Riemann, Langevin, Hamilton, &tc

Today was the deadline for sending discussions on the Read Paper by Girolami and Calderhead. Along with Magali Beffy (who is doing a PhD with Nicolas Chopin and myself) and Jean-Michel Marin, we submitted three discussions, running along the arguments made in this earlier post. They are available as

  1. Marin and Robert’s discussion,
  2. Beffy and Robert’s discussion,
  3. Robert’s discussion.

6 Responses to “Riemann, Langevin, Hamilton, &tc”

  1. […] (I think I rediscovered the topic during the talks, rephrasing almost the same questions as for Girolami’s and Calderhead’s Read Paper!) One thing that still intrigues me is the temporal dimension of the Hamiltonian representation. […]

  2. Links 1 and 3 should be swapped, shouldn’t they ?

  3. I still don’t see how that works with the non-Gaussian likelihood terms. As far as I know, the standard algorithm for the SV model is still the mixture sampler of Kim et al, 1998. I haven’t tried this, but I would guess that the manifold HMC sampler would have comparable performance?

    • Tim, sorry for the terrible delay in replying. I aimed at checking this and could not find the time. Now the deadline for closing the discussion has come and gone, and I am still unsure about this! Each non-Gaussian term can be simulated by an accept-reject algorithm proposed in Cappé et al. (my copy has been lost, hence the lack of reply!), but this does not mean the whole sequence is manageable (as a whole)…

  4. Interesting discussions!

    In 3. you write “We however wonder at the appeal of this involved scheme when considering that the full conditional distribution of the volatility can be simulated exactly.”

    I take it you mean that each volatility component x_i can be sampled conditional on all the other x_j’s (and the parameters) Gibbs style? Don’t you think this would give huge autocorrelation in the draws?

    • Blame the 400 word limit on Read Paper discussions for the lack of clarity! What I meant by this cryptic comment is that a stochastic volatility model being a Gaussian hidden Markov chain allows for a closed form representation of the joint, not only of the full conditionals as in an inefficient Gibbs sampler… Details are in Cappé et al. (2005)

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