Research opportunities in Hidden Markov Models & Complex Systems


The New Zealand Institute of Mathematics and its Applications (NZIMA) is sponsoring a programme on Hidden Markov Models & Complex Systems (HMMCS) as part of its overall programme for 2005. The HMMCS programme provides funds for post-doctoral and post-graduate research as set out below. The general aim of the HMMCS programme is to enhance the work on stochastic modelling and forecasting via hidden Markov models currently being undertaken or planned in New Zealand. Successful applicants will be attached to one or other of the research groups working on these topics in New Zealand. These include, among others, groups working on earthquake modelling and probability forecasting (in Wellington); modelling of economic and financial time series (in Wellington); modelling of rainfall and meteorological processes (in Wellington); developments in image reconstruction and related techniques (in Auckland), electrical engineering applications (in Christchurch). The fellowships and scholarships will be available from the beginning of the 2005 academic year (March 2005) onwards.

Post-Doctoral Fellowship

The deadline for applications is is well in the past and and some of the successful applicants are now in Wellington. If additional money becomes available it will be noted here.

General. The NZIMA invites applications for one 2-year (or possibly two 1-year) post-doctoral fellowships to be held in conjunction with its HMMCS programme. The post-doctoral fellow will be attached to one of the New Zealand universities (most probably but not necessarily Victoria University of Wellington), but will be expected to spend some time discussing HMM work with scientists in other centres.

Qualifications required. The successful applicant should have a PhD degree in some branch of probability theory or statistics, some initial acquaintance with HMM models, EM algorithm or related inference procedures, and an interest in applications. Some experience with point processes and/or stochastic differential equations would be an additional advantage, as would experience in statistical inference and simulation procedures.

Salary. NZ$55,000/year.

Starting date. Any time from 1st April 2005. It would be desirable for the appointee to be in place in time to participate in the first HMMCS Workshop, 29th June-1st July, 2005.

Application procedure. Applications should be sent to: Margaret Woolgrove, Executive Director, NZIMA, Auckland (e-mail m.woolgrove at, with a copy to the Programme Director, David Vere-Jones, Statistics Research Associates, Wellington, e-mail dvj at

Information needed. The application should include a copy of the applicant's cv, with a half-page statement of his/her current interests and research experience, and the names of three persons who would be willing to be approached for a reference. The applicant should also indicate the date at which he/she would be available to take up the fellowship, and any initial preferences for the particular application area and/or location within New Zealand.

Special circumstances. The applicant may also indicate whether there are special circumstances which might justify him/her in seeking special consideration for additional travel or relocation allowances.

Deadline for applications. Please email expressions of interest by 14th February with a final application by 21st February, 2005.

Post-graduate Scholarships (PhD & Masters)

General. The NZIMA invites applications for PhD and MSc scholarships associated with its HMMCS programme. This programme links researchers in New Zealand working on a variety of topics involving Hidden Markov Models, some of which are listed below. Successful applicants will be attached to one or other of the research groups working on these topics in New Zealand, and will need to be formally attached to one of the New Zealand universities, the decision depending on the research group that they join. The scholarships are available from the beginning of the 2005 academic year (March 2005) onwards.

Background. Applicants should have a minimum qualification of an honours degree (1st class) or Masters degree for selection to a PhD scholarship, or of an honours degree (2(i) or better) for selection to a Masters scholarship. In either case applicants should have taken some advanced courses in mathematics/statistics in their programme.

Stipend. PhD scholars are guaranteed a minimum of $NZ 20,000 per annum for a maximum of three years. Masters students are guaranteed a minimum of $NZ 12,000 per annum for a maximum of 1.5 years. The scholarships are tenable at any of the major New Zealand universities, but in general will be held at the university most closely associated with the relevant research group. In the event of scholarships from more than one source being obtained by the applicant, negotiation between the two funding bodies will be required in order to come to an agreement over proportional funding, which may, in some cases, slightly exceed the maxima suggested.

Application procedure. Potential applicants are invited to contact initially the HMMCS programme director (David Vere-Jones, dvj at or one of the persons nominated in the research areas outlined below, with a copy of their academic record and an indication of their interests. After some informal discussion, a decision will be taken on whether or not they can be supported through the HMMCS programme or in other ways. If they are successful in being recommended for a scholarship, they will then need to apply to one or other of the suggested universities for acceptance into their graduate programme. The student must be accepted into a university PhD or MSc programme before any scholarship payments can be made.

Research opportunities

The main, although not the only, research areas covered by the HMMCS programme are indicated below. Applicants should nominate one or more of these in their application, or else indicate their own particular fields of interest and qualification.


Hidden Markov models in Seismology

A joint research programme on stochastic modelling and probability forecasting for earthquakes has been in operation for several years between Victoria and Massey Universities, Statistics Research Associates and the Institute of Geological and Nuclear Sciences, which has responsibility for New Zealand's seismic networks and earthquake prediction programme. The need for hidden Markov models arises because some key features of the earthquake process, in particular the local and regional stress fields, are not accessible to direct observation. Projects immediately in view include hidden Markov models for deep earthquakes, and extension of existing models to incorporate more explicit modelling of the stress field, possibly incorporating information from GPS measurements. These projects are likely to require both extensions to existing HMM methodology, and simulation and statistical analysis of earthquake catalogue data. On the theoretical side, the most urgent need is to extend existing theory and algorithms to cover the case of point process observations governed by a piecewise-linear Markov process, possibly with measurements also available on an auxiliary continuous process. The research team includes David Vere-Jones, David Harte, Mark Bebbington, and Russell Robinson. For further information contact David Vere-Jones (dvj at or David Harte (david at Students interested in this application would most probably be attached to Victoria University, with principal supervisor one of the four research staff mentioned.


