矩约束条件下测量误差数据的贝叶斯推断

Bayesian Inference of Measurement Error Data Under Moment Constraints

在贝叶斯统计中,如果没有足够的模型信息构造似然函数,可以利用广义矩估计方法构造拟似然用于相关问题的推断。然而,这一方法在实际应用中经常由于数据含有测量误差而不能直接使用。文章研究矩约束条件下测量误差数据的贝叶斯推断问题,通过结合矩约束拟似然方法和非参数贝叶斯方法,解决了矩约束条件下包含测量误差数据的统计推断问题。最后将该方法应用到含有测量误差的回归模型中,证明了该方法的可行性。

The generalized method of moments can be used to construct quasi-likelihood for the inference of related problems if there is not enough model information to construct a likelihood function in Bayesian statistics.However,this method can not be used directly in practical applications because the data contains measurement errors.This paper studies the Bayesian inference of measurement error data under moment constraints,solves the statistical inferences with measurement error data under moment constraints by combining the moment-constrained quasi-likelihood method and the non-parametric Bayesian method.Finally,the paper applies the proposed method to the regression model with measurement errors,which confirms the feasibility of the new method.