Probabilistic modeling

The current section is dedicated to probabilistic methods and concepts.

Distributions

• Parametric models
• Copulas
• Conditional distributions
• Affine combination of independent univariate random variables

Stochastic process

• Stochastic process definitions
  • Notations
  • Spatial (temporal) and Stochastic Mean
  • Normal process
  • Weak stationarity (second order stationarity)
  • Stationarity
  • Spectral density function
• Covariance models

Transformation of fields

• Trend computation
• Box Cox transformation
  • Marginal Box Cox transformation
  • Estimation of the Box Cox transformation
  • Case 1: General linear models
  • Case 2: Linear models

ARMA stochastic process

• ARMA stochastic process
• ARMA process estimation
  • Multivariate estimation

Normal processes

• Parametric stationary covariance models
  • Example: the multivariate exponential model
• Estimation of a stationary covariance model
• Estimation of a non stationary covariance model
• Estimation of a spectral density function
• Parametric spectral density functions
  • Example: the Cauchy spectral model

Process transformation

• Field functions
  • Value function
  • Vertex value function
• Process transformation
  • General case
  • Trend modifications
  • Box Cox transformation

Stationarity tests

• Dickey-Fuller stationarity test