Archive for Kii peninsula

non-reversible guided Metropolis–Hastings

Posted in Mountains, pictures, Statistics, Travel with tags , , , , , , , , , , , , on June 4, 2020 by xi'an

Kengo Kamatani and Xiaolin Song, whom I visited in Osaka last summer in what seems like another reality!, just arXived another paper on a non-reversible Metropolis version. That exploits a group action and the associated Haar measure.

Following a proposal of Gustafson (1998), a ∆-guided Metropolis–Hastings kernel is based on a statistic ∆ that is totally ordered and determine the acceptance of a proposed value y~Q(x,.) by adding a direction (-,+) to the state space and moving from x if ∆x≤∆y in the positive direction and if ∆y≤∆x in the negative direction [with the standard Metropolis–Hastings acceptance probability]. The sign of the direction switches in case of a rejection. And the statistic ∆ is such that the proposal kernel Q(x,.) is unbiased, i.e., agnostic to the sign, i.e., it gives the same probability to ∆x≤∆y and ∆y≤∆x. This modification reduces the asymptotic variance compared with the original Metropolis–Hastings kernel.

To construct a random walk proposal that is unbiased, the authors assume that the ∆ transform takes values in a topological group, G, with Q further being invariant under the group actions. This can be constructed from a standard proposal by averaging the transforms of Q under all elements of the group over the associated right Haar measure. (Which I thought implied that the group is compact, except I forgot to account for the data update into a posterior..!) The worked-out example is based on a multivariate autoregressive kernel with ∆x being a rescaled non-central chi-squared variate. In dimension 24. The results show a clear improvement in effective sample size per second evaluation over off-the-shelf random walk and Hamiltonian Monte Carlo versions.

Seeing the Haar measure appearing in the setting of Markov chain Monte Carlo is fun!, as my last brush with it was not algorithmic. I would think the proposal only applies to settings where the components of the simulated vector are somewhat homogeneous in that the determinationthe determination of both the group action and a guiding statistic seem harder in cases where these components take different meaning (or live in a weird topology). I also lazily wonder if selecting the guiding statistic as a gradient of the log-target would have any interest.

夢幻花 [Dream flower]

Posted in Statistics with tags , , , , , , , , , , , on January 18, 2020 by xi'an

Another Japanese mystery novel by Higashino Keigo, which I read in French under the title La fleur de l´illusion [on a sunny Sunday afternoon, under my fig tree] and enjoyed both for its original, convoluted (and mostly convincing) plot and for the well-rendered interaction between the young protagonists. And also for having a few connections with my recent trip, from one protagonist studying nuclear physics at the University of Osaka to a visit to the back country of Katsuura. (The author himself graduated from Osaka Prefecture University with a Bachelor of Engineering degree.) Spoiler warning: the only annoying part of the plot was the resolution of the mystery via a secret society run by a few families of civil servants, which as always sounds to me like a rather cheap way out. But not enough to ruin the entire novel.

 

Japanese mushrooms [jatp]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , on October 12, 2019 by xi'an

the three Kumano shrines [jatp]

Posted in Statistics with tags , , , , , , , , on August 26, 2019 by xi'an

bye and thank you for all the fish!

Posted in pictures, Travel with tags , , , , , , , , , , on August 24, 2019 by xi'an