Parameter Estimation And Model Selection Of Computer Virus Transmission Mechanism

Research for the purpose of suppressing the spread of computer viruses has been around for a long time,but it is carried out under the assumption that the propagation model is known and the parameters are fixed.In real life,it is impossible to accurately predict the propagation model and parameters?This will lead to many research results deviating from the actual meaning?In this paper,through statistical methods,whether the model is determined or not and whether the data is complete,different algorithms are used to study the computer virus propagation model selection and parameter estimation?The third and fourth chapters are based on the determined stochastic SIR model,based on the observed data?Whether to complete different statistical methods to solve the parameter estimation problem.In the third chapter,under the condition of complete data,according to the new data in unit time is a random variable and then using the Maximum Likelihood Estimation method to construct the approximation function of the approximation of the infection rate 0 and the removal rate y respectively.If there is no explicit solution,the approximate likelihood function is obtained according to the equivalent infinitesimal,and the likelihood function estimation of infection rate and removal rate is obtained.The fourth chapter is based on the incomplete data.This paper mainly introduces two algorithm estimation model parameters:one is the Ensemble Kalman Filter?In this paper,the random variable expectation is used to replace the value of the random variable in the random SIR model?The predictive mapping of Kalman filtering;secondly,because the EM algorithm can not calculate the expectation of the unknown initial value,we propose the ABC-EM algorithm,which can replace the posterior distribution of the initial value and replace the E step of the EM algorithm?Infection rate and removal rate?In this chapter we use ABC-EM algorithm,Ensemble Kalman Filter,Maximum Likelihood Estimation and Least Squares method for parameter estimation?By simulation comparison,we find the parameters of ABC-EM algorithm simulation?The accuracy of the estimate is much higher than the parameter estimates of the other three algorithms?Therefore,the proposed algorithm has high precision.The fifth chapter discusses the problem of model selection and parameter estimation under the condition of model uncertainty and incomplete data.In this paper,the Approximate Bayesian Computation-Sequence Monte Carlo(ABC-SMC)is used to achieve the purpose of model selection and accurate parameter values?The idea of the algorithm is to randomly extract the model and parameters from the prior distribution of the optional model and parameters?If the variance between the simulated data and the observed data generated by the model and the parameter is less than the predetermined threshold,the model and parameters?Then it is accepted,and then the interference factor is added.to adjust the precision of the parameters in the ABC-SMC iteration process?The algorithm just avoids the shortcomings of Bayesian algorithm when calculating the model parameters and the calculation is large?The simulation results show that the ABC-SMC?The model selected is consistent with the model for generating observation data and the parameters are very small.