This is the fourth and last chapter of the first section. As chapter 3 introduced the mathematical tools of probability theory needed to understand all the concepts in the book, chapter 4 does the same concerning statistics. It fills the gap between probability theory and real data coming from stochastic processes, highlighting the great amount of potential applications of the different fields of statistics—particularly estimation theory—in state-of-the-art science and engineering. Topics covered in this chapter include the fundamental tools needed in probabilistic robotics: probabilistic convergence, theory of estimators, hypothesis tests, etc. Special stress is on recursive Bayesian estimators, due to their central role in the problems of probabilistic robot localization and mapping.
TopChapter Guideline
Top1. Introduction
Statistics is the branch of mathematics dealing with the collection, analysis, interpretation and presentation of numerical data (Merrian-Webster, 2011). It is, therefore, the science of making effective use of data acquired from stochastic processes in order to describe them, infer new information, or making predictions. Statistics is based on probability theory (the subject of chapter 3), but it is a different science, more practical and, sometimes, less abstract. Its historical development was intertwined with that of probability theory, as depicted in the previous chapter.
Statistics has its own diverse branches, each focused on the different aspects of the analysis of data. Descriptive statistics has to do with synthesizing the main characteristics of collected data, while statistical inference draws conclusions from these data in spite of their randomness. In mobile robot localization and mapping, the most relevant area is that of estimation: inferring the characteristics of the current uncertainty exposed by r.v.s from the observation of the values they yield. Other branches, such as prediction (estimation of the information that the r.v.s will expose in the future) have currently a marginal presence in mobile robotics, mostly in task or motion planning, which are outside the scope of this book.