Application Of Monte-carlo Simulation In Population Forecast Model

The essence of Markov Chain Monte Carlo(referred to as MCMC) method is used to obey a certain distribution of random number to simulate the realization of random phenomena that may occur in the system.It is widely used in the field of physics and communications research,describing some difficult or impossible to solve stochastic processes by mathematical theory.In this paper, the ideas are transplanted to the population forecast in this complex system,which has become an important tool and means of population forecast model,such as the research of random numbers,the random sampling experiment of population samples, the population distribution function and the population simulation etc..We study the queue element population prediction macro-model and population micro-simulation model based on the MCMC method and give a detailed process and application key of queue element prediction algorithm,analyzing the existing mirco-simulation algorithm based on MCMC, proposing ideological definition of the MCMC method in population prediction, demonstrating its feasibility and giving specific solve ideas by MCMC algorithm in population simulation.This paper firstly use queue element prediction algorithm to predict and analyze the development of population in Henan Province, then we design reaction-type selected method of initial year based on multi-source historical data, completing the screening,cleaning and preparation of population data of initial year as well as mortality and fertility parameters selected, using PADIS-INT software by high, medium and low three schemes to predict the changes in population development in Henan Province between 2015-2050.At last,we predict and analyze the characteristic and situation of population development based on prediction results.Secondly, we propose a micro population simulation model based on Monte Carlo algorithm and establish Probability Distribution Function related to demographic,which are Age Probability Distribution Function,Death Probability Distribution Function in predict year and Birth Probability Distribution Function of childbearing age women in predict year.And we design a sampling algorithm based on the principle of MCMC random.This algorithm in Wolfram mathematica platform has a large number of simulation experiments, whichconcludes the simulation curve of total,birth and death population from 2015 to 2050 in Henan province. In the end,we analyze the error of the simulation,which shows that the algorithm can effectively simulate population change rule.Finally,we analysis the micro population simulation results based on MCMC algorithm,and it is compared the corresponding macro simulation results, which shows that microscopic model of population prediction proposed in this paper can simulate the ideal prediction results in the number of total,birth and dead population.We analyze microsimulation based on MCMC could get the micro individual change process in the system. Our simulation results show that Micro MCMC computer simulation results are similar to Macro Poly-factor algorithm simulation results when the number of simulation is greater than 5000,which proves its validity and reliability.