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Proposed Change: Adopt Better Adaptive Beahvior for MCMC #364

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mikegilchrist opened this issue Jul 7, 2021 · 0 comments
Open

Proposed Change: Adopt Better Adaptive Beahvior for MCMC #364

mikegilchrist opened this issue Jul 7, 2021 · 0 comments

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@mikegilchrist
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I my experience the adaptive MCMC works, but

  1. seems rather inefficient with the acceptance rates of 4+ amino acid CSP not meeting the target.
    I believe this stems from the fact the only 'memory' is the previous proposal matrix which gets a weighted update based on the most recent acceptance matrix and, as a result, loses information on previous behavior quickly.
  2. Might prevent the algorithm from sampling the stationary distribution while it is on (and, in turn, samples collected immediately afterwards might also be off since the burnin is to something other than the target distribution)

It seems like Vihola (2012) Stat Comput might be a good solution to implement.
Pros:

  • Computationally efficient updating.
    Relies on a rank one Cholesky update/downdate of the the proposal distribution
  • Proven to retain the MCMC's desired behavior of sampling from the posterior distribution

Cons:

  • Updates itself every step
    Seems like we could modify this aspect without violating any assumptions, but it's unclear to me if that's really the case.
  • Requires keeping track of additional parameter gamma which, in turn, requires a few minor settings.
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