  This paper details a methodology proposed for the EVA 2021 conference data
challenge. The aim of this challenge was to predict the number and size of
wildfires over the contiguous US between 1993 and 2015, with more importance
placed on extreme events. In the data set provided, over 14\% of both wildfire
count and burnt area observations are missing; the objective of the data
challenge was to estimate a range of marginal probabilities from the
distribution functions of these missing observations. To enable this
prediction, we make the assumption that the marginal distribution of a missing
observation can be informed using non-missing data from neighbouring locations.
In our method, we select spatial neighbourhoods for each missing observation
and fit marginal models to non-missing observations in these regions. For the
wildfire counts, we assume the compiled data sets follow a zero-inflated
negative binomial distribution, while for burnt area values, we model the bulk
and tail of each compiled data set using non-parametric and parametric
techniques, respectively. Cross validation is used to select tuning parameters,
and the resulting predictions are shown to significantly outperform the
benchmark method proposed in the challenge outline. We conclude with a
discussion of our modelling framework, and evaluate ways in which it could be
extended.
