How to calibrate a model to multiple data sets?
This is related to meta-analysis where we may have more than one study informing model parameters. A possible way of approaching this problem could be split in to three
- Combine the data sets before doing a single calibration
- Perform separate, multiple calibrations for each data set and then combine the set of model parameters afterwards
- Use each data set one at a time in a sequential fashion
This last approach is what we will pursue in this work. One sequential approach is to use the ABC posterior after analysing the
This is an idea taken from
Fearnhead, P. and Prangle, D. (2012) ‘Constructing summary statistics for approximate Bayesian computation: Semi-automatic approximate Bayesian computation’, Journal of the Royal Statistical Society. Series B: Statistical Methodology, 74(3), pp. 419–474. doi: 10.1111/j.1467-9868.2011.01010.x.
Calculate a set of approximate likelihoods, one for each data set.
Then sequentially update each posterior