Exploring Multivariate Data with the Forward Search

Why We Wrote This Book This book is about using graphs to explore and model continuous multi- variate data. Such data are often modelled using the multivariate normal distribution and, indeed, there is a literatme of weighty statistical tomes presenting the mathematical theory of this activity. Our book is very dif- ferent. Although we use the methods described in these books, we focus on ways of exploring whether the data do indeed have a normal distribution. We emphasize outlier detection, transformations to normality and the de- tection of clusters and unsuspected influential subsets. We then quantify the effect of these departures from normality on procedures such as dis- crimination and duster analysis. The normal distribution is central to our book because, subject to our exploration of departures, it provides useful models for many sets of data. However, the standard estimates of the parameters, especially the covari- ance matrix of the observations, are highly sensitive to the presence of outliers. This is both a blessing and a curse. It is a blessing because, if we estimate the parameters with the outliers excluded, their effect is appre- ciable and apparent if we then include them for estimation. It is however a curse because it can be hard to detect which observations are outliers. We use the forward search for this purpose.