Computer Intensive Statistics 1. Introduction

The principle aim of these notes is to provide context and motivation for the APTS Computer Intensive Statistics Module and to make the module as self-contained as is feasible. Statistics is a broad discipline and the APTS cohort naturally has a diverse range of backgrounds. If you have attended the earlier APTS modules this year, especially Statistical Computing and Statistical Inference, then you should be well prepared for this module. As we have the luxury of having, essentially, no need to make use of anything beyond elementary material which everyone pursuing a Ph.D. in statistics or applied probability is undoubtedly familiar we can make use of this preliminary material to make things self-contained and to provide some contextual material. Although it's likely that everyone attending the module will know everything they need to follow the lectures, there is one area which will require some preparation if it's something with which you are not already comfortable. Indeed, there is one thing from which there is no escaping in computer intensive methods of any sort: implementation. It's impossible to really understand the ideas which we'll be discussing without experimenting with them yourself. As such, perhaps the most important prerequisite, is competence with basic computer programming. In addition to the material that is described here, it's important that you are able to use the R (R Core Team, 2013) programming language. If you haven't already done so, then do please complete the R Programming Course for APTS Students before the start of the APTS week itself. Two appendices are provided. You might very well already know everything in these appendices — if that's the case, then great. If you have a less conventional statistical background and haven't managed to attend the earlier APTS modules then you may find some parts of these notes less familiar in which case some references are provided, but rest assured that the module should be accessible to anyone who is pursuing a PhD in any aspect of statistics or applied probability (both interpreted broadly). Appendix A provides a compact summary of some statistical tasks which we will aim to address in this module. It's likely than anyone pursuing a PhD in statistics — especially anyone who has attended an APTS module on Statistical Inference — will be familiar with this material, and (re)reading the notes provided for that module would be good preparation for the 4