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Im trying to implement ABC SMC for ODE model which has 2 parameters to estimate. I stopped in the step when calculating the weights as it appear in this answer. My question is should I calculate the weights for each parameter separately and then use this weights to resample ( each parameter will have its own weights vector) !! or should I calculate common weight for all the parameters?

Xi'an
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Sarah
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  • What do you mean the weights for each parameter? Are you doing some form of Gibbs ABC? – Xi'an Mar 19 '20 at 10:50
  • No,I estimate both parameters (beta and delta), in the same time. I calculate the weights for each accepted parameter pair separately. Thus, I will have two different vectors of weights, one for beta and one for delta. Then I use this weights (after normalising) in the kernel to re sample. Is that correct or I suppose have a common vector of weights for both parameter! I'm confused. – Sarah Mar 19 '20 at 11:35
  • You are supposed to have a single vector of weights, ie prior / importance density. I do not understand where the two vectors of weights come from. – Xi'an Mar 19 '20 at 15:34
  • so the calculation of the weight for two parameters will be: w=prior(beta)*prior(delta)/ sum( weights[t-1,]*dnorm(beta)*dnorm(delta)), where dorm is the kernel density for beta and delta, and weights[t-1,] is the weights from pervious population? – Sarah Mar 19 '20 at 23:11
  • Yes, this is exactly the case. Note that we recently studied a [Gibbs version of ABC](https://arxiv.org/abs/1905.13599) where ABC can be run one parameter at a time, but it would seem delicate to combine it with SMC. – Xi'an Mar 20 '20 at 08:01
  • Thanks, this help a lot. – Sarah Mar 20 '20 at 08:21

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