Straight from the article Theory for PEST Users, by Zhulu Lin, University of Georgia:
Its lognormal mode gives a better manageable linear function.
To a given equation, the Q and H variables are mediated by the b and d coefficients.
This notation, known as a simple linear regression model, helps the estimation process of the original b and d coefficients.
In a multiple linear regression model,
the y is the dependent or response variable
while any amount of x’s constitute the independent or predictor variables.
Writing a bunch of n observations together, we have:
... in the matrixial formulation it becomes:
Then better indeed, just:
Here, finally,
we reach the X matrix
as the derivative of Xβ with respect to β.
The parameter estimation process seeks for the best map of Heads (observations), through various attempts to find a good distribution of its set of parameters or variables (k)
In summary PEST varies, incrementally, all of its the predefined parameters (P1 to n), and register the correspondent results for each observation (O1 to n).
This is the Jacobian Matrix First-Order partial derivatives of a multivariate function.
Here the derivatives provides a way to estimate the coefficients of a nonlinear equation.
Beta μ
Here we go!
One of the first PEST control variables is Noptmax.
Use Noptmax = -1, to find out a first, previous, parameters sensibilities data set (SEN).
Beta μ
But to grasp the meaning of this variables, visually, there is a need of a couple of more concepts, about singular value decomposition, mainlly.
Further on, the control variables Rlambda, RlamFAC e NumLAM comes to enhance your chances to find the best parameter set.