The Construction And Application Of Bayesian Chane-point Model

The change-point problem is a key research topic in the field of statistics.In the context of the big data era,the change-point detection problem has become particularly important,with a wide range of applications in the estimation of climate change,earthquake prediction and biometrics.A number of frequency-based change-point detection methods exist,the idea of which is mainly to use hypothesis testing for change-point detection,but they do not make use of a prior information about the sample.Some researchers have studied the change-point problem based on Bayesian theory,these detection methods do not distinguish well for proportional type,i.e.data ranging from 0 to 1,resulting in a low accuracy rate of change-point recognition.To address these problems,this paper proposes a new Bayesian model for single change-point detection,which is used to improve the efficiency of change-point detection for such data.In the model construction part,the distribution of the sample is fitted with the Beta distribution according to the characteristics of the sample data,since it is not possible to give a direct prior distribution for each of the two parameters of the Beta distribution,the prior distribution is selected using the reparameterisation technique,and then the joint posterior distribution of the parameters and change-point is obtained by combining the prior distribution of the change-point.Afterwards,the posterior distribution is sampled by a Markov Monte Carlo method,and then we determine the criterion for determining the change-point and thus infer the location of the change-point.In order to verify the effectiveness of the Bayesian change-point detection model,two simulation experiments and an empirical study are designed.In the simulation part of the experiments,the validity of the model proposed in this paper was verified by numerical experiments with gradually increasing the number of positive samples,different difference Beta distributions and different sample sizes,respectively.In the empirical analysis,we obtain RNA-seq sequencing data at 16 time points during the differentiation process of 19 cell lines,and obtain 6479 high quality alternative transcription start site usage data through a series of bioinformatics analyses such as comparison,quality control and quantification.Based on the previously constructed change-point detection model,in order to reduce iterative errors,a posterior sampling was performed using the NUTS algorithm to infer the presence and location of change-point at each alternative transcription start site.Finally,bioinformatics analysis is performed on alternative transcription start sites at each time point to elucidate their dynamic mechanisms during cell differentiation,and the model is validated by the relevant literature to demonstrate the correctness of change-point identification.The analysis of simulated data and alternative transcription start site data sequences by the Bayesian change-point detection model successfully estimates change-point in the sequences and provides some assistance in the detection of change-point in proportional data.