Measurement error model with a large sample?



I have a large sample of data – around 360,000 data points. I am trying to fit a simple measurement error model to start. Though ideally would like to fit this measurement error model within a hierarchical model structure.

Given the Bayesian measurement error treats each data point as an unknown parameter this becomes untenable to estimate (i.e. it takes days to compute) given our sample size.

What would you recommend?

Thank you,