Causal Inference Of Observational Data Based On Bayesian Method

Causal inference is a critical research topic across many domains,such as statistics,computer science,education,public policy,and economics,for decades.One fundamental problem in causal inference is the estimation of treatment effect,which is often used in precision medicine,policy intervention and recommendation system.The key is to eliminate the confounding bias caused by the different distribution of confounders between the treatment group and the control group.The best way to eliminate this bias is randomized controlled trial,but due to the limitations of randomized controlled trial,we are most exposed to observational data at present.In this thesis,we estimate the average treatment effect in the Bayesian framework.Firstly,a regression model for outcome variable is established,and then the binary indicator for the treatment is analyzed by probit regression model;After introducing Bayesian framework,normal distribution and inverse gamma distribution priors are applied to the mean and variance in the outcome regression model respectively;For the Bayesian probit regression assumed by propensity score model,the posterior distribution is easy to obtain by introducing the method of latent variable.Secondly,in this thesis,we use the variational inference method to quickly generate posterior samples to derive the posterior inference formula of parameters,and give the VBEATE algorithm.Finally,the effectiveness of the proposed algorithm in estimating the average treatment effect is evaluated through the simulation data in various scenarios.At the same time,an example is analyzed based on the Canadian labor and income data to illustrate the rationality of the method.