To launch the Gaussian Process platform, choose Analyze > Modeling > Gaussian Process from the main menu bar. Here, we illustrate the platform with 2D Gaussian Process Example.jmp data set, found in the sample data folder.
introduces a ridge parameter into the estimation procedure. This is useful if there is noise or randomness in the response, and you would like the prediction model to smooth over the noise instead of perfectly interpolating.
lets you choose the correlation structure used in the model. The platform fits a spatial correlation model to the data, where the correlation of the response between two observations decreases as the values of the independent variables become more distant.
Gaussian restricts the correlation between two points to always be non-zero, no matter the distance between the points.
Cubic lets the correlation between two points to be zero for points far enough appart. This method can be considered a generalization of a cubic spline.
lets you set the minimum theta value used in the fitted model. The default is 0. The theta values are analogous to a slope parameter in regular regression models. If a theta value is 0 in the fitted model, then that X variable has no influence on the predicted values.
In this example, we are interested in finding the explanatory power of the two x-variables (X1 and X2) on Y. A plot of X1 and X2 shows their even dispersal in the factor space.
Since this is generated data, we can look at the function that generates the Y values. It is this function that we want to estimate.