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How do I provide a prior distribution for a coefficient with mean in the range 1e-05 and standard deviation (sd) in the range 1e-06?

What are the distributions to choose for such high precision (sd <= 1e-06) parameters in rstanarm?

1) Student t family

2) Hierarchical shrinkage family

3) Laplace family

4) Dirichlet family

5) others

I have tried using prior = normal(location = 1e-05, scale = 1e-06, autoscale = FALSE), but it takes a lot of time for sampling.

Mukund Komati
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I think prior = normal(location = 1e-05, scale = 1e-06, autoscale = FALSE) is your best bet. The fact that it takes a lot of time for sampling is not an indication that anything is wrong with the draws it produces. But I would multiply the outcome by 1 million or divide the predictor by 1 million so that prior = normal(location = .1, scale = 1, autoscale = FALSE) is sensible.

Ben Goodrich
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  • Thanks for the suggestion, re-scaling has significantly improved sampling time. Also, what does prior_PD = TRUE and QR = TRUE mean inside stan_lmer(...) call? How does it effect the computation? – Mukund Komati May 29 '20 at 15:59
  • Both (actual all) of those arguments to `stan_lmer` are [documented](http://mc-stan.org/rstanarm/reference/stan_glmer.html). – Ben Goodrich May 29 '20 at 16:33