Hidden Markov models for rainfall

As part of a larger FRST research programme Climate-related risks for energy supply and demand, a team from NIWA and SRA are currently developing and extending two parallel and complimentary (partially) hidden Markov and semi-Markov models for rainfall precipitation. Each operates on its own time scale with one based on daily accumulations and the other on high resolution breakpoint data. In New Zealand the former has limited time resolution, but greater space resolution, while the latter has very high temporal resolution, but limited spatial resolution. The long-term objectives are to develop suitable forecasting models of rainfall in hydro generation catchments which reliably estimate rainfall related risk over forecast horizons of months to years, provide realistic scenarios of future rainfall variability over diverse spatial and temporal scales, and account for seasonality, ENSO, IPO and other external forcings. This research programme builds on existing work by the team (e.g. Katz and Zheng 1999; Sansom 1998, 1999; Sansom and Thompson 2003; Sansom and Thomson 1998, 2001; Thompson and Mullan 2002). Major technical challenges are the incorporation of evolving seasonality and parsimonious multi-site modelling. An aspect of this research programme would make a good topic for a suitably qualified PhD student registered at a New Zealand university. For further information contact Jim Renwick (J.Renwick at or Peter Thomson (peter at


Katz, R. W., and Zheng, X. (1999) Mixture model for overdispersion of climate time series. Journal of Climate, 12, 2528-2537.

Sansom, J. (1998). A hidden Markov model for rainfall using breakpoint data. Journal of Climate, 11, 42-53.

Sansom, J (1999). Large scale variability of rainfall through hidden semi-Markov models of breakpoint data. Journal of Geophysical Research, 104 (D24), 31631-31643.

Sansom, J. and Thompson, C.S. (2003). Mesoscale spatial variation of rainfall through a hidden semi-Markov model of breakpoint data. Journal of Geophysical Research, 108(D8), 8379, doi:10.1029/2001JD001447.

Sansom, J. and Thomson, P.J. (1998). Detecting components in censored and truncated meteorological data. Environmetrics 19, 673-688.

Sansom, J. and Thomson, P.J. (2001). Fitting hidden semi-Markov models to breakpoint rainfall data. Journal of Applied Probability 38A, 152-167.

Thompson, C.S. and Mullan, A.B. (2002) Comparing the rainfall-producing models in stochastic weather generators. Weather and Climate, 21, 35-46.


Multivariate Markov switching models in Economics

A recent research project commissioned by New Zealand Treasury looked at fitting hidden Markov models to New Zealand GDP data. This was the first time such a model had been applied to New Zealand GDP and resulted in a number of publications (e.g. Buckle, Haugh and Thomson 2002, 2004). In this application a specially tailored, parsimonious family of hidden Markov models had to be constructed due to the limited number of quarterly data points available. It should be noted that a major weakness of HMM models in general, is that the number of parameters required to specify the hidden chain increases quadratically with the number of states. Major technical challenges in this research programme are the extension of multivariate analyses such as Hall, Kim and Buckle (1998) and Buckle, Haugh and Thomson (2003) to correlated HMM models involving common switching processes that have economic meaning, yet remain parsimonious and are readily fitted to the limited data available. A suitably qualified post-doctoral fellow or PhD student would provide the impetus necessary to make progress in this important, yet ambitious, research programme. For further information contact Viv Hall (Viv.Hall at or Bob Buckle (Bob.Buckle at or Peter Thomson (peter at


Buckle, R.A., Haugh, D. and Thomson, P.J. (2002) Growth and volatility regime switching models for New Zealand GDP data. Working Paper 02/08, New Zealand Treasury, Wellington, New Zealand.

Buckle, R.A., Haugh, D. and Thomson, P.J. (2003) Calm after the storm?: Supply-side contributions to New Zealand's GDP volatility decline. New Zealand Economic Papers 37, 217-243.

Buckle, R.A., Haugh, D. and Thomson, P.J. (2004) Markov switching models for GDP growth in a small open economy: the New Zealand experience. Journal of Business Cycle Measurement and Analysis 1, 227-257.

Hall, V.B., Kim, K.H. and Buckle, R.A. (1998) Pacific Rim business cycle analysis: synchronisation and volatility. New Zealand Economic Papers 32(2), 129-159.


Temporal/Spatio-Temporal Probabilistic Hazard Models in Volcanology

A joint research programme Learning to Live with Volcanic risk is centred at Massey University (Palmerston North) with links to Auckland and Waikato Universities. Part of the programme is to provide probabilistic hazard forecasts for Mt Taranaki and Mt Ruapehu, using radiocarbon data and magma cycle models (possibly as a Hidden Markov Model). The major need will be to incorporate uncertainties in dating into the Point Processes framework. An aspect of the project would make a good topic for a suitably qualified Masters student registered at Massey University. For further information contact Associate Professor Mark Bebbington (m.bebbington at


Cronin, S.J., Bebbington, M.S., Lai, C.D. (2001) A probabilistic assessment of eruption recurrence on Taveuni volcano, Fiji. Bulletin of Volcanology 63, 274--288.

Bebbington, M.S., Lai, C.D. (1996) On nonhomogeneous models for Volcanic Eruptions. Mathematical Geology 28, 585-600.