1
$\begingroup$

I want to estimate the required sample size to reach a specified width (precision) of the Bayesian credible intervals of the parameter of interest by using the standard error (posterior standard deviation) returned by the Bayesian regression for that parameter.

Does it make sense to use the standard error formula to obtain the (crude approximation of the) required sample size by plugging in the known standard error?

For example, if I get a SE = 4 with N = 500, can I calculate the required N to obtain SE = 1 by using $SE = s / \sqrt{n}$?

$\endgroup$

1 Answer 1

1
$\begingroup$

In principle you can do this, but you have to correct for autocorrelation in the Markov chain. This is done by various packages (e.g. coda) that calculate naive (uncorrected) and corrected SEs for the mean and other statistics (see summary in coda). With coda, you can also calculate what is called the "effective sample size", i.e. an effective n for the Markov Chain, corrected for autocorrelation. You could use the effective sample size in your formula, if you want to calculate SEs for non-standard outputs.

Note, however, that this method assumes that the autocorrelation is homogenous, while in practice it often changes when the MCMC explores different areas of the parameter space. If that is the case, correcting with the average autocorrelation is likely anti-conservative.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.