Who is a probabilist? Someone who knows the odds of drawing an ace of diamonds, or the waiting time at a ticket office? A mathematician who uses a special vocabulary? And who is a statistician? Someone who is capable of determining whether tobacco encourages cancer, or the number of votes which a certain candidate will poll at the next elections? Each one perceives the link: chance. The probabilist, guided by his intuition of poker or queues, constructs an abstract model; having fixed the mathematical framework, he calmly follows through his logical reasoning, which sometimes him very far from his starting point. The statistician takes works on solid ground. When a doctor asks him if it is worth using a new drug, he uses the tools of a probabilist. However he must reach a decision, the least harmful option, based on analyzing the doctor's observations, while taking into account the various risks involved. In short, a probabilist keeps his hands clean while dreaming of models, while a statistician must dirty his hands while working with concrete facts. Relations between the two have often been difficult; but the barriers to their dialogue are broken down by the interest in the concrete to supplement theoretical dreams or in complicated models to describe various phenomena. However, few students have a chance to overcome these barriers.

Probability and Statistics: Volume I

Science & Math

Marie Duflo

David McHale Marie Duflo Didier Dacunha-Castelle

Mathematics

Springer

How can we predict the future without asking an astrologer? When a phenomenon is not evolving, experiments can be repeated and observations therefore accumulated; this is what we have done in Volume I. However history does not repeat itself. Prediction of the future can only be based on the evolution observed in the past. Yet certain phenomena are stable enough so that observation in a sufficient interval of time gives usable information on the future or the mechanism of evolution. Technically, the keys to asymptotic statistics are the following: laws of large numbers, central limit theorems, and likelihood calculations. We have sought the shortest route to these theorems by neglecting to present the most general models. The future statistician will use the foundations of the statistics of processes and should satisfy himself about the unity of the methods employed. At the same time, we have adhered as closely as possible to present day ideas of the theory of processes. For those who wish to follow the study of probabilities to postgraduate level, it is not a waste of time to begin with the least difficult technical situations. This book for final year mathematics courses is not the end of the matter. It acts as a springboard either for dealing concretely with the problems of the statistics of processes, or viii In trod uction to study in depth the more subtle aspects of probabilities.

Probability and Statistics: Volume II

See the best price to sell, buy, or rent books by Marie Duflo. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Marie Duflo

See the best price to sell, buy, or rent books by Marie Duflo. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Probability and Statistics: Volume I

Probability and Statistics: Volume II