gpsmoothllik

Marginal log-likelihood and gradient as a function of GP hyper-parameters phi and observation noise standard deviation sigma. For use in Gaussian process smoothing where values of phi and sigma may be optimized.

Provides fast and accurate inference for the parameter estimation problem in Ordinary Differential
Equations, including the case when there are unobserved system components. Implements the MAGI method
(MAnifold-constrained Gaussian process Inference) of Yang, Wong, and Kou (2021) <doi:10.1073/pnas.2020397118>.
A user guide is provided by the accompanying software paper Wong, Yang, and Kou (2024) <doi:10.18637/jss.v109.i04>.

Shihao Yang

magi

MAnifold-Constrained Gaussian Process Inference

Samuel W.K. Wong

S.C. Kou

gpsmoothllik function

<dl><dt>phisig</dt>
<dd>vector containing GP hyper-parameters phi and observation noise SD sigma. See <code>calCov</code> for the definitions of the hyper-parameters.</dd>
<dt>yobs</dt>
<dd>vector of observations</dd>
<dt>rInput</dt>
<dd>distance matrix between all time points of <code>yobs</code></dd>
<dt>kerneltype</dt>
<dd>the covariance kernel, types <code>matern</code>, <code>rbf</code>, <code>compact1</code>, <code>periodicMatern</code>, <code>generalMatern</code> are supported. See <code>calCov</code> for their definitions.</dd></dl>

Arguments

Marginal log-likelihood for Gaussian process smoothing — gpsmoothllik

<dl>

<dt>phisig</dt>
<dd>vector containing GP hyper-parameters phi and observation noise SD sigma. See <code>calCov</code> for the definitions of the hyper-parameters.</dd>


<dt>yobs</dt>
<dd>vector of observations</dd>


<dt>rInput</dt>
<dd>distance matrix between all time points of <code>yobs</code></dd>


<dt>kerneltype</dt>
<dd>the covariance kernel, types <code>matern</code>, <code>rbf</code>, <code>compact1</code>, <code>periodicMatern</code>, <code>generalMatern</code> are supported. See <code>calCov</code> for their definitions.</dd>

</dl>

gpsmoothllik: Marginal log-likelihood for Gaussian process smoothing

Description

Usage

Value

Arguments

Examples