There will be a Statistics seminar at UMIST on Wednesday 10th November. The
details are given below. All those interested are welcome to attend.
Advance notice is also given of a seminar on 1st December to be presented by
Professor Clive Anderson, University of Sheffield.
Wednesday 10th November, 3.00pm - 4.30pm
Venue: UMIST, MSS/M12.
Speaker: Professor Anatoly Zhigljavsky, Cardiff University.
Title: Principal Component Expansions of Time Series: Singular Spectrum
Analysis and Related Technique
Abstract:
SSA, the Singular Spectrum Analysis, is a general term referring to the
technique of time series analysis based on singular value decomposition of
the 'trajectory matrix' formed by combining several lagged copies of a
single series. SSA could be considered as an extension of the Principal
Component Analysis from independent to time-correlated observations.
There is a certain flexibility in the methodology that could make it
extremely powerful. We use a large amount of real data from different fields
to elucidate the key ideas of the methodology, to demonstrate its power, and
to caution about snags.
We also describe some underlying mathematical/statistical models and related
theoretical results. The basic problems here are separation of one signal
from another and separation of a signal from noise. The signals are, roughly
speaking the time series that are well approximated by solutions of
finite-difference equations, and the noise is what could not be well
approximated by solutions of such equations. Noise is thus modelled in a
non-stochastic manner but it could certainly include stochastic components.
The problems we consider are: analysis of structure of time series,
continuation (forecast) of time series, change-point detection. In
developing specific algorithms geometrical ideas and tools are at least as
important as analytical and statistical.
Wednesday 1st December, 4pm
Venue: UMIST, MSS/M12 (to be confirmed).
Speaker: Professor Clive Anderson, University of Sheffield.
Title: The Largest Inclusions Within a Piece of Steel
Abstract:
Imagine a solid object, homogeneous except for the presence within it of
small particles of foreign material of different sizes. Interest lies in the
size of the largest of these particles, and how that size relates to the
volume of the solid. Direct observation inside the solid is impossible, but
particles intersecting the surface can be seen in section.
This is a problem with particular relevance to new high quality steels. All
steels contain inclusions - small particles of impurity - which influence
fatigue strength. In the new so-called clean steels the number and size of
inclusions are much reduced and it becomes particularly important for safety
reasons to estimate the likely size of the largest. Measurement of the
cross-sections of inclusions exposed in sampled polished surfaces of the
steel can be made reasonably routinely.
Without the emphasis on the largest particles, inference about particle
sizes on the basis of two-dimensional sections is a standard problem in
stereology (Wicksell's corpuscle problem of 1925). The talk will describe a
development which concentrates specifically on inferences about large
particles, combining modern extreme value modelling with stereological
ideas. Both likelihood-based and Bayesian approaches will be presented.
The problem raises some general questions about the choice of models in the
analysis of extremes.
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