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Statistical analysis of stochastic processes in time /

"Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeab...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lindsey, James K. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2004.
Colección:Cambridge series on statistical and probabilistic mathematics ; 14.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-title
  • Series-title
  • Title
  • Copyright
  • Contents
  • Preface
  • Notation and symbols
  • Part I Basic principles
  • 1 What is a stochastic process?
  • 1.1 Definition
  • 1.1.1 Time
  • 1.1.2 State space
  • 1.1.3 Randomness
  • 1.1.4 Stationarity, equilibrium, and ergodicity
  • Multivariate distributions
  • Stationarity
  • Equilibrium
  • Ergodicity
  • Regeneration points
  • 1.1.5 Replications
  • 1.2 Dependence among states
  • 1.2.1 Constructing multivariate distributions
  • 1.2.2 Markov processes
  • 1.2.3 State dependence
  • 1.2.4 Serial dependence
  • 1.2.5 Birth processes.
  • 1.3 Selecting models
  • 1.3.1 Preliminary questions
  • 1.3.2 Inference
  • Further reading
  • Exercises
  • 2 Basics of statistical modelling
  • 2.1 Descriptive statistics
  • 2.1.1 Summary statistics
  • 2.1.2 Graphics
  • 2.2 Linear regression
  • 2.2.1 Assumptions
  • 2.2.2 Fitting regression lines
  • Likelihood
  • Multiple regression
  • Interactions
  • 2.3 Categorical covariates
  • 2.3.1 Analysis of variance
  • Baseline constraint
  • Mean constraint
  • 2.3.2 Analysis of covariance
  • Interactions
  • 2.4 Relaxing the assumptions
  • 2.4.1 Generalised linear models
  • Gamma distribution.
  • Log normal and inverse Gauss distributions
  • 2.4.2 Other distributions
  • Weibull distribution
  • Other distributions
  • 2.4.3 Nonlinear regression functions
  • Logistic growth curve
  • Further reading
  • Exercises
  • Part II Categorical state space
  • 3 Survival processes
  • 3.1 Theory
  • 3.1.1 Special characteristics of duration data
  • Interevent times
  • Intensity of events
  • Absorbing states
  • Time origin
  • 3.1.2 Incomplete data
  • Censoring
  • Stopping rules
  • Time alignment
  • 3.1.3 Survivor and intensity functions
  • 3.1.4 Likelihood function
  • 3.1.5 Kaplan-Meier curves.
  • 3.2 Right censoring
  • 3.2.1 Families of models
  • Proportional hazards
  • Accelerated failure times
  • 3.2.2 Intensity and survivor functions
  • 3.3 Interval censoring
  • 3.3.1 Probability models
  • 3.4 Finite mixtures
  • 3.4.1 Probability models
  • 3.5 Models based directly on intensities
  • 3.5.1 Durations and counts of events
  • 3.6 Changing factors over a lifetime
  • 3.6.1 Complex regression function
  • 3.6.2 Overdispersion
  • Further reading
  • Exercises
  • 4 Recurrent events
  • 4.1 Theory
  • 4.1.1 Counting processes
  • Basic concepts
  • Some simple special cases
  • Modelling intensities.
  • 4.1.2 Poisson process
  • Poisson distribution
  • Exponential distribution
  • Modifications of Poisson processes
  • Nonhomogeneous Poisson processes
  • 4.1.3 Departures from randomness
  • 4.1.4 Renewal processes
  • Asymptotics
  • Stationarity
  • Recurrence times
  • Variability
  • Types of failure
  • 4.2 Descriptive graphical techniques
  • 4.2.1 Detecting trends
  • Cumulative events and counts of events
  • 4.2.2 Detecting time dependence
  • 4.2.3 Kaplan-Meier curves
  • 4.3 Counts of recurrent events
  • 4.3.1 Poisson regression
  • 4.3.2 Over- and underdispersion
  • 4.4 Times between recurrent events.