simulated summary statistics [in the sky]

Posted in Statistics with tags , , , , , , , on October 10, 2018 by xi'an

Thinking it was related with ABC, although in the end it is not!, I recently read a baffling cosmology paper by Jeffrey and Abdalla. The data d there means an observed (summary) statistic, while the summary statistic is a transform of the parameter, μ(θ), which calibrates the distribution of the data. With nuisance parameters. More intriguing to me is the sentence that the correct likelihood of d is indexed by a simulated version of μ(θ), μ'(θ), rather than by μ(θ). Which seems to assume that the pseudo- or simulated data can be produced for the same value of the parameter as the observed data. The rest of the paper remains incomprehensible for I do not understand how the simulated versions are simulated.

“…the corrected likelihood is more than a factor of exp(30) more probable than the uncorrected. This is further validation of the corrected likelihood; the model (i.e. the corrected likelihood) shows a better goodness-of-fit.”

The authors further ressort to Bayes factors to compare corrected and uncorrected versions of the likelihoods, which leads (see quote) to picking the corrected version. But are they comparable as such, given that the corrected version involves simulations that are treated as supplementary data? As noted by the authors, the Bayes factor  unsurprisingly goes to one as the number M of simulations grows to infinity, as supported by the graph below.

València 9 snapshot [1]

Posted in Mountains, Running, Statistics, Travel, University life with tags , , , , , on June 5, 2010 by xi'an

Last morning, I attended the talks of Michael Goldstein and Herbie Lee, which were very interesting from very different perspectives. Michael talked about computer models, like the climate models that have been so much attacked recently for being “unrealistic”. The difficulty is obviously in dealing with the fact that the model is incorrect, what Michael calls external uncertainty. As statisticians, we are trained to deal with internal uncertainties, i.e. those conditional on the model. Michael did not propose a generic solution to this difficult problem, but he presented a series of principles towards this goal and his paper in the proceeedings (I have not [yet] read) contains examples of conducting this assessment. (I am not sure building a [statistical] model on top of the current [physical] models stands a chance to convince climato-skeptics, but this is interesting nonetheless.) Herbie addressed a completely different problem, namely the maximisation of a function under constraints when the constraints are partly unknown. (Think of a set whose boundaries are not precisely known.) This was a problem new to me and I plan to read the paper asap, as the design perspective added to the maximisation per se is made in order to decide about the worth of making new [costly] evaluations of the function to maximise.

Otherwise, the morning was spent in a fruitless pursuit of a wireless connection in the hotel where the conference takes place, as so many people were trying to connect at the same time! I eventually resolved the issue by crossing the road to an internet café and renting an ethernet cable for one hour. The hotel is unsurprisingly the soulless and unhelpful place I expected and I do not find any appeal in the high rise landscape constituting the neighbourhood. There is however a small track in the bush nearby that makes for a good running place in the early morning. (Finding a cliff that is both bolted and in the shade is going to prove a challenge!)