NZIMA Programme on Hidden Markov Models and Complex Systems

Wellington Seminar Series

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.


Seminar 6.

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.


Seminar 7.

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.


Seminar 8.

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.


Seminar 9.

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.


Seminar 10.

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.


Seminar 11.

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.