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 -- 4.4.1 Renewal processes -- 4.4.2 Nonhomogeneous renewal processes -- Further reading -- Exercises -- 5 Discrete-time Markov chains -- 5.1 Theory -- 5.1.1 Transition matrices -- Marginal and conditional probabilities -- Stationarity -- Reversibility -- Aggregation -- 5.1.2 Time spent in a state -- Duration in a state -- Recurrence of a state -- 5.1.3 Random walks -- General case -- Application to Markov chains -- 5.2 Binary point processes -- 5.2.1 Transition matrices -- 5.2.2 Logistic regression -- Binary time series -- Contingency table -- 5.2.3 Log linear models -- 5.3 Checking the assumptions -- 5.3.1 Homogeneous transitions -- Global homogeneity -- Local homogeneity -- 5.3.2 Order -- 5.4 Structured transition matrices.

5.4.1 Reversibility and equilibrium -- 5.4.2 Random walks -- 5.4.3 Mover-stayer model -- Further reading -- Exercises -- 6 Event histories -- 6.1 Theory -- 6.1.1 Diagrams -- 6.1.2 Defining the states -- 6.1.3 Continuous-time Markov chains -- Differences with respect to discrete time -- Embedded Markov chain -- 6.1.4 Semi-Markov processes -- 6.2 Models for missing observations -- 6.2.1 Erratic and permanent missingness -- 6.2.2 Trends in missingness -- 6.3 Progressive states -- 6.3.1 Constant intensities within states -- 6.3.2 Intensities depending on time -- 6.3.3 Intensities depending on covariates -- Further reading -- Exercises -- 7 Dynamic models -- 7.1 Serial dependence -- 7.1.1 Single count responses -- 7.1.2 Binary count responses -- 7.1.3 Overdispersion -- 7.1.4 Changing variability over time -- 7.2 Hidden Markov models -- 7.2.1 Theory -- Hidden state space -- Fitting a model -- Continuous time -- Discretized hidden Poisson process -- 7.2.2 Clustered point process -- 7.3 Overdispersed durations between recurrent events -- 7.3.1 Theory -- Gamma mixture -- Updating the parameters -- 7.3.2 Frailty -- 7.3.3 Longitudinal dependence -- 7.4 Overdispersed series of counts -- 7.4.1 Theory -- Further reading -- Exercises -- 8 More complex dependencies -- 8.1 Birth processes -- 8.1.1 Birth or contagion -- 8.1.2 Learning models -- 8.1.3 Overdispersion -- 8.2 Autoregression -- 8.2.1 Theory -- Conditional exponential family -- Exponential dispersion family -- 8.3 Marked point processes -- 8.3.1 Theory -- Compound Poisson processes -- Finite mixture models -- 8.3.2 Markov chains with marks -- 8.4 Doubly stochastic processes -- 8.4.1 Theory -- Gamma mixture of Weibull distributions -- 8.5 Change points -- 8.5.1 Theory -- 8.5.2 Hidden Markov model -- Exercises -- Part III Continuous state space -- 9 Time series -- 9.1 Descriptive graphical techniques.

9.1.1 Graphics -- 9.1.2 Correlograms -- Autocorrelation function -- Partial autocorrelation function -- 9.2 Autoregression -- 9.2.1 AR(1) -- Conditional approach -- Covariance matrix -- Continuous time -- Autocorrelation functions -- 9.2.2 Transformations -- 9.2.3 Random walks -- 9.2.4 Heteroscedasticity -- 9.3 Spectral analysis -- 9.3.1 Periodograms -- Estimation -- Cumulative periodogram -- 9.3.2 Models for spectra -- Autoregression -- Exponential model -- Exercises -- 10 Diffusion and volatility -- 10.1 Wiener diffusion process -- 10.1.1 Theory -- Measurement error -- Likelihood function -- 10.2 Ornstein-Uhlenbeck diffusion process -- 10.2.1 Theory -- Integrated Ornstein-Uhlenbeck process -- 10.2.2 Modelling velocity -- 10.3 Heavy-tailed distributions -- 10.3.1 Stable distributions -- Definition -- Special cases -- Properties -- Estimation -- 10.3.2 Other heavy-tailed distributions -- 10.4 ARCH models -- 10.4.1 Theory -- Normal distribution -- Extensions -- 10.4.2 Biological variability -- Further reading -- Exercises -- 11 Dynamic models -- 11.1 Kalman filtering and smoothing -- 11.1.1 Theory -- Autoregression models -- Model specification -- 11.1.2 Continuous-time autoregression -- 11.2 Hidden Markov models -- 11.3 Overdispersed responses -- Further reading -- Exercises -- 12 Growth curves -- 12.1 Characteristics -- 12.2 Exponential forms -- 12.2.1 Exponential growth -- Distributional assumptions -- 12.2.2 Monomolecular growth -- 12.3 Sigmoidal curves -- 12.3.1 Logistic growth -- 12.3.2 Gompertz growth -- 12.4 Richards growth curve -- Further reading -- Exercises -- 13 Compartment models -- 13.1 Theory -- 13.1.1 First-order kinetics -- 13.1.2 Open, first-order, one-compartment model -- 13.2 Modelling delays in elimination -- 13.2.1 Random walk -- 13.2.2 Gamma distribution -- 13.3 Measurements in two compartments -- 13.3.1 Models for proportions.

Further reading -- Exercises -- 14 Repeated measurements -- 14.1 Random effects -- 14.1.1 Mixture models -- Construction of a mixture distribution -- Choice of random parameters -- 14.1.2 Choice of mixing distribution -- Conjugate distributions -- Other mixtures -- 14.2 Normal random intercepts -- 14.2.1 Collections of time series -- 14.2.2 Cross-over trials -- 14.3 Normal random coefficients -- 14.3.1 Random coefficients in time -- 14.4 Gamma random effects -- Further reading -- Exercises -- References -- Author index -- Subject index.