[Statlist] Talk on statistics

[Susanne Kaiser-Heinzmann]

Invitation to a talk in the series Seminar über Statistik

*Monday, November 10, 2008,  11.15-13.00,
with John Haslett, Department of Statistics, Trinity College, Dublin*

*ETH Zürich, Zentrum - ML H 37.1, 11.15-13.00,
Sonnegstrasse 3, 8092 Zürich Statistik*

Sampling the palaeoclimate of the past 15000 years using Bayesian models'

The central difficulty in understanding future climate change -
and most especially possible abrupt climate change - is that most
of what we know about climate derives from data collected over
only the past century or so. Much of the important data - for
example, variation in ice coverage -covers no more than a few
decades, since the advent of satellites. There is almost no ocean
temperature data older than 100 years; similarly there is very
little Southern Hemisphere of any sort older than 100 years.
Access to pre-historic records is indirect and via proxies in
ice-cores, or in sediment in lakes and the ocean.

This paper will report on Bayesian modelling of the European
palaeoclimate for the past 15000 years using pollen data in lake
sediment; specifically it will report on progress since the
proof-of-concept paper read to the Royal Statistical Society in
2006. Technical interest lies in the use of high dimensional
priors based, for different aspects of the problem, on monotone,
long-tailed and Gaussian stochastic processes.

The essential statistical problem may be stated thus. Modern
training data $(y^m, c^m)$ are available, as are ancient data
$y^a$. The task is to study $[c^a|y^a, (y^m, c^m)]$,
by high dimensional Monte Carlo sampling. The y represent
multivariate (here $dim(y) = 28$) counts of different types of
pollen - here dim(y) = 28; c represents multivariate climate -
here $dim(c) = 2$. The key scientific idea is that pollen tells us
about vegetation and vegetation tells us about climate.

One technical statistical task is the Bayesian inversion of a
multivariate non-parametric regression, using Gaussian priors.
We report on progress using Laplace approximations in place of MCMC.

A second is that there are many $y^a$ in a single core representing
many values in a changing climate, depth representing age. The
prior models the entire climate history, jointly. We use a prior
corresponding to a long tailed random walk with Normal Inverse Gaussian 
increments.

Finally, the depth age relationship is incompletely known, but is 
monotone. We use a novel
monotone Compound Poisson Gamma process (Haslett and Parnell, 2008).

Results will be presented that confirm an abrupt change about 10,000 
years ago.
Some aspects of the technical work will be discussed, given time.

The abstract is to be found under the following link:  
http://stat.ethz.ch/talks/research_seminar/2008.

Listeners are welcome!

-- 
ETH Zürich
Cecilia Rey-Lutz		rey at stat.math.ethz.ch
Seminar für Statistik
Leonhardstr. 27, LEO D11	phone: +41 44 6326518
CH-8092 Zurich, Switzerland	fax  : +42 44 6321228