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What to do with the discrepancy between a point process
Joel Chadoeuf
Venue:
Fylde SCR - Lancaster University
2006-01-26 16:00
The way one looks at the discrepancy between a data set and a fittted model
depends in fact on the problem we are interested in and so on the role of the model:
(i) In a classical approach, the model is used to summarize the main features of
the data set and analysing at the residuals is done mainly to check if the model is
adequate or if modifications (as for example introduction of covariates) are needed.
This approach, formalized by Baddeley et al (2005), is illustrated on an example of
plant invasion.
(ii) In some cases, the question is not in estimating the parameters of a model, but
rather in deciding between much more crude assumptions. The use of CSR tests
can be seen as a typical example. The problem is then to decide how to use the
discrepancy between the model under null hypothesis and the data with respect to
alternative assumptions. Ecological assumptions about gannets behaviour are tested
using their spatial repartition in the Bay of Biscay from that point of view.
(iii) In several cases, the situation lies between (i) and (ii), in the sense that we know
that the basic model we use is not correct as it does not take into account of some
known processes. We may know where to modify the model, but not how. This can
be the case for hierarchical models, where the first level is well known, whereas the
second level is generally not, as it involves seldom observed parameter distributions.
Specifying these distributions may then be done by using a residual analysis. We
present an example of a procedure within an asymptotic framework.
depends in fact on the problem we are interested in and so on the role of the model:
(i) In a classical approach, the model is used to summarize the main features of
the data set and analysing at the residuals is done mainly to check if the model is
adequate or if modifications (as for example introduction of covariates) are needed.
This approach, formalized by Baddeley et al (2005), is illustrated on an example of
plant invasion.
(ii) In some cases, the question is not in estimating the parameters of a model, but
rather in deciding between much more crude assumptions. The use of CSR tests
can be seen as a typical example. The problem is then to decide how to use the
discrepancy between the model under null hypothesis and the data with respect to
alternative assumptions. Ecological assumptions about gannets behaviour are tested
using their spatial repartition in the Bay of Biscay from that point of view.
(iii) In several cases, the situation lies between (i) and (ii), in the sense that we know
that the basic model we use is not correct as it does not take into account of some
known processes. We may know where to modify the model, but not how. This can
be the case for hierarchical models, where the first level is well known, whereas the
second level is generally not, as it involves seldom observed parameter distributions.
Specifying these distributions may then be done by using a residual analysis. We
present an example of a procedure within an asymptotic framework.
