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...
Clasificación: | Libro Electrónico |
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Autor principal: | |
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.