Statistical estimation: univariate case

Xb = forecast(or background field)

Xo = observation

Xa = analysis

and Xt = true state

eb = (Xb - Xt): forecast error

eo = (Xo - Xt): observation error

ea = (Xa - Xt): analysis error

Underlying hypotheses to statistical interpolation

• Observation and forecast error is unbiased áebñ = áeoñ = 0
• error variances sb2 et so2 are known

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