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juliohm committed Sep 10, 2021
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35 changes: 13 additions & 22 deletions docs/src/kriging/estimators.md
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Expand Up @@ -26,35 +26,17 @@ The `fit` function takes care of building the Kriging system and factorizing the
an appropriate decomposition (e.g. Cholesky, LU):

```@docs
KrigingEstimators.fit
fit(::KrigingEstimator, ::Any)
```

and the `predict` function performs the estimation at a given location:
and the `predict` function performs the estimation for a given variable and location:

```@docs
KrigingEstimators.predict
predict(::KrigingEstimators.FittedKriging, ::Any, ::Any)
```

Alternative constructors are provided for convenience that will immediately fit the Kriging
parameters to the data. In this case, the data is passed as the first argument. For example:

```julia
OrdinaryKriging(data, var, γ)
```

creates a `OrdinaryKriging(γ)` estimator and fits it to `(data, var)`.

A typical use of the interface is as follows:

```julia
# build and factorize the system
sk = OrdinaryKriging(data, var, γ)

# estimate at various points
for pₒ in [p₁, p₂, p₃]
μ, σ² = predict(sk, pₒ)
end
```
parameters to the data. In this case, the data is passed as the first argument.

For advanced users, the Kriging weights and Lagrange multipliers at a given location can be accessed
with the `weights` method. This method returns a `KrigingWeights` object containing a field `λ` for
Expand All @@ -64,6 +46,15 @@ the weights and a field `ν` for the Lagrange multipliers:
weights
```

These weights can be combined with a vector of observations using the `combine` function:

```@docs
KrigingEstimators.combine
```

This functionality can be useful in real-time applications when the locations of the observations are
fixed and an online stream of data is available.

## Simple Kriging

In Simple Kriging, the mean ``\mu`` of the random field is assumed to be constant *and known*.
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