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Perturbative renormalization group: Explicit calculations

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter uses the assumptions introduced in Chapter 9 to show that it is indeed possible to find a non-Gaussian fixed point in dimension d = 4 - e, both in models with reflection and rotation ... More


Likelihoods and likelihood ratios

Thomas D. Wickens

in Elementary Signal Detection Theory

Published in print:
2001
Published Online:
April 2010
ISBN:
9780195092509
eISBN:
9780199893812
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195092509.003.0009
Subject:
Psychology, Cognitive Psychology

Likelihoods — the probabilities treated as a function of their parameters — are a key concept in statistical decision theory. When applied to signal detection, they give a general method for ... More


Basic Concepts for Smoothing and Semiparametric Regression

Ludwig Fahrmeir and Thomas Kneib

in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.003.0002
Subject:
Mathematics, Probability / Statistics, Biostatistics

This chapter reviews basic concepts for smoothing and semiparametric regression based on roughness penalties or — from a Bayesian perspective — corresponding smoothness priors. In particular, it ... More


Generalized Linear Mixed Models

Ludwig Fahrmeir and Thomas Kneib

in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.003.0003
Subject:
Mathematics, Probability / Statistics, Biostatistics

This chapter gives an introduction to linear and generalized linear mixed models. The primary goal is to describe concepts for statistical modelling and inference in this class of models that are ... More


Approximate filtering and smoothing

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0010
Subject:
Mathematics, Probability / Statistics

This chapter discusses approximate filtering and smoothing methods for the analysis of non-Gaussian and nonlinear models. The chapter is organized as follows. Sections 10.2 and 10.3 consider two ... More


Importance sampling for smoothing

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter develops the methodology of importance sampling based on simulation for the analysis of observations from the non-Gaussian and nonlinear models that were specified in Chapter 9. It shows ... More


Particle filtering

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0012
Subject:
Mathematics, Probability / Statistics

This chapter discusses the filtering of non-Gaussian and nonlinear series by fixing the sample at the values previously obtained at times …, t − 2, t − 1 and choosing a fresh value at time t only. A ... More


Non-Gaussian and nonlinear illustrations

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0014
Subject:
Mathematics, Probability / Statistics

This chapter discusses examples which illustrate the methods that were developed in Part II for analysing observations using non-Gaussian and nonlinear state space models. These include the monthly ... More


Introduction

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0001
Subject:
Mathematics, Probability / Statistics

This introductory chapter provides an overview of the main themes covered in the present book, namely linear Gaussian state space models and non-Gaussian and nonlinear state space models. It also ... More


Tricks of the trade

Paul T. Callaghan

in Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199556984
eISBN:
9780191774928
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556984.003.0012
Subject:
Physics, Condensed Matter Physics / Materials, Nuclear and Plasma Physics

This chapter gives pointers to the experimentalist on how to avoid artifact in the practical implementation of Pulsed Gradient Spin Echo NMR, and explores the role of the instrumental diffusion ... More


The renormalization group applied to turbulence

W. David McComb

in Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199689385
eISBN:
9780191768255
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199689385.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The basic algorithm of RG applied to turbulence is really very simple. Naturally, there are practical difficulties in the way, and so we can only expect to carry the procedure out as an ... More


Introduction to the Kalman filter

C. Snyder

in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198723844
eISBN:
9780191791185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198723844.003.0003
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter introduces The Kalman filter, which implements Bayesian data assimilation for linear, Gaussian systems. Its update equations can also be derived as the best linear unbiased estimator ... More


Quantum Optomechanics: from Gravitational Wave Detectors to Macroscopic Quantum Mechanics

Yanbei Chen

in Quantum Optomechanics and Nanomechanics: Lecture Notes of the Les Houches Summer School: Volume 105, August 2015

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198828143
eISBN:
9780191866920
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198828143.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of ... More


Data assimilation in meteorology

F. Rabier and M. Fisher

in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198723844
eISBN:
9780191791185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198723844.003.0019
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter discusses some of the implementation details that are necessary to apply data assimilation in the context of numerical weather prediction (NWP). It is divided into three parts. The first ... More


Forecasting the Boat Race

Geert Mesters and Siem Jan Koopman

in Unobserved Components and Time Series Econometrics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.003.0007
Subject:
Economics and Finance, Econometrics

This chapter looks at the forecasting of the yearly outcome of the Boat Race between Cambridge and Oxford. The relative performance of different dynamic models for forty years of forecasting is ... More


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