Comments for València 9

Following discussions at CREST, we have contributed comments on the following papers

Bernardo, José M. (Universitat de València, Spain)
Integrated objective Bayesian estimation and hypothesis testing. [discussion]

Consonni, Guido (Università di Pavia, Italy)
On moment priors for Bayesian model choice with applications to directed acyclic graphs. [discussion]

Frühwirth-Schnatter, Sylvia (Johannes Kepler Universität Linz, Austria)
Bayesian variable selection for random intercept modeling of Gaussian and non-Gaussian data. [discussion]

Huber, Mark (Claremont McKenna College, USA)
Using TPA for Bayesian inference. [discussion]

Lopes, Hedibert (University of Chicago, USA)
Particle learning for sequential Bayesian computation. [discussion]

Polson, Nicholas (University of Chicago, USA)
Shrink globally, act locally: Sparse Bayesian regularization and prediction. [discussion]

Wilkinson, Darren (University of Newcastle, UK)
Parameter inference for stochastic kinetic models of bacterial gene regulation: a Bayesian approach to systems biology. [discussion]

(with a possible incoming update on Mark Huber’s comments if we manage to get the simulations running in due time).

9 Responses to “Comments for València 9”

  1. [...] to make any sense to a decision analyst. Or even to a statistician. We discussed earlier the València 9 paper of Guido Consonni, in connection with more realistic loss functions. Also the authors seem to [...]

  2. [...] paper on Riemann manifold Langevin and Hamiltonian Monte Carlo methods and I hope we will again produce a joint arXiv preprint out of our comments. (The above picture is reproduced from Radford [...]

  3. [...] in the fields of statistics and econometrics. Arnold was 83 and, although I had met him in several Valencia meetings—including one in Alicante where we sat together for breakfast with Persi Diaconis and  [...]

  4. [...] wonder how closely related the second (volume tesselation) algorithm is to Huber and Schott’s TPA algorithm, in the sense that TPA also requires of a “smaller” [...]

  5. Clearly I need more education in measure theory.

    • Corey, this is a subtlety of measure theory and a lot of people are convinced that MAP estimators are associated with 0-1 losses. Actually, in Bayesian Choice (Section 4.1.2, MAP estimator), I actually justify the use of the MAP via a limit of estimators associated with a sequence of losses, but this is only an approximation. Strictly speaking, the MAP estimator is not a decision-theoretic object!

  6. [...] reading Christian Robert’s blog highlighting some of the discussion of the invited program for Valencia 9, I realized that the entire invited program was available on the Valencia website. For anybody who [...]

  7. I noticed that in your comments on the “Shrink globally, act locally” article, you wrote that MAP estimators do not fit in a decision-theoretic framework. If the loss function is -delta(estimate – true_val), (mathematically capturing the the English idiomatic expression “a miss is as good as a mile“) then the expected loss of the estimate is the negative of the probability density, and is minimized by the MAP estimator. It’s true that that’s a brutal loss function, but sometimes life isn’t fair. How does the above argument fail?

    • The problem with the delta loss function in continuous settings is that if you consider it as an indicator function (1 everywhere except at a specific value) the expectation of the loss function is always one by measure theoretic arguments: the value at a given point does not matter. To make a difference at the MAP, you would need to use the delta function as a distribution, which is not acceptable… Besides, the MAP depends on the dominating measure, another difficulty…

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