Probability and statistics
著者
書誌事項
Probability and statistics
Springer, c1986
- v. 1 : us
- v. 1 : gw
- v. 2 : us
- v. 2 : gw
- v. 2 : pbk : us
- タイトル別名
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Probabilités et statistiques
大学図書館所蔵 件 / 全46件
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v. 1 : us417/PS150040234,
v. 2 : us417/PS250040222, Vol. 1417//PS2T5004022*, Vol. 2417//PS2T5004023* -
Vol. 1417.1||D11||105104743,
Vol. 2417.1||D11||205129912, Vol. l417.1||D11||1510474 -
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注記
Translation of: Probabilités et statistiques
Bibliography: v. 1, p. [344]-348; v. 2, [389]-396
Includes index
内容説明・目次
- 巻冊次
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v. 1 : us ISBN 9780387960678
内容説明
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.
目次
1 Censuses.- 1.1. Census of Two Qualitative Characteristics.- 1.2. A Census of Quantitative Characteristics.- 1.3. First Definitions of Discrete Probabilities.- 1.4. Pairs of R.V.'s and Correspondence Analysis.- 2 Heads or Tails. Quality Control.- 2.1. Repetition of n Independent Experiments.- 2.2. A Bernoulli Sample.- 2.3. Estimation.- 2.4. Tests, Confidence Intervals for a Bernoulli Sample, and Quality Control.- 2.5. Observations of Indeterminate Duration.- 3 Probabilistic Vocabulary of Measure Theory. Inventory of the Most Useful Tools.- 3.1. Probabilistic Models.- 3.2. Integration.- 3.3. The Distribution of a Measurable Function.- 3.4. Convergence in Distribution.- 4 Independence: Statistics Based on the Observation of a Sample.- 4.1. Sequence of n Observations-Product Measure Spaces.- 4.2. Independence.- 4.3. Distribution of the Sum of Independent Random Vectors.- 4.4. A Sample from a Distribution and Estimation of this Distribution.- 4.5. Nonparametric Tests.- 5 Gaussian Samples, Regression, and Analysis of Variance.- 5.1. Gaussian Samples.- 5.2. Gaussian Random Vectors.- 5.3. Central Limit Theorem on ?k.- 5.4. The X2 Test.- 5.5. Regression.- 6 Conditional Expectation, Markov Chains, Information.- 6.1. Approximation in the Least Squares Sense by Functions of an Observation.- 6.2. Conditional Expectation-Extensions.- 6.3. Markov Chains.- 6.4. Information Carried by One Distribution on Another.- 7 Dominated Statistical Models and Estimation.- 7.1. Dominated Statistical Models.- 7.2. Dissimilarity in a Dominated Model.- 7.3. Likelihood.- 8 Statistical Decisions.- 8.1. Decisions.- 8.2. Bayesian Statistics.- 8.3. Optimality Properties of Some Likelihood Ratio Tests.- 8.4. Invariance.- Notation and Conventions.
- 巻冊次
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v. 2 : us ISBN 9780387962139
内容説明
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.
- 巻冊次
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v. 2 : pbk : us ISBN 9781461293392
内容説明
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.
目次
0 Introduction to Random Processes.- 0.1. Random Evolution Through Time.- 0.2. Basic Measure Theory.- 0.3. Convergence in Distribution.- 1 Time Series.- 1.1. Second Order Processes.- 1.2. Spatial Processes with Orthogonal Increments.- 1.3. Stationary Second Order Processes.- 1.4. Time Series Statistics.- 2 Martingales in Discrete Time.- 2.1. Some Examples.- 2.2. Martingales.- 2.3. Stopping.- 2.4. Convergence of a Submartingale.- 2.5. Likelihoods.- 2.6. Square Intergrable Martingales.- 2.7. Almost Sure Asymptotic Properties.- 2.8. Central Limit Theorems.- 3 Asymptotic Statistics.- 3.1. Models Dominated at Each Instant.- 3.2. Contrasts.- 3.3. Rate of Convergence of an Estimator.- 3.4. Asymptotic Properties of Tests.- 4 Markov Chains.- 4.1. Introduction and First Tools.- 4.2. Recurrent or Transient States.- 4.3. The Study of a Markov Chain Having a Recurrent State.- 4.4. Statistics of Markov Chains.- 5 Step by Step Decisions.- 5.1. Optimal Stopping.- 5.2. Control of Markov Chains.- 5.3. Sequential Statistics.- 5.4. Large Deviations and Likelihood Tests.- 6 Counting Processes.- 6.1. Renewal Processes and Random Walks.- 6.2. Counting Processes.- 6.3. Poisson Processes.- 6.4. Statistics of Counting Processes.- 7 Processes in Continuous Time.- 7.1. Stopping Times.- 7.2. Martingales in Continuous Time.- 7.3. Processes with Continuous Trajectories.- 7.4. Functional Central Limit Theorems.- 8 Stochastic Integrals.- 8.1. Stochastic Integral with Respect to a Square Integrable Martingale.- 8.2. Ito's Formula and Stochastic Calculus.- 8.3. Asymptotic Study of Point Processes.- 8.4. Brownian Motion.- 8.5. Regression and Diffusions.- Notations and Conventions.
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