Statistical Inference And Application Of Mean Change Point Of Normal Distribution Based On Bayesian Analysis

With the development of statistical computing,the Bayesian method for statistical inference of change-point model becomes more popular.The Bayesian method has a difficult problem is complex computation.Recently proposed Markov chain Monte Carlo(MCMC)method is a simple and effective the Bayesian method,which can simplify the change-point problem.At present,many scholars have used MCMC method to study the single change-point problem of Poisson process,complex Poisson process single change-point model and other distributions.In order to improve the accuracy of experimental results,the degenerated random approximation Monte Carlo(ASAMC)algorithm proposed by Kim,J.and Cheon,S in 2010 handles data.In this paper,the change-point theory is applied in two fields: one is to study the mutation of oxygen content in soil,the other is to study the change of the number of cancerous cells in human cells.Considering the large data background,the limit distribution of each distribution is normal distribution.The authors standardized the oxygen content in geological formation and the number of cancerous cells in human cells.Based on the prior distribution of the parameters,the posterior distribution function of the parameters is deduced,and the position of the change-point of the parameters in the model is detected by ASAMC algorithm.The change of oxygen content in soil at different temperatures and seasons was studied.The ASAMC algorithm was used to detect the change of the number of cancerous cells in human cells and the factors affecting the change of the number of cancerous cells.The innovation of this article lies in the application of the theory of change-point to practical problems,the application of the theory of change-point combined with ASAMC algorithm to the data obtained from the soil quality test of the hot spring campus of our college,which is carried out by the Institute of Geographic Information and Tourism.It is found that temperature,precipitation and season will affect the content of oxygen in the soil of our school's hot spring campus.The ASAMC method is applied to the first step.Step-by-step detection found that most of the change points of oxygen content appeared in summer and autumn,and according to the maximum logarithmic probability value,we obtained the number and location of the change points.In this paper,another important episode analysis of the change-point theory is studied.We choose the air condition in Dong'an District of Mudanjiang as the control experimental group and use the relevant data to study theair quality in Shayibake District of Urumqi.We can draw the following conclusions:With the aggravation of air pollution,the number of cancerous cells in human cells increases.The increase of ozone content,sulfur dioxide content and solid particle content in the air will aggravate the air pollution in this area.The aggravation of air pollution will increase the content of ozone,sulfur dioxide and solid particles in the air,which will lead to the increase of cancer phenomena and the enhancement of the activity of cancer cells.In this paper,the change-point theory is applied to deal with the change of oxygen content in soil and detect the change of the number of cancerous cells in human cells by using ASAMC algorithm.The combination of the change-point theory with geology and biology shows the application value of the change-point theory.