Past Seminars
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Diagnosing mental diseases with discriminant analysis
Speaker: Yao-ban Chan
Institution: The University of Melbourne
Date: Fri 1 Sep 2006
Time: 3:15 pm
Location: Theatre 1, Ground Floor, 111 Barry Street, CarltonAbstract: The Mental Health Research Institute of Victoria has been using a technique called electrophoresis to analyse the proteomic structure of brains with mental diseases, in particular schizophrenia and bipolar
disorder. In this talk, I shall explain how we use various statistical methods on these electrophoresis scans to diagnose these patients. In particular, we concentrate on a classification technique called Fisher's linear discriminant analysis, and some of its extensions and variants.
Queues with Advance Reservations
Speaker: Professor Peter Taylor
Institution: MASCOS, The University of Melbourne
Date: Fri 25 Aug 2006
Time: 3:15 pm
Location: Theatre 1, Ground Floor, 111 Barry Street, CarltonAbstract: Queues where on "arrival" customers make a reservation for service at some time in the future are endemic in practice and relatively under-analysed in theory.
Simulations illustrate some interesting implications of the facility to make such reservations. For example introducing independent and identically distributed reservation periods into an Erlang loss system changes the blocking probability from that given by the Erlang B formula, despite the fact that the process of 'reserved arrivals' is still Poisson.
In this talk we shall discuss some preliminary analyses of such queues. In particular, we shall obtain various transient and stationary distributions associated with the "bookings diary" for the infinite server system, and discuss attempts to extend the analysis to blocking probability calculations.
An Involution for Enumerating Osculating Lattice Paths and Alternating Sign Matrices
Speaker: Paul Fijn
Institution: The University of Melbourne
Date: Wed 9 Aug 2006
Time: 3:15 pm
Location: AMSI Seminar Room, Ground Floor, 111 Barry Street, CarltonAbstract: Enumerative combinatorics is concerned with the establishment of "nice" formulae for the counting of various sets of objects. This talk is primarily concerned with paths on an integer lattice which can share vertices (but not edges) and must remain consistently ordered---osculating lattice paths.
It is known that there are many methods of enumerating two osculating lattice paths, and two methods for the problem of three paths. Unfortunately, none of these generalise to the N paths case. An outline of a proof for N paths is given, along with an introduction to basic enumerative techniques. Connections to other areas of statistical mechanics and combinatorics, such as Alternating Sign Matrices, the Bethe Ansatz and the 6-vertex model, will also be briefly discussed.
Optimal Monitoring for Fox Management
Speaker: Alana Moore (Ph.D. student)
Institution: The University of Melbourne
Date: Fri 4 Aug 2006
Time: 3:45 pm
Location: Theatre 1, Ground Floor, 111 Barry Street, CarltonAbstract: Since its introduction in the 1900's, the European red fox has had a major negative impact on native Australian fauna and is held responsible for the extinction of several Australian marsupial species. Once established, complete eradication of invasive species such as foxes is usually infeasible and control strategies employed in an attempt to save native species are often expensive and require intensive management programs. It is intuitive that effective management requires information about the system in question, but how much? Given obtaining information is usually difficult and costly, and budgets for park management are limited, it is unclear how effort should be split between monitoring and control in order to most effectively manage fox populations. I present a simple model which may be used to calculate optimal monitoring and management regimes.
Truncation schemes for Markov chains and QBDs
Speaker: Allan Motyer (Ph.D. student)
Institution: The University of Melbourne
Date: Fri 4 Aug 2006
Time: 3:15 pm
Location: Theatre 1, Ground Floor, 111 Barry Street, CarltonAbstract: When modelling a random system with an infinite number of states as a Markov chain it may not be possible to find a closed form solution for the equilibrium distribution. In this situation we truncate the state space of the system to a sufficiently large but finite number of states in order to find a numerical solution. It is desirable that as the number of states in the truncated system is increased, the numerical solution converges to the (unknown) solution for the system with infinite states. This is not something that can be taken for granted. I will outline conditions under which such convergence occurs, give examples of when it doesn't, and apply the known results to a special type of Markov chain - the quasi-birth-and-death process.
Survival Analysis with Long-term Survivors
Speaker: Xian Zhou
Institution: The Hong Kong Polytechnic University
Date: Thu 27 Jul 2006
Time: 1:15 pm
Location: Theatre 2, Old Geology Building, The University of MelbourneAbstract: Survival analysis deals with data representing time durations before the occurrence of a certain event of interest, such as death from a particular disease, committing another crime, making an insurance claim, etc. Such data are typically subject to censoring and/or truncation, so that special techniques are required to account for these situations. A long-term survivor is an individual who will never experience the event of interest, such as a cancer patient who has been completely cured of the cancer, a HIV carrier who will never develop AIDS symptoms, and an insurance policyholder who never needs to make a claim, etc. The presence of long-term survivors could have a significant impact on the analysis of survival data.
