Format:
1 online resource (354 pages)
Edition:
2009 Electronic reproduction; Available via World Wide Web
ISBN:
9780511211942
,
0511211945
,
0521837413
Series Statement:
Cambridge Series in Statistical and Probabilistic Mathematics v.14
Content:
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.
Content:
This introduction to ways of modelling phenomena that occur over time is accessible to anyone with a basic knowledge of statistical ideas. Examples from physical, biological and social sciences show how the principles can be put into practice: data sets and R code for these are supplied on author's website
Note:
Description based on publisher supplied metadata and other sources
,
Cover; Half-title; Series-title; Title; Copyright; Contents; Preface; Notation and symbols; 1 What is a stochastic process?; 2 Basics of statistical modelling; 3 Survival processes; 4 Recurrent events; 5 Discrete-time Markov chains; 6 Event histories; 7 Dynamic models; 8 More complex dependencies; 9 Time series; 10 Diffusion and volatility; 11 Dynamic models; 12 Growth curves; 13 Compartment models; 14 Repeated measurements; References; Author index; Subject index
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
9780521837415
Additional Edition:
Erscheint auch als Druck-Ausgabe Lindsey, James K. Statistical analysis of stochastic processes in time Cambridge [u.a.] : Cambridge University Press, 2004 0521837413
Additional Edition:
Print version Statistical Analysis of Stochastic Processes in Time
Language:
English
Subjects:
Mathematics
Keywords:
Markov-Kette
;
Stochastischer Prozess
;
Stochastischer Prozess
URL:
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