Programme
| 9:15 | Chris Jones, Open University
The Cauchy-Schlomilch transformation, its extensions, and a useful analogue
Let g be the density of a symmetric univariate continuous distribution.
I identify a wide class of "transformation of scale" functions t(x) such
that functions of the form 2g(t(x)) are also densities; notice that I am
not transforming the random variable associated with g and, importantly,
that the normalising constant is just (that of g times) 2. Families of
distributions are thereby generated by t and g. The basic version of
this is the remarkable, simple but largely unknown, Cauchy-Schlomilch
transformation. This turns out to be a special case of a more general
approach to the problem. It is then seen that these "extended Cauchy-
Schlomilch distributions" have close connections to a popular existing
method of generating families of distributions and a number, perhaps a
greater number, of interesting properties. Their "useful analogue" arises
from application of much the same idea to distributions on the circle ...
to much the same effect in a context where achieving the same effects as
on the real line is not always as easy as it might seem!
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| 10.00 | Jochen Einbeck, Durham University
Data compression and regression based on local principal curves and manifolds
We consider principal curves and surfaces in the context of multivariate regression modelling.
For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of the data tends to be very small due to the high redundancy induced by the dependencies. In situations of this type, it is useful to approximate the high-dimensional predictor space through a low-dimensional manifold (i.e., a curve or a surface), and use the projections onto the manifold as compressed predictors in the regression problem. In the case that the intrinsic dimensionality of the predictor space equals one, we use the local principal curve algorithm
for the the compression step. We provide a novel algorithm which extends this idea to local principal surfaces, thus covering cases of an intrinsic dimensionality equal to two, which is in principle extendible to manifolds of arbitrary dimension. The techniques are applied and motivated using data examples from the physical sciences. (joint work L. Evers, University of Glasgow) .
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| 10:30 | Coffee
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| 11:00 | Jordan Stoyanov, Newcastle University
Non-linear transformations of random data: moment determinacy of their distributions
Functional transformations (Box-Cox) of random data are intensively studied and widely used in statistical practice. Data come from observations of random variables or of stochastic processes. Our goal is to analyse the distributions of the data, before and after transforming, and their properties expressed in terms of the moments. Some distributions are uniquely determined by their moments (M-determinate) while others are non-unique (M-indeterminate). The determinacy property of a distribution is essential in inference problem. We use classical and/or modern criteria to analyse specific stochastic models. General statements will be given and well-illustrated with popular distributions. Some of the reported facts are not so well-known, and even surprising. If time permits, a couple of open questions will be outlined.
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| 11:45 | Gero Walter, University of Munich
The effect of prior-data conflict in Bayesian linear regression
Prior-data conflict appears in Bayesian analysis if the observed data
are very unlikely with respect to the prior model and the sample size
is not large enough to eliminate the influence of the prior. Prior-data
conflict is often not reflected in posterior inferences. We consider
Bayesian linear regression models based on conjugate priors, and demonstrate
that a standard prior model may show some reaction to prior-data conflict.
A restricted version of this prior, derived via a general construction
procedure for exponential family sampling models, offers clearer insight
in some aspects of the update process and is well suited for a generalization
towards an imprecise probability model, where, by considering sets of
prior distributions instead of a single prior, prior-data conflict can be
handled in an appealing and intuitive way. (joint work with T.
Augustin, University of Munich).
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| 12:15 | Lunch
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| 13:00 | Tahani Maturi, Durham University
Nonparametric predictive inference for comparison of lifetime data
In this talk we will introduce nonparametric predictive inference (NPI) for multiple comparisons. NPI is a recently developed frequentist statistical framework that makes few modelling assumptions apart from exchangeability of random quantities, with inferences explicitly in terms of future observations, and with uncertainty quantified by lower and upper probabilities. The comparison involves different right censoring schemes, e.g. censoring resulting from early termination of an experiment, progressive censoring and competing risks. (joint work with F.
Coolen, Durham University).
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| 13:30 | Narayanaswamy Balakrishnan, McMaster University, Canada
Permanents, order statistics, outliers and robustness (Part I)
In this talk, after briefly introducing order statistics and
some relevant literature, I will describe single-outlier model and some
relevant distribution theory for order statistics arising from such a
model. In order to facilitate the generalization of this work to the
case of the multiple-outlier model, I will describe the approach based
on permanents. I will then present some key results and then
illustrate their applications to robustness studies by taking the case
of exponential and logistic as illustrative examples.
Biography of the speaker: N. Balakrishnan is a Professor in the Department
of Mathematics and Statistics at McMaster University. His research
interests include order statistics, distribution theory, robust
inference, multivariate analysis, reliability, and statistical
inference. He is a Fellow of the American Statistical Association,
Fellow of the Institute of Mathematical Statistics, and an Elected
Member of the International Statistical Institute. He is currently the
Editor-in-Chief of Communications in Statistics and Encyclopedia of
Statistical Sciences and the Executive Editor of Journal of Statistical
Planning and Inference. He has authored/coauthored many books
including the four volumes on Distributions in Statistics with Norman
Johnson and Samuel Kotz, published by John Wiley & Sons.
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| 14:30 | Tea
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| 15:00 | Narayanaswamy Balakrishnan, McMaster University, Canada
Permanents, order statistics, outliers and robustness (Part II)
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| 16:00 | Discussion and Close
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General Details
Registration and Lunch
There is no registration fee, but if you wish to join the buffet lunch we ask for a contribution of £7.50, to be paid on the day.
Please let us know by Friday 9th of April if you would like to attend, and whether you intend to have lunch (and if there are any dietary requirements). Please inform us also if you will attend the lecture day but do not intend to have lunch (for our planning wrt coffee breaks).
Accommodation
If you are planning an overnight stay, then information
on suitable accommodation (en-suite rooms, B&B, in Durham colleges) is available here. All colleges
offer suitable accommodation, if you wish a recommendation then we would suggest Collingwood College.
For those arriving the day before the lecture day, there are plans to go for dinner on the evening on the 13th April (at participants' own costs). Please let us know if you would like to join.
Travel
The Department is easily accessible by bus, taxi or foot from the
railway station. More information about travelling to Durham can be found here and here. A useful map
can be found here, where the Department of Mathematical Sciences is marked (15).
Car parking at the Department of Mathematical Sciences is in extremely limited supply. For those arriving by car, it will be possible to obtain a day-permit at the entrance barriers - however this is no guarantee that you will find a place.
A preferable alternative would be to use the Durham Park and Ride at the nearby Howlands Park site which offers a large supply of secure parking.
Contact
To confirm attendance, or in case of any questions, please contact Frank Coolen or Jochen Einbeck, telephone (0191) 3343125.
Notes
Prof. Balakrishnan's visit to the UK is supported by an LMS Scheme 2 grant. Further activities include seminar talks at Edinburgh University on Monday 12 April
(`Over- and under-dispersed Poisson distributions and processes', for details contact Natalia Bochkina ), and Newcastle University on Thursday 15 April ('On some stochastic orderings and related characterizations for some discrete and continuous distributions', for details contact Jordan Stoyanov ).
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