Time-series are often modelled probabilistically as sequences of segments using first-order Markovian hidden variables representing different dynamics regimes. Such dynamics-regime variables implicitly define a geometric segment-duration distribution. A more flexible distribution requires introducing extra variables into the model with increased computational cost. This can be achieved in different ways, whose properties and categorization are still unclear. This book describes in a simple way different approaches to modelling the segment-duration distribution by categorizing them into three...

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many...