Bayesian Computation Methods for Inference in Stochastic Kinetic Models

Algorithm 2

Nonlinear PMC targeting .

Iteration ():

1. Draw a set of samples from the proposal density :

(i) at iteration , let .

(ii) at iterations the proposal is the Gaussian approximation of obtained at iteration .

2. For , run a SMC scheme with particles targeting and compute the marginal likelihood

estimate .

3. For , compute the unnormalized IWs

4. For , compute normalized TIWs, , by clipping the original IWs as

,

where the threshold value denotes the -th highest unnormalized IW , with .

5. Resample to obtain an unweighted set : for , let with probability .

6. Construct a Gaussian approximation of the posterior , where the mean vector and

covariance matrix are computed as