Inference scratch

For $k= 1 ... K$ where $K$ is the length of the MCMC chain, add to the sequence of parameter values :

• Generate a proposed set of parameters $\Theta^*$from the current chimeric parameters using the proposal distribution $$g(\Theta^*|\Theta^C_{m,k-1})$ ;

• Generate an epidemic trajectory with these proposed parameters, $Z(\Theta^*)$

• Calculate the likelihood of the data given the proposed parameters for each subpopulation,

• Calculate the overall likelihood with the proposed parameters,

• Make "global" decision about proposed parameters

  • Generate a uniform random number

  • Calculate the overall likelihood with the current global parameters,

• End making global decision

End for $K$ iterations of each MCMC chain

If $\alpha^G > u^G$: ACCEPT the proposed parameters to the global and chimeric parameter chains

• Set \Theta^G_{m,k} =$$$$\Theta^*

• Set $\Theta_{m,k}^C=\Theta^*$

• Update the recorded subpopulation-specific likelihood values (chimeric and global) with the likelihoods calculated using the proposed parameter ;

Else: REJECT the proposed parameters for the global chain and make subpopulation-specific decisions for the chimeric chain

• Set $\Theta^G_{m,k} = \Theta^G_{m,k-1}$

• Make "chimeric" decision:

  • For

    • Generate a uniform random number

    • Calculate the acceptance ratio

    • If

  • End for subpopulations

• End making chimeric decisions

End if

Else: REJECT the proposed parameters for the chimeric parameter chain for this location

• Set ​

`End if ;