Compute double integral of the covariance kernel over a [0,1]^d domain

Performs Gaussian process regression with heteroskedastic noise following the model by Binois, M., Gramacy, R., Ludkovski, M. (2016) <doi:10.48550/arXiv.1611.05902>, with implementation details in Binois, M. & Gramacy, R. B. (2021) <doi:10.18637/jss.v098.i13>. The input dependent noise is modeled as another Gaussian process. Replicated observations are encouraged as they yield computational savings. Sequential design procedures based on the integrated mean square prediction error and lookahead heuristics are provided, and notably fast update functions when adding new observations.

Mickael Binois

hetGP

Heteroskedastic Gaussian Process Modeling and Design under
Replication

Wij function

<dl><dt>mu1, mu2</dt>
<dd>input locations considered</dd>
<dt>theta</dt>
<dd>lengthscale hyperparameter of the kernel</dd>
<dt>type</dt>
<dd>kernel type, one of "<code>Gaussian</code>", "<code>Matern5_2</code>" or "<code>Matern3_2</code>", see <code>cov_gen</code></dd></dl>

Arguments

Compute double integral of the covariance kernel over a [0,1]^d domain — Wij

<dl>

<dt>mu1, mu2</dt>
<dd>input locations considered</dd>


<dt>theta</dt>
<dd>lengthscale hyperparameter of the kernel</dd>


<dt>type</dt>
<dd>kernel type, one of "<code>Gaussian</code>", "<code>Matern5_2</code>" or "<code>Matern3_2</code>", see <code>cov_gen</code></dd>

</dl>

Wij: Compute double integral of the covariance kernel over a [0,1]^d domain

Description

Usage

Arguments

References