Bayesian combine semiologies: how to

[thenineteen]

When using the Bayesian method with multiple semiologies, we can do the following:

1. treat each dataset separately. This is what is done in #222 . Concretely, using the SS dataset, it combines the semiologies (e.g. inverse variance) then using posterior-TS it combines the semiologies (using inverse variance), then takes the mean of the two estimates.

2. Instead, integrate the SS and posterior-TS estimates per semiology first, then combine semiologies using inverse variances.

Could argue for both: the second method gives a single estimate for each semiology, then combines. The first method queries each database separately for all the semiologies, then combines the results at the end.

Which is best?

[thenineteen]

3. give the same combining semiology options to Bayesian-TS data and SS data integration, as SS each have individually:
   • inverse variance with marginal probabilities or data-query estimates for variances
   • equal weights/mean,