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Functional data analysis is a statistical framework where data are assumed tofollow some functional form. This method of analysis is commonly applied totime series data, where time, measured continuously or in discrete intervals,serves as the location for a function's value. Gaussian processes are ageneralization of the multivariate normal distribution to function space and,in this paper, they are used to shed light on coastal rainfall patterns inBritish Columbia (BC). Specifically, this work addressed the question over howone should carry out an exploratory cluster analysis for the BC, or anysimilar, coastal rainfall data. An approach is developed for clusteringmultiple processes observed on a comparable interval, based on how similartheir underlying covariance kernel is. This approach provides interestinginsights into the BC data, and these insights can be framed in terms of ElNi\~{n}o and La Ni\~{n}a; however, the result is not simply one clusterrepresenting El Ni\~{n}o years and another for La Ni\~{n}a years. From oneperspective, the results show that clustering annual rainfall can potentiallybe used to identify extreme weather patterns.

Detecting British Columbia Coastal Rainfall Patterns by Clustering Gaussian Processes