Abstract
We develop newtools for formal inference and informalmodel
validation in the analysis of spatial point pattern data. The score test
is generalised to a ‘pseudo-score’ test derived from Besag’s pseudolikelihood,
and to a class of diagnostics based on point process residuals.
The results lend theoretical support to the established practice
of using functional summary statistics such as Ripley’s K-function,
when testing for complete spatial randomness; and they provide new
tools such as the compensator of the K-function for testing other fitted
models. The results also support localisation methods such as the
scan statistic and smoothed residual plots. Software for computing the
diagnostics is provided.
validation in the analysis of spatial point pattern data. The score test
is generalised to a ‘pseudo-score’ test derived from Besag’s pseudolikelihood,
and to a class of diagnostics based on point process residuals.
The results lend theoretical support to the established practice
of using functional summary statistics such as Ripley’s K-function,
when testing for complete spatial randomness; and they provide new
tools such as the compensator of the K-function for testing other fitted
models. The results also support localisation methods such as the
scan statistic and smoothed residual plots. Software for computing the
diagnostics is provided.
Original language | English |
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Publisher | Department of Mathematical Sciences, Aalborg University |
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Number of pages | 47 |
Publication status | Published - Aug 2010 |
Series | Research Report Series |
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Number | R-2010-06 |
ISSN | 1399-2503 |
Keywords
- compensator
- functional summary statistics
- model validation
- point process residuals
- pseudo-likelyhood