{"id":198,"date":"2020-04-17T13:06:46","date_gmt":"2020-04-17T13:06:46","guid":{"rendered":"http:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/edward-mellor\/?p=198"},"modified":"2020-04-30T15:05:26","modified_gmt":"2020-04-30T15:05:26","slug":"introduction-to-extreme-value-theory","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/edward-mellor\/2020\/04\/17\/introduction-to-extreme-value-theory\/","title":{"rendered":"Introduction to Extreme Value Theory"},"content":{"rendered":"\n

In my last post I promised an overview of my two research topics. We were encouraged to choose one topic from Statistics and the other from Operational Research. Today we will focus on the more statistical topic which I was introduced to by Emma Eastoe<\/a>.<\/p>\n\n\n\n

In statistics we are often interested in determining the most likely behaviour of a system. The usual way to do this would be to fit a model to the observations from the system. This can be done by finding a family of distributions that approximately describes the shape of the data. This family of distributions (or model) will have certain parameters. The observations can then be used to estimate the value of these parameters which maximises the probability of that set of observations occurring. In some situations however, the normal behavior of a system is of less concern to us and we are instead interested in the maximum (or minimum) outcome that we would expect to observe over an extended period of time. For example, if a local council is considering investment in flood defences they are not interested in the average height of the river but only in the events where the volume of water would exceed the river\u2019s maximum capacity and cause flooding.<\/p>\n\n\n\n

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The problem here is that we are considering very unusual events that any distribution which was fitted to the entire set of observations would be unable to reliably estimate. We therefore require models that can be fitted to just the extreme events. There are two main approaches to consider: the Block Maxima Model and the Threshold Excess Model. Each of these approaches can by characterised by their different way of classifying an event as extreme.<\/p>\n\n\n\n