GP

class luas.GP(kf: Kernel, x_l: Array, x_t: Array, mf: Callable | None = None, logPrior: Callable | None = None, jit: bool | None = True)

Bases: object

Gaussian process class specialised to make the analysis of 2D data sets simple and efficient. Can be used with any Kernel such as LuasKernel to perform the required log-likelihood calculations in addition to performing GP regression. Support for calculating Laplace approximations of the posterior with respect to the input parameters is also provided as it can be very useful when sampling large numbers of parameters (such as for tuning the MCMC).

Must have two separate input dimensions which are used to compute the covariance matrix and may additionally be used to compute the deterministic mean function. The observed data Y is assumed to have shape (N_l, N_t) and will be a parameter of most methods.

The first input x_l is the wavelength/vertical dimension of the observed data Y and is expected to have shape (N_l,) or (d_l, N_l) where N_l is the number of rows of Y and d_l is the number of regression variables along the wavelength/vertical dimension used for kernel inputs and/or mean function inputs. Similarly x_t is assumed to lie along the time/horizontal dimension of the observed data with shape (N_t,) or (d_t, N_t) where N_t is the number of columns of Y and d_t is the number of regression variables along the column dimension used as kernel inputs and/or mean function inputs.

Parameters:

• kf (Kernel) – Kernel object which has already been initialised with the desired kernel function.

• x_l (JAXArray) – Array containing wavelength/vertical dimension regression variable(s). May be of shape (N_l,) or (d_l,N_l) for d_l different wavelength/vertical regression variables.

• x_t (JAXArray) – Array containing time/horizontal dimension regression variable(s). May be of shape (N_t,) or (d_t,N_t) for d_t different time/horizontal regression variables.

• mf (Callable, optional) – The deterministic mean function, by default returns a JAXArray of zeros. Needs to be in the format mf(params, x_l, x_t) and returns a JAXArray of shape (N_l, N_t). matching the shape of the observed data Y.

• logPrior (Callable, optional) – Log prior function, by default returns zero. Needs to be in the format logPrior(params) and return a scalar.

• jit (bool, optional) – Whether to jax.jit compile the likelihood, posterior and GP prediction functions. If set to False then mean functions not written in JAX are supported and can still be used with PyMC (but not NumPyro which requires JIT compilation). Defaults to True.

GP.calculate_stored_values(p)	Calculate a PyTree of stored values from the decomposition of the covariance matrix.
GP.logL(p, Y)	Computes the log likelihood without returning any stored values from the decomposition of the covariance matrix.
GP.logL_hessianable(p, Y)	Computes the log likelihood without returning any stored values from the decomposition of the covariance matrix.
GP.logP(p, Y)	Computes the log posterior without returning any stored values from the decomposition of the covariance matrix.
GP.logP_hessianable(p, Y)	Computes the log posterior without returning any stored values from the decomposition of the covariance matrix.
GP.sigma_clip(p, Y, sigma[, plot, use_gp_mean])	Performs GP regression and replaces any outliers above a given number of standard deviations with the GP predictive mean evaluated at those locations.
GP.plot(p, Y[, x_l_plot, x_t_plot])	Visualises the fit to the data.
GP.autocorrelate(p, Y[, max_sep_l, ...])	Performs a quick (and approximate) 2D autocorrelation using jax.scipy.signal.correlate2d on the observed data after subtraction of the GP predictive mean to examine if there is any remaining correlation in the residuals.
GP.laplace_approx(p, Y[, regularise, ...])	Computes the Laplace approximation at the location of p with options to regularise values which are poorly constrained.
GP.laplace_approx_with_bounds(p, Y, param_bounds)	Computes the Laplace approximation at the location of p but within the transformed parameter space used by PyMC and NumPyro to deal with parameters bounded by a lower and upper bound.
GP.predict(p, Y[, x_l_pred, x_t_pred, ...])	Performs GP regression and computes the GP predictive mean and the GP predictive uncertainty as the standard devation at each location or else can return the full covariance matrix.
GP.logL_stored(p, Y, stored_values)	Computes the log likelihood and also returns any stored values from the decomposition of the covariance matrix.
GP.logL_hessianable_stored(p, Y, stored_values)	Computes the log likelihood and also returns any stored values from the decomposition of the covariance matrix.
GP.logP_stored(p, Y, stored_values)	Computes the log posterior and also returns any stored values from the decomposition of the covariance matrix.
GP.logP_hessianable_stored(p, Y, stored_values)	Computes the log posterior and also returns any stored values from the decomposition of the covariance matrix.