In this talk, we will introduce appropriate statistical models for survival data with long-term survivors. Nonparametric and parametric approaches are used to estimate the distributions and/or parameters under such models. Test for the presence of long-term survivors will also be discussed.
Structured population epidemic models
Speaker: Frank G Ball
Institution: University of Nottingham
Date: Tue 18 Jul 2006
Time: 3:15 pm
Location: Russell Love Theatre, Richard Berry Building, The University of MelbourneAbstract: Standard deterministic models of epidemics implicitly assume that the
population among which the disease is spreading is locally as well as globally large, in the sense that if the population is partitioned into groups, e.g. by age, sex and/or geographical location, then each of these groups, and not just the total population, is large. The same
assumption is made when analysing the large-population behaviour of many
stochastic epidemic models. However, this assumption is unrealistic for
many human epidemics, since such populations contain small social groups, such as households, school classes and workplaces, in which transmission is likely to be enhanced. Thus, there has been a growing interest in models for epidemics among populations whose structure
remains locally finite as the population becomes large.
This talk is concerned with a general class of structured-population epidemic models, in which individuals mix at two levels: global and local.
After some introductory comments, a stochastic model for SIR (susceptible - infected - removed) epidemics among a closed finite population is described, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution centred on that infective and each global contact is with an individual chosen independently and uniformly from the whole population. The threshold behaviour of the model is determined, as is the asymptotic final outcome in the event of an epidemic taking off. The theory is specialised to (i) the
households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective's household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts
are nearest-neighbour. A main use of epidemic models is to evaluate the efficacy of control measures, such as vaccination, and optimal vaccination policies for the households model are also considered.
Info-Gap Forecasting and the Advantage of Sub-Optimal Models
Speaker: Professor Yakov Ben-Haim
Institution: Technion - Israel Institute of Technology
Date: Fri 14 Jul 2006
Time: 3:15 pm
Location: Theatre 1, Old Geology Building, The University of MelbourneAbstract: We consider forecasting in linear discrete-time systems. Historical data indicate that the transition matrix is constant over time. However, the underlying laws governing the system are unknown and it is uncertain that the system properties will remain constant. An info-gap model is used to represent uncertainty in the future transition matrix. The forecaster desires the average forecast of a specific state variable to be within a specified interval around the correct value. Traditionally, forecasting is based on using a model which has optimal fidelity to historical data. Our first theorem asserts the existence, and indicates the construction, of models with sub-optimal fidelity to historical data which are more robust to model error than the optimal model. Our second theorem identifies
conditions in which the probability of forecast success increases with increasing robustness to model error. Combining these results leads to a methodology for identifying reliable forecasting models for systems whose trajectories evolve in unknown ways over time.
Algorithmic differentiation for analysis of global change and the carbon cycle
Speaker: Prof. Ian Enting
Institution: MASCOS, University of Melbourne
Date: Fri 23 Jun 2006
Time: 3:15 pm
Location: AMSI Seminar Room, Ground Floor, 111 Barry Street, CarltonAbstract: Numerical models of natural systems are often expressed as sets of differential equations (DEs), generally first-order in time. Commonly 'the model' refers to a computer implementation that integrates these DEs. However many of the processes involved in analysing models involve differentiation: sensitivity analysis, calibration by minimising a cost-function based on data-mismatch, etc. For large numerical models, it is convenient to have tools that generate such derivatives directly from the 'model' source code.
This talk describes the use of operator overloading in C++ and Fortran-90 to transform a model into a tangent linear model that integrates DEs corresponding to parameter sensitivities.
Penalised spline support vector classifiers
Speaker: Matt Wand
Institution: The University of NSW
Date: Fri 16 Jun 2006
Time: 3:15 pm
Location: Russell Love Theatre, Richard Berry Building, The University of MelbourneAbstract: Support vector machines are an elegant and often effective means of building a classifier. They are defined up to choice of a kernel function and some auxiliary parameters. However, for many popular kernels, support vector classifiers can suffer from poor scalability for large training sample sizes; lack of interpretability and the
curse of dimensionality. This talk describes kernels based on the notion of penalised splines (from nonparametric regression) and explains how they can alleviate the aforementioned problems.
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