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2703 results in General statistics and probability

Page 76 of 136

Model Selection and Model Averaging
  • Gerda Claeskens, Nils Lid Hjort
  • Published online:
    05 September 2012
    Print publication:
    28 July 2008
  • Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code.

Risk Modelling in General Insurance
  • From Principles to Practice
  • Roger J. Gray, Susan M. Pitts
  • Published online:
    05 August 2012
    Print publication:
    28 June 2012
  • Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short-term risk modelling, model-based pricing, risk-sharing, ruin theory and credibility. It covers much of the international syllabuses for professional actuarial examinations in risk models, but goes into further depth, with worked examples, exercises and detailed case studies. The authors also use the statistical package R to demonstrate how simple code and functions can be used profitably in an actuarial context. The authors' engaging and pragmatic approach, balancing rigour and intuition and developed over many years of teaching the subject, makes this book ideal for self-study or for students taking courses in risk modelling.

Exercises in Probability
  • A Guided Tour from Measure Theory to Random Processes, via Conditioning
  • 2nd edition
  • Loïc Chaumont, Marc Yor
  • Published online:
    05 August 2012
    Print publication:
    19 July 2012
  • Derived from extensive teaching experience in Paris, this second edition now includes over 100 exercises in probability. New exercises have been added to reflect important areas of current research in probability theory, including infinite divisibility of stochastic processes, past-future martingales and fluctuation theory. For each exercise the authors provide detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.

The Estimation and Tracking of Frequency
  • B. G. Quinn, E. J. Hannan
  • Published online:
    05 August 2012
    Print publication:
    05 February 2001
  • Many electronic and acoustic signals can be modelled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterise the periodicity or near-periodicity of a signal and consequently to identify its source. This book presents and analyses several practical techniques used for such estimation. The problem of tracking slow frequency changes over time of a very noisy sinusoid is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large. Each chapter begins with a detailed overview, and many applications are given. Matlab code for the estimation techniques is also included. The book will thus serve as an excellent introduction and reference for researchers analysing such signals.

  • Preface to the first edition

  • Loïc Chaumont, Université d'Angers, France, Marc Yor, Université de Paris VI (Pierre et Marie Curie)
  • Book:
    Exercises in Probability
    Published online:
    05 August 2012
    Print publication:
    19 July 2012, pp xvii-xviii

  • Summary

    Originally, the main body of these exercises was developed for, and presented to, the students in the Magistère des Universités Parisiennes between 1984 and 1990; the audience consisted mainly of students from the Écoles Normales, and the spirit of the Magistère was to blend “undergraduate probability” (≟ random variables, their distributions, and so on …) with a first approach to “graduate probability” (≟ random processes). Later, we also used these exercises, and added some more, either in the Préparation à l'Agrégation de Mathématiques, or in more standard Master courses in probability.

    In order to fit the exercises (related to the lectures) in with the two levels alluded to above, we systematically tried to strip a number of results (which had recently been published in research journals) of their random processes apparatus, and to exhibit, in the form of exercises, their random variables skeleton.

    Of course, this kind of reduction may be done in almost every branch of mathematics, but it seems to be a quite natural activity in probability theory, where a random phenomenon may be either studied on its own (in a “small” probability world), or as a part of a more complete phenomenon (taking place in a “big” probability world); to give an example, the classical central limit theorem, in which only one Gaussian variable (or distribution) occurs in the limit, appears, in a number of studies, as a one-dimensional “projection” of a central limit theorem involving processes, in which the limits may be several Brownian motions, the former Gaussian variable appearing now as the value at time 1, say, of one of these Brownian motions.

Page 76 of 136