EpiABC Posterior Performance about epiabc HOT 4 OPEN

Solution 1: Estimate parameters attuned to HIV prevalence and STI rates separately; i.e. f_1 and f_2 are two separate ABC processes targeting 10.86 and 0.26 respectively.
Result: Convergence issues for HIV prevalence. Low HIV prevelance when using rates estimated from STI target stats only.

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Solution 2: Change estimation algorithm from Lenormand to Drovandi. The Lenormand method attempts to filter posterior through waves, settling on a final sample posterior when proportion of new candidate particles falls below a pre-set threshold. The Drovandi method instead advances through steps using a pre-specified tolerance level (difference between simulated and sample data).
Result: Drovandi method produces "similar" results to that of Lenormand.

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Solution 3: Diagnose each of the epi. curves associated with particles that are accepted under Lenormand algorithm. Note - proper posterior sampling is crucial. Can not just select mean of each posterior when re-simulating (minimum tolerance, i.e. maximum of obj. fuction, is not neccesarily achieved at mean of individual posteriors. For example given theta = (x1, x2,x3), minimum distance to targets stats may not be achieved at mean of x4).
Question: particle filtering is based on one run of EpiModel (N = 1). Is this done in practice? No, multiple simulations are run, and a smoothed curve is produced (targets stats as mean, with variability). Should we be filtering particles based on a single run or on their ability to, over N sims, produce epi. stats close to target stats? Why would this be 'better?' What is the difference between the two?
Result: Pending (4/16) Looking at multiple runs for each accepted particle from ABC method, with N = 100. Will look at (S-S_obs) where S is simulation statistics and S_obs are observed statistics. Essentially, recovering tolerance for individual particles, but N = 100 vs N = 1.

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Update: 5/17/2019
Transitioning to new ARTnet workflow; only focused on HIV prevalence. Will make calibration easier (one statistic versus two) however should still focus on a solution that allows for multivariate target statistic calibration.

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