Setting informative priors from pilot study for lognormal model


#1

Hi all,

I’m new to Bayesian statistics using brms and stan, hence apologies if my question seems very basic.

I’m trying to fit a regression model in brms with informative priors. The prior knowledge is based on a previously conducted pilot study, for which I produced posterior distributions of the intercept, group level effects and population level effects. I am then using this information of the posteriors from my pilot study as priors for my actual study (including of course only the recent data collected).

My pilot model was:
fitdur <- brm(formula = Duration ~ DSI + rankdiff + agediff + sexcode +(1|Initiator), data=entryduration, family=lognormal(), warmup= 1000, iter = 2000, chains = 4, control = list(adapt_delta = 0.99, stepsize=0.01, max_treedepth=15))

I am, however, struggling to understand how to set the right distribution of priors for my final updated model; I see that, by using prior_summary, the default priors of my pilot model were all student-t-priors. But since I used a model with the family “lognormal”, I wonder whether I should change the default priors of my final, updated model (including the new data collected and the prior of the pilot study) to lognormal priors for all parameters (i.e., intercept, b’s, sd, sigma)? Or, should I leave the default prior distributions as they are and just insert the posterior means and sd of my pilot model? If so, should I transform these values (means and sd), considering they stem from a lognormal model?
As a more general question - should you inform your model by including the distribution of your previous posteriors as your new prior distributions?

Any advice would be of great help, thank you!

Best, Raphaela


#2

There is no reason to set priors to lognormal just because your likelihood is lognormal.

If you analyse your final data set including both data from pilot and main study, I wouldn’t let the priors be informed too much by the data of the pilot study, because then you end up including this data twice into your model (one as data and one as prior).

If you have the raw data of previous studies available, I would usually prefer putting all data into the same model (with extended structure) instead of trying to use the posterior of one study as prior of the other. The latter is really hard to do correctly.


#3

Thanks for the tip!

In this case, I was not planning to include both the data from pilot and main study in my final model; my plan was to include only the raw data from the main study and the posteriors of the pilot study as priors.