This is the tentative Wellington seminar series. **Times, dates and locations
are subject to jitter**.
Visitors are most welcome to these seminars.

**Seminars seem to have finished for the year. The
next event is the
workshop in
December**.

Speaker: **Pierre Ailliot** (VUW and
NIWA) *Markov-switching autoregressive models for wind time series*

(Pierre recently completed a thesis in France on application of hidden Markov and related models to wind behaviour. He is working with Jim Renwick, Peter Thomson and colleagues at NIWA, as well as being part of the NZIMA programme based at Vic).

Time and Place 12 Noon, Friday Sept 30th, Cotton CO249

*Abstract*: Hidden Markov Models (HMM) have successfully
been used to describe different kind of meteorological time-series, the hidden
Markov chain representing the meteorological regime (or *weather type*). In
the case of wind time series, HMM can not catch the strong relation which
exists between successive observations. In this case, Markov Switching
auto regressive (MS-AR) models, which are simple extensions of HMM, suit the
data better. In this talk, I will present several specific MS-AR models which
have been introduced for wind time-series and briefly discuss the statistical
inference in these models.

Speaker: **Paul Malcolm** (Canberra) *Parameter
Estimation for Asset-Price Evolution Dynamics via M-ary Detection*

Time and Place 12 Noon Friday Oct 7th Cotton CO249

*Abstract*:
This seminar reviews joint work with R.J.Elliott. In it we consider a dynamic
M-ary detection problem for Markov modulated partially observed
systems. Here, *Markov modulated* refers to dynamics with one or more parameters which change
value according to a known law. Such systems are sometimes referred to as jump
stochastic systems, or stochastic hybrid systems. The basic detection
objective is to estimate the so-called mode probabilities from an observation
process. The mode probabilities are the estimated conditional probabilities of
a given model parameter set, (taken from a finite list of candidate parameter
sets), being in effect at the time of estimation, or best explaining the data.
The corresponding filtering problem usually concerns utilising these estimated
probabilities to estimate a hidden state process.

In our seminar we suppose that one of M candidate volatility models best explains a given asset price process. Sequential estimators are computed for each of the M candidate models. These schemes compute an estimate for the relative likelihood of a given model explaining an observation process. Two classes of model are considered. In the first model, volatility states are determined by a continuous-time Markov chain. An important practical feature of the detection schemes we compute for this model, is that they do not include stochastic integration. Here we develop a version of the J. M. C. Clark Transformation based on a Hadamard product, resulting in detector dynamics where the observation process appears as a parameter, rather than an integrator. Our main objective is to illustrate how M-ary detection ideas and techniques, developed largely in Electrical Engineering, can be applied to solve common problems in mathematical finance and to present a new transformation technique to eliminate certain stochastic integrations.

Speaker: Xiaogu Zheng (NIWA) *A Mixture Model for
Simulation of Precipitation in the Upper Waitaki Catchment, New Zealand, and
its Relation with Interdecadal Pacific Oscillation*

Time and place: 12 noon, Friday Oct 14th, Cotton CO249 (?)

*Abstract*: We aim to simulate time series of daily
precipitation amounts within a season over many years. The simulated
intraseasonal variability, such as distributions of dry and wet-day durations,
and the means and tails of the distribution of daily precipitation, should be
close to that observed. Simulated interannual variability, such as the mean
and variance of seasonal precipitation totals, should also be close to the
observed. If the observed precipitation is related to a climate variable that
varies on yearly time-scales, then the simulated precipitation should also
show this relation. Such simulations are highly desirable in hydroclimatic
research, particularly, in forecasting the capacity of future hydroelectricity
generation. In this study, we proposed a rainfall generator based on a
mixture model for both precipitation and a climate variable, Interdecadal
Pacific Oscillation index. An EM algorithm is used to estimate the parameters
of the generator. Its application in simulating precipitation in the upper
Waitaki catchment, New Zealand, over 1950-2000 shows that specified the
requirements are achieved to acceptable levels.

Speaker: **Paul Mullowney** (Christchurch) *The role
of variance in capped-rate stochastic growth models*

Time and Place: 12 Noon, Friday Oct 21st, Cotton CO249

*Abstract*: The role of environmental variability in the growth of
larval fish and their subsequent recruitment into the adult population is poorly
understood. In this talk, a capped-rate stochastic growth model is considered
where the underlying feeding mechanism of the fish is based on an M/G/1 or G/D/1
queue. In the first scenario, larval fish (typically cod or herring) encounter
and consume prey (plankton) according to a Poisson process. The service time of
the consumed prey depends on its size and linear (capped-rate) growth occurs
during the *busy periods* of the queue. Distributions for the time to maturity
and recruitment (those fish not consumed by a whale) are analyzed as a
function of the moments of the prey spectra. These results are compared to the
limiting case where all prey have unit size (no variance). In the second
situation (G/D/1), the consumed prey are assumed to have unit size. Here
however, the predator-prey encounter rate is no longer Poisson, with variance
independent from the mean. Distributions for the time to maturity and
recruitment are studied (numerically) as a function of the variance.

Speaker: **Mike Paulin** (Department of Zoology and Centre
for Neuroscience, Otago) *The Neural Particle Filter: A model of neural
computations for dynamical state estimation in the brain*

Time and Place: 12 Noon, Friday Oct 28th, Cotton CO249

*Abstract*: Recent experimental work in collaboration with Larry
Hoffman at UCLA has shown that, as a consequence of fractional order dynamical
characteristics of vestibular sensory transduction mechanisms, single spikes
generated by vestibular motion-sensing neurons can be regarded as measurements
of the dynamical state of the head. We hypothesize that this measurement is
translated into an explicit Monte Carlo representation in the brainstem
vestibular nucleus, which forms a central map of head state. In this
representation, neural spikes are regarded as particles and their spatial
distribution over the map at any instant represents the brain's knowledge of
head state. Particles are constrained to move along axons, corresponding to
pre-defined state trajectories. A network can be constructed so that the
distribution of spikes in the map approximates the Bayesian posterior
distribution of states given the sense data. The neural particle filter model
generates the circuit topology and response properties of real neurons in the
brain, from purely statistical principles.

Speaker: **David Bryant** (Dept. of Mathematics/NZ Institute of
Bioinformatics, University of Auckland) *Continuous and (mostly) tractable
models for the variation of evolutionary rates*

04 Nov 2005, Time: 12:00pm, Seminar Room, Cotton 249

*Abstract: *Applications of hidden Markov models abound in evolutionary
biology. In phylogenetics (the reconstruction of evolutionary history),
evolutionary changes at a position in a sequences are modelled using a
continuous time Markov chain. Under conventional models, the rate of change is
constant. This is unrealistic, and several models have been proposed to capture
the variation in rates. In this talk, I'll give a general introduction to Markov
models used in phylogenetics, and then describe a model that does allow
variation in rate. The evolution at a site is still modelled using a continuous
time Markov chain, however the rate of change is governed by a random diffusion
called the CIR process. We have derived exact formula for the transition
probabilities under this model. I'll finish with a discussion of several models
for which I would dearly like to have transition probabilities but which,
unfortunately, appear intractable. This is joint work with Thomas Lepage,
Stephan Lawi and Paul Tupper.