Basic notions of statistics

Author:Pierre Gauthier

Email: pierre.gauthier@ec.gc.ca

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  • Basic notions of statistics
  • Diapositive PPT
  • Gaussian distribution
  • Example: Rayleigh distribution
  • Log-normal distribution
  • Log-normal distribution
  • Joint probability distribution for N random variables
  • Covariances, correlations and statistical moments
  • Properties of the statistical mean
  • Estimator for the statistical mean
  • Estimator for the variance
  • Diapositive PPT
  • Summary
  • Gaussian distribution for several random variables
  • Covariances, variances and correlations
  • Correlations
  • Representation of matrix of covariances
  • Statistically independent variables associated with B
  • Example illustrating fT B-1f when f =(f1,f2)T
  • Error covariance of a temperature field
  • Statistical estimation: univariate case (1 point)
  • Best Linear unbiased estimate (BLUE)
  • Observation operator
  • Variational form
  • Statistical interpolation (or method of Gauss-Markov) (Gandin, 1963; Rutherford, 1973; Schlatter,1977; Daley, 1991)
  • Minimum variance estimate: univariate case
  • Derivation of the gain matrix that will minimize the analysis error variance
  • Proof:
  • Gain matrix
  • Analysis error covariances
  • Summary: equations of statistical interpolation
  • Dimensionality of the problem
  • Example: 1D case T(x)
  • Analysis error covariance
  • Hypotheses used in the derivation

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