Description Usage Arguments Details Value References Examples

Fit (train) a GaSP model.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
Fit(
x,
y,
reg_model,
sp_model = NULL,
cor_family = c("PowerExponential", "Matern"),
cor_par = data.frame(0),
random_error = c(FALSE, TRUE),
sp_var = -1,
error_var = -1,
nugget = 1e-09,
tries = 10,
seed = 500,
fit_objective = c("Likelihood", "Posterior"),
theta_standardized_min = 0,
theta_standardized_max = .Machine$double.xmax,
alpha_min = 0,
alpha_max = 1,
derivatives_min = 0,
derivatives_max = 3,
log_obj_tol = 1e-05,
log_obj_diff = 0,
lambda_prior = 0.1,
model_comparison = c("Objective", "CV")
)
``` |

`x` |
A data frame containing the input (explanatory variable) training data. |

`y` |
A vector or a data frame with one column containing the output (response) training data. |

`reg_model` |
The regression model, specified as a formula, but note the left-hand side of the formula is unused; see example. |

`sp_model` |
An optional stochastic process model, specified as a formula,
but note the left-hand side of the formula and the intercept are unused.
The default |

`cor_family` |
A character string specifying the (product, anisoptropic) correlation-function family: "PowerExponential" for the power-exponential family or "Matern" for the Matern family. |

`cor_par` |
An optional data frame containing the correlation parameters
with one row per |

`random_error` |
A boolean for the presence or not of a random (measurement, white-noise) error term. |

`sp_var, error_var` |
The stochastic process and error variances;
legal values are only used if |

`nugget` |
For numerical stability the proportion of the total variance
due to random error is fixed at this value ( |

`tries` |
Number of optimizations of the objective from different random starting points. |

`seed` |
The random-number seed to generate starting points. |

`fit_objective` |
The objective that |

`theta_standardized_min, theta_standardized_max` |
The minimum and maximum of the standardized |

`alpha_min, alpha_max` |
The minimum and maximum
of the |

`derivatives_min, derivatives_max` |
The minimum and maximum
of the |

`log_obj_tol` |
An absolute tolerance for terminating the maximization of the log of the objective. |

`log_obj_diff` |
The critical value for the change in the log objective for informal tests during optimization of correlation parameters. No testing is done with the default of 0; a larger critical value such as 2 may give a more parsimonious model. |

`lambda_prior` |
The rate parameter of an exponential prior
for each |

`model_comparison` |
The criterion used to select from multiple solutions
when |

Fit numerically maximizes the profile objective function with respect to the correlation parameters; the mean and overall variance parameters are estimated in closed form given the correlation parameters.

A `cor_par`

data frame supplied by the user is the starting point
for the first optimization try.
If `random_error = TRUE`

,
then `sp_var`

/ (`sp_var`

+ `error_var`

) is another
correlation parameter to be optimized;
`sp_var`

and `error_var`

values supplied by the user
will initialize this parameter for the first try.

Set `random_error = TRUE`

to estimate the variance of the
random (measurement, white-noise) error;
a small `nugget`

error variance is for numerical stability.

For term *j* in the stochastic-process model,
the estimate of *θ_j* is constrained between
`theta_standardized_min`

/ *r_j^2* and
`theta_standardized_max`

/ *r_j^2*,
where *r_j* is the range of term *j*.
Note that `Fit`

returns unscaled estimates relating to the original, unscaled inputs.

A `GaSPModel`

object, which is a list with the following components:

`x` |
The data frame containing the input training data. |

`y` |
The training output data, now as a vector. |

`reg_model` |
The regression model, now in the form of a data frame. |

`sp_model` |
The stochastic process model, now in the form of a data frame. |

`cor_family` |
The correlation family. |

`cor_par` |
A data frame for the estimated correlation parameters. |

`random_error` |
The boolean for the presence or not of a random error term. |

`sp_var` |
The estimated stochastic process variance. |

`error_var` |
The estimated random error variance. |

`beta` |
A data frame holding the estimated regression-model parameters. |

`objective` |
The maximum value found for the objective function: the log likelihood (fit_objective = "Likelihood") or the log posterior (fit_objective = "Posterior"). |

`cond_num` |
The condition number. |

`CVRMSE` |
The leave-one-out cross-validation root mean squared error. |

Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P. (1989)
"Design and Analysis of Computer Experiments", *Statistical Science*, 4, pp. 409-423,
doi:10.1214/ss/1177012413.

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