Statistics Seminars at Imperial College
Friday 10 March, Room 408, Department of Mathematics, 4th floor
Huxley Building, 180 Queen's Gate, South Kensington, London.
Program:
2:00 -- 3:00 Mikis Stasinopoulos, University of North London
Generalized Autoregressive Moving Average Models
3:00 -- 3:30 Coffee Break (served in the same room - 408)
3:30 -- 4:30 Thomas Richardson, University of Warwick
Ancestral Graph Markov models: an Alternative to Models
with Latent or Selection Variables
Abstracts of the talks:
Generalized Autoregressive Moving Average models
M. Stasinopoulos, University of North London
A class of Generalized Autoregressive Moving Average (GARMA) models is
developed which extends the univariate Gaussian ARMA time series model
to a flexible observation driven model for non-Gaussian time series
data. The dependent variable is assumed to have a conditional
Exponential Family distribution given the past history of the process.
It is demonstrated that model estimation can be carried out using an
iteratively reweighted least squares algorithm. Properties of the model
including stationarity and marginal moments are either derived
explicitly or investigated using Monte Carlo simulation. The
relationship of the GARMA model to other models is shown, including the
autoregressive models of Zeger and Qaqish (1988), the moving average
models of Li (1994) and also the reparameterised GARCH model (providing
the formula for its fourth marginal moment not previously derived). The
model is demonstrated by two applications of the GARMA model. The first
application is to a well known time series data set of poliomyelitis
counts using a Negative Binomial conditional distribution. The second is
to river flow data using a Gamma conditional distribution.
Ancestral Graph Markov models: an Alternative to Models with Latent
or Selection Variables
Thomas S. Richardson,University of Warwick
A graphical model is a set of multivariate distributions obeying the
conditional independence properties encoded by a graph. Two types of
graph have commonly been used: undirected graphs and directed acyclic
graphs.
Graphical models are often used for the purpose of gaining insight into
possible mechanisms which may have generated a given set of data. Such
interpretation of the model becomes inherently more difficult when
unmeasured `confounding' variables may be present, or when there may be
bias in the sampling procedure. Latent variable models present one
possible approach in these circumstances, but lack many of the nice
statistical properties associated with standard graphical models.
This talk will present the class of maximal ancestral graph (MAG) models
which provide an alternative approach to this problem. A MAG can be used
to represent the Markov structure among the observed variables in a data
generating process. In the Gaussian case MAG models can be parametrized
via a recursive set of linear equations with correlated errors. MAG
models also retain many of the desirable properties of models based on
directed and undirected graphs.
EVERYBODY WELCOME!!!!!!!!!!!!!
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