Archive for sunrise

snapshop di Padova

Posted in Kids, pictures, Running, Travel with tags , , , , , , , on May 12, 2018 by xi'an

red Capitol [jatp]

Posted in pictures, Running, Travel with tags , , , , , on December 12, 2017 by xi'an

sunrise over Colorado [jatp]

Posted in pictures, Running, Travel, University life with tags , , , , , , on December 11, 2017 by xi'an

[Astrostat summer school] fogrise [jatp]

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2017 by xi'an

[Astrostat summer school] sunrise [jatp]

Posted in Statistics with tags , , , , , , , , , , , on October 10, 2017 by xi'an

unbiased HMC

Posted in Books, pictures, Statistics with tags , , , , , , , on September 25, 2017 by xi'an

Jeremy Heng and Pierre Jacob arXived last week a paper on unbiased Hamiltonian Monte Carlo by coupling, following the earlier paper of Pierre and co-authors on debiasing by coupling a few weeks ago. The coupling within the HMC amounts to running two HMC chains with common random numbers, plus subtleties!

“As with any other MCMC method, HMC estimators are justified in the limit of the number of iterations. Algorithms which rely on such asymptotics face the risk of becoming obsolete if computational power keeps increasing through the number of available processors and not through clock speed.”

The main difficulty here is to have both chains meet (exactly) with large probability, since coupled HMC can only bring these chain close to one another. The trick stands in using both coupled HMC and coupled Hastings-Metropolis kernels, since the coupled MH kernel allows for exact meetings when the chains are already close, after which they remain happily and forever together! The algorithm is implemented by choosing between the kernels at random at each iteration. (Unbiasedness follows by the Glynn-Rhee trick, which is eminently well-suited for coupling!) As pointed out from the start of the paper, the appeal of this unbiased version is that the algorithm can be (embarrassingly) parallelised since all processors in use return estimators that are iid copies of one another, hence easily merged into a better estimator.

maggiore alba [jatp]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , on August 17, 2017 by xi'an