gp {brms} | R Documentation |

Set up a Gaussian process (GP) term in brms. The function does not evaluate its arguments – it exists purely to help set up a model with GP terms.

gp( ..., by = NA, k = NA, cov = "exp_quad", iso = TRUE, gr = TRUE, cmc = TRUE, scale = TRUE, c = NULL )

`...` |
One or more predictors for the GP. |

`by` |
A numeric or factor variable of the same length as each predictor. In the numeric vector case, the elements multiply the values returned by the GP. In the factor variable case, a separate GP is fitted for each factor level. |

`k` |
Optional number of basis functions for computing approximate
GPs. If |

`cov` |
Name of the covariance kernel. By default,
the exponentiated-quadratic kernel |

`iso` |
A flag to indicate whether an isotropic ( |

`gr` |
Logical; Indicates if auto-grouping should be used (defaults
to |

`cmc` |
Logical; Only relevant if |

`scale` |
Logical; If |

`c` |
Numeric value only used in approximate GPs. Defines the
multiplicative constant of the predictors' range over which
predictions should be computed. A good default could be |

A GP is a stochastic process, which
describes the relation between one or more predictors
*x = (x_1, ..., x_d)* and a response *f(x)*, where
*d* is the number of predictors. A GP is the
generalization of the multivariate normal distribution
to an infinite number of dimensions. Thus, it can be
interpreted as a prior over functions. Any finite sample
realized from this stochastic process is jointly multivariate
normal, with a covariance matrix defined by the covariance
kernel *k_p(x)*, where *p* is the vector of parameters
of the GP:

*f(x) ~ MVN(0, k_p(x))*

The smoothness and general behavior of the function *f*
depends only on the choice of covariance kernel.
For a more detailed introduction to Gaussian processes,
see https://en.wikipedia.org/wiki/Gaussian_process.

Below, we describe the currently supported covariance kernels:

"exp_quad": The exponentiated-quadratic kernel is defined as

*k(x_i, x_j) = sdgp^2 exp(- || x_i - x_j ||^2 / (2 lscale^2))*, where*|| . ||*is the Euclidean norm,*sdgp*is a standard deviation parameter, and*lscale*is characteristic length-scale parameter. The latter practically measures how close two points*x_i*and*x_j*have to be to influence each other substantially.

In the current implementation, `"exp_quad"`

is the only supported
covariance kernel. More options will follow in the future.

An object of class `'gp_term'`

, which is a list
of arguments to be interpreted by the formula
parsing functions of brms.

## Not run: # simulate data using the mgcv package dat <- mgcv::gamSim(1, n = 30, scale = 2) # fit a simple GP model fit1 <- brm(y ~ gp(x2), dat, chains = 2) summary(fit1) me1 <- conditional_effects(fit1, nsamples = 200, spaghetti = TRUE) plot(me1, ask = FALSE, points = TRUE) # fit a more complicated GP model fit2 <- brm(y ~ gp(x0) + x1 + gp(x2) + x3, dat, chains = 2) summary(fit2) me2 <- conditional_effects(fit2, nsamples = 200, spaghetti = TRUE) plot(me2, ask = FALSE, points = TRUE) # fit a multivariate GP model fit3 <- brm(y ~ gp(x1, x2), dat, chains = 2) summary(fit3) me3 <- conditional_effects(fit3, nsamples = 200, spaghetti = TRUE) plot(me3, ask = FALSE, points = TRUE) # compare model fit LOO(fit1, fit2, fit3) # simulate data with a factor covariate dat2 <- mgcv::gamSim(4, n = 90, scale = 2) # fit separate gaussian processes for different levels of 'fac' fit4 <- brm(y ~ gp(x2, by = fac), dat2, chains = 2) summary(fit4) plot(conditional_effects(fit4), points = TRUE) ## End(Not run)

[Package *brms* version 2.15.0 Index]