlepoint approximation which consists, for basic models, in calculating this Laplace transform with respect to a homogeneous Poisson point process. In this paper, we develop an approximation which consists in calculating the same Laplace transform with respect to a specific determinantal point process. This new approximation is efficiently implemented and turns out to be more accurate than the Poisson-saddlepoint approximation, as demonstrated by some numerical examples.
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