Research On Detection And Parameter Estimation Of Random Point Pattern

Random point pattern is a theory to study the pattern distribution of random point process,its cardinal number(number of points)and pattern characteristics(such as location and size)change randomly.Description of many problems in nature can be modeled by random point pattern,which is widely used in queuing theory,spatial point process,planetary distribution,vegetation distribution and other fields.Random point pattern detection,parameter estimation and non-parametric estimation are the main problems of random point pattern,this paper carried out research around these three aspects.The specific research contents are as follows:(1)Aiming at the problem of random point pattern detection,a random point pattern detection algorithm based on multi-feature likelihood ration is proposed.Firstly,the random point pattern is introduced and its characteristics are analyzed.A conclusion is drawn:random point pattern has many characteristics,which is embodied in its cardinal number and pattern characteristics.Secondly,the likelihood ratio and distribution parameters of the random point pattern are used as evaluation indicators.The detection threshold is obtained through the Monte Carlo experiment to judge the input.Finally,the proposed algorithm is used to detect five kinds of random point patterns with different parameters.The results show that detection result are consistent with the real situation.(2)Aiming at the problem of random point pattern parameter estimation,a random point pattern finite mixture model estimation algorithm based on Gibbs sampling is proposed.Firstly,the random point mode finite mixture model is constructed.Secondly,the traditional Gibbs sampling algorithm is extended to estimate the parameters of the mixture model,and the BIC criterion is used to evaluate the model order.Finally,the Gaussian mixture distribution is used as the characteristic distribution of the random point pattern,several groups of random point pattern distributions are considered and compared with the traditional non-point pattern description algorithm.The results show that the algorithm proposed in this paper is more accurate for parameter estimation.(3)Aiming at the problem of non-parametric estimation of random point pattern,a non-parametric random point pattern estimation algorithm based on Dirichlet process mixture is proposed.Firstly,according to the distribution function of the random point pattern and the construction form of the Dirichlet process,a Dirichlet process mixture random point pattern model is constructed.Secondly,the Gibbs sampling method is applied to the model,and the parameters and order of the model are derived.Finally,based on simulation experiments,it is verified that the algorithm continuously optimizes the model parameters and forms an appropriate number of clusters during the sampling process.