## Workshop: Topics in Advanced Monte Carlo Methods

March, 9-10 2016

The Institute of Statistical Mathematics

Tachikawa, Tokyo

Room
Seminar Room 4 (3F): D312B

Organizers
Yukito Iba (ISM)
Koji Hukushima (University of Tokyo, Komaba)

### Abstract of Invited Lecture

Arnaud Doucet (Oxford)

TALK 1: New MCMC methods to perform Bayesian inference in latent variable models

Pseudo-marginal methods have become very popular in statistics over the past 5-10 years to perform inference in latent variable models such as state-space models. However, in many scenarios, their computational complexity is essentially of order T^2 at each iteration when one has T data points. We will show that it is possible to obtain an alternative algorithm of computational complexity T (up to logarithmic factors) to address similar problems. In our numerical examples, the efficiency of computations is increased relative to the pseudo-marginal algorithm by several orders of magnitude.

TALK 2: Transport-based ideas for Monte Carlo simulation

A measurable function T mapping R^d to itself such that $T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is called a transport map transporting the measure $\pi_{0}$, e.g. a prior distribution, to $\pi_{1}$, e.g. a posterior distribution. If one could obtain an analytical expression for a transport map from any $\pi_{0}$ to any $\pi_{1}$ then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distribution $\pi_{0}$ to the target distribution $\pi_{1}$ using this transport map. Although it is usually impossible to obtain an explicit transport map for complex target distributions, we show here how to build a tractable approximation of a novel transport map. This is achieved by moving samples from $\pi_{0}$ using an ordinary differential.

### March 9 (Wed.)

13:30-15:00
Arnaud Doucet (Oxford)
TALK 1: New MCMC methods to perform Bayesian inference in latent variable models

(break)

15:30-16:10
Yukito Iba (ISM) and Shinichi Takayanagi(SOKENDAI)
Sampling time-reversed path ensembles

### March 10 (Tur.)

10:30-11:30
Arnaud Doucet (Oxford)
TALK 2: Transport-based ideas for Monte Carlo simulation

(lunch break)

13:00-13:40
Masayuki Ohzeki (Kyoto Univ)
Accelerated Langevin Dynamics and its applications

13:40-14:20
Kazutaka Takahashi (Tokyo Inst. Tech.)
Optimization of Markov process violates detailed balance condition

(break)

15:00-15:40
Hidemaro Suwa (Univ. of Tokyo)
Irreversible Quantum Monte Carlo Algorithm and Unbiased Spectral Gap Estimation

15:40-16:20
Koji Hukushima (Univ. of Tokyo)
Event-chain Monte Carlo algorithm for continuous spin systems