Cosmologists discover Bayesian design …

I’ve been a bit too busy lately taking care various housing issues in Oxford to work up any significant new blog posts (e.g. to discuss last week’s intriguing/confusing contribution from Jasche & Lavaux), so just a quick update today to keep the ball rolling …

I noticed a new paper on astro ph (Seehars et al.) describing work by cosmologists at ETH Zurich (one of my previous institutions; and indeed the author list includes a friend of mine, Adam Amara) presenting the Kullback-Liebler divergence as a measure of the information gained in posterior parameter updates from a series of experiments; and hence as a Bayesian design criterion.  Sorry to say but for statisticians these ideas are really quite ‘old hat’, having been covered by studies dating back to the 1970s (and conceptually, although not ‘computationally’, even earlier than that): e.g. Bernado 1979 and see Chaloner & Verdinelli 1995 or Clyde 2005 (who has, I notice, been to a few astrostats conferences) for reviews.  So I was a little surprised that they are new ideas to cosmology; but we have indeed seen time and time again the lack of communication between the astronomical and statistical fields.  I’m sure there must be (Bayesian) experimental design statisticians with students/postdocs looking for interesting application challenges, on the one hand—and stats-curious cosmologists, on the other, who we could match up for some high-powered collaboration??  I’m willing to provide an introduction service here for payment in Swiss francs to my secret numbered account only.

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11 Responses to Cosmologists discover Bayesian design …

  1. It is an old idea and it certainly seems “right” to me, but it’s bloody hard to actually calculate. People who think the marginal likelihood is hard should try this!

  2. Chris Drovandi says:

    SMC can be quite useful for estimating this, see for example
    http://www.sciencedirect.com/science/article/pii/S0167947312002137

    • Interesting, Chris … I forgot you’d been working on SMC design solutions! This afternoon I’ll be attending the comp stat reading group to hear about a neat trick (PGAS) for improving the mixing of SMC in (particularly non-Markov) state space models (which I’ll probably blog about next week): http://arxiv.org/abs/1401.0604

      • Chris Drovandi says:

        Sweet as. Yeah particle Gibbs was a hot topic at MCMski. Sort of came out of nowhere given the initial popularity of PMMH. I must admit to only understanding particle Gibbs at a very high level.

  3. One application we could have here is to an SIR type epidemiological model where the compartment transition probabilities at the current time depend on what the balance of states was at all previous times due to the effect of exposure-driven immunity.
    Did you shred it up on the slopes btw.?

  4. Do either of you have a good introductory reference for this particle stuff? I tried reading some Doucet papers back in the day, but found them impenetrable. I want to know if I’m missing out on something by focusing on MCMC.

    • Liu’s “Monte Carlo Strategies in Scientific Computing” is a great reference: esp. the target tracking example of section 1.6 and then chapters 3 & 4 are specifically about SMC.
      The Doucet paper has been described as famously impenetrable, which is fair because they describe about 5 variants of SMC simultaneously and switch from one to the other every few paragraphs!
      Chris might have some more suggestions?

      • Thanks! I’ll check it out.

        “The Doucet paper has been described as famously impenetrable, which is fair because they describe about 5 variants of SMC simultaneously and switch from one to the other every few paragraphs!”

        Lol. I’m glad it’s not just me.

  5. Adam Amara says:

    Hi Ewan,

    Happy to hear you noticed our recent paper. Just to note a couple of things. This isn’t the first time that relative entropy has been used in Cosmology – it’s not even the first paper on the topic that I’ve been on. I’m sure that you remember, Julian used to bring interesting things to talk about along these lines to astro-ph discussions. Such as his first paper in 2011 that tried to look at lensing differently. That said, it’s true that a lot of the materials covered in Sebastian’s paper are not common knowledge in Cosmology, so he has had to recap things and point to appropriate textbooks and reviews. The most interesting thing about his work is the main results table, which I think is important. Also getting stable results was tricky, but Sebastian is very carful and methodical so I trust what he’s done.

    Let me know when you’re in Zurich. It would be great to meet up.

    Adam

  6. lindonslog says:

    “who we could match up for some high-powered collaboration??”
    I’m a PhD student of Merlise Clyde and have an MPhys from Warwick and we are both interested in the application of Bayesian methods to astrophysics data. If you have an application and a data set then lets talk – my email is on the about page of my blog.

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