Workshop on Bayesian Inference at ISM
Taking advantage of the simultaneous presence of different international
researchers in Tokyo by mid-august, an informal workshop on Bayesian Statistics
will be held on August 21th 2007 at the Institute of Statistical Mathematics,
Tokyo, Japan. Many thanks to all speakers and participants!
NEW: Slides can be downloaded below!
[ Program ]
| 15:15 - 15:20 | Opening Remarks | |
| 15:20 - 16:00 | Tutorial: Inference methods for Nonparametric Bayes models | Naonori Ueda |
| 16:00 - 16:55 | The Infinite Markov Model: A Nonparametric Bayesian approach | Daichi Mochihashi | | 16:55 - 17:10 |
Break |
| 17:10 - 18:05 | Particle Markov chain Monte Carlo: Applications to Non-linear Dynamic Models | Arnaud Doucet |
| 18:05 - 19:00 | Inference for Levy driven stochastic volatility models via sequential Monte Carlo | Ajay Jasra |
[ Access ]
Please follow this link for access
information. The Workshop will be held in the Kenshu-Shitsu room
(2F).
[ Organizer ]
Please contact Tomoko Matsui for any questions
regarding the workshop.
[ Detailed Program And Slides]
| slides | Tutorial: Inference methods for Nonparametric Bayes models | Naonori Ueda |
| Nonparametric Bayes modeling, specifically, Dirichlet process mixture (DPM)
modeling have been at the center of recent research in machine learning.
The major difference between parametric Bayes and nonparametric one is
that in the latter the number of mixture components can infinitely increase
depending on the number of observed samples. This flexible modeling has
attracted both basic reseachers and practitioners. In this talk, focusing
on practical inference methods for DPM models, first I will briefly review
the basics of DPM models, and then will explain several inference methods
based on the variational approximation and Markov chain Monte Carlo. I
also show the Gibbs sampling methods for hierarchical Dirichlet process
mixture (HDM) models. |
| slides | The Infinite Markov Model: A Nonparametric Bayesian approach | Daichi Mochihashi | | Markov models are very simple but effective tools widely employed in discrete
sequence modeling, such as natural language processing, music modeling,
compression, and bioinformatics. However, the crucial problem with a Markov
model is that we must determine its order. Not knowing the true Markov
orders in advance, this restriction often imposes us using short and fixed
range dependencies that are set heuristically to avoid an explosion in
the number of parameters associated with the model. In this talk, we will
present a complete nonparametric Bayesian generative model of variable
order Markov sequences. Introducing a simple prior over the tree structures
of hierarchical Chinese Restaurant processes, our model can infer the latent
Markov orders from which each symbol originated. We show that it also yields
an efficient inference and scientifically interesting results on language
streams of words and characters. This model can interpreted as a complete
Bayesian replacement of the pruning approaches to variable order Markov
models by Buhlmann (1999) in statistics and Ron et al. (1994) in machine
learning. |
| slides | Particle Markov chain Monte Carlo: Applications to Non-linear Dynamic Models | Arnaud Doucet |
| Markov chain Monte Carlo (MCMC) are now routinely used to perform Bayesian
inference but, for complex models, standard MCMC algorithms mix slowly
and can easily get trapped in local maxima. In this talk, I will present
a new method to build very high dimensional proposal distributions for
MCMC and will demonstrate its performance on non-linear state-space models.
Our method relies on Sequential Monte Carlo/particle filtering methods.
It can be interpreted as an extension of the popular Configurational Bias
Monte Carlo (CBMC) method developed in molecular simulation but it enjoys
much nicer theoretical properties than CBMC and outperforms this latter
by several orders of magnitude in simulation. |
| slides | Inference for Levy driven stochastic volatility models via sequential Monte
Carlo | Ajay Jasra |
| In the following talk I investigate simulation and inference for a class
of continuous-time stochastic volatility (SV) models: when the price includes
an additive variance gamma process. This model assumes that movements of
the log price of an asset is modelled through a Brownian and L\'evy component,
with the volatility process following a correlated diffusion (a Cox-Ingersoll-Ross
model). The infinite activity nature of the driving gamma process can capture
the observed behaviour of many financial time series, and a discretized
version has been found to be very useful for modelling such (daily) data.
However, it is well-known that when a fine-scale discretization of the
diffusion is adopted, Markov chain Monte Carlo (MCMC) methods can mix very
slowly. In this paper we introduce an approach which can be more efficient;
we can provide more accurate discretizations of the diffusions, and simultaneously
maintain a better mixing MCMC algorithm. In addition, for complex problems,
we introduce a fully adaptive sequential Monte Carlo (SMC) sampler algorithm
to simulate from the posterior density. Our approach can be adopted for
any SV model where discretization is required (that is, exact inference
is not currently possible). We illustrate the methodology with an analysis
of high frequency (5 minute) S&P 500 share index data. From the inferential
point of view, we find that the discretized variance gamma model does not
capture, at least, the correlation structure of the volatility and is not
always appropriate for high frequency financial data. |
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