MakeSparseGP

Functional data sample of size n, sparsely sampled from a Gaussian process

A versatile package that provides implementation of various
methods of Functional Data Analysis (FDA) and Empirical Dynamics. The core of this
package is Functional Principal Component Analysis (FPCA), a key technique for
functional data analysis, for sparsely or densely sampled random trajectories
and time courses, via the Principal Analysis by Conditional Estimation
(PACE) algorithm. This core algorithm yields covariance and mean functions,
eigenfunctions and principal component (scores), for both functional data and
derivatives, for both dense (functional) and sparse (longitudinal) sampling designs.
For sparse designs, it provides fitted continuous trajectories with confidence bands,
even for subjects with very few longitudinal observations. PACE is a viable and
flexible alternative to random effects modeling of longitudinal data. There is also a
Matlab version (PACE) that contains some methods not available on fdapace and vice
versa. Updates to fdapace were supported by grants from NIH Echo and NSF DMS-1712864 and DMS-2014626.
Please cite our package if you use it (You may run the command citation("fdapace") to get the citation format and bibtex entry).
References: Wang, J.L., Chiou, J., Müller, H.G. (2016) <doi:10.1146/annurev-statistics-041715-033624>; Chen, K., Zhang, X., Petersen, A., Müller, H.G. (2017) <doi:10.1007/s12561-015-9137-5>.

Yidong Zhou

fdapace

Functional Data Analysis and Empirical Dynamics

Han Chen

Su I Iao

Poorbita Kundu

Hang Zhou

Satarupa Bhattacharjee

Cody Carroll

Yaqing Chen

Xiongtao Dai

Jianing Fan

Alvaro Gajardo

Pantelis Z. Hadjipantelis

Kyunghee Han

Hao Ji

Changbo Zhu

Paromita Dubey

Shu-Chin Lin

Hans-Georg Müller

Jane-Ling Wang

MakeSparseGP function

<dl><dt>n</dt>
<dd>number of samples to generate.</dd>
<dt>rdist</dt>
<dd>a sampler for generating the random design time points within [0, 1].</dd>
<dt>sparsity</dt>
<dd>A vector of integers. The number of observation per sample is chosen to be one of the elements in sparsity with equal chance.</dd>
<dt>muFun</dt>
<dd>a function that takes a vector input and output a vector of the corresponding mean (default: zero function).</dd>
<dt>K</dt>
<dd>scalar specifying the number of basis to be used (default: 2).</dd>
<dt>lambda</dt>
<dd>vector of size K specifying the variance of each components (default: rep(1,K)).</dd>
<dt>sigma</dt>
<dd>The standard deviation of the Gaussian noise added to each observation points.</dd>
<dt>basisType</dt>
<dd>string specifying the basis type used; possible options are: 'sin', 'cos' and 'fourier' (default: 'cos') (See code of 'CreateBasis' for implementation details.)</dd>
<dt>CovFun</dt>
<dd>an alternative specification of the covariance structure.</dd></dl>

Arguments

Create a sparse Functional Data sample for a Gaussian Process — MakeSparseGP

<dl>

<dt>n</dt>
<dd>number of samples to generate.</dd>


<dt>rdist</dt>
<dd>a sampler for generating the random design time points within [0, 1].</dd>


<dt>sparsity</dt>
<dd>A vector of integers. The number of observation per sample is chosen to be one of the elements in sparsity with equal chance.</dd>


<dt>muFun</dt>
<dd>a function that takes a vector input and output a vector of the corresponding mean (default: zero function).</dd>


<dt>K</dt>
<dd>scalar specifying the number of basis to be used (default: 2).</dd>


<dt>lambda</dt>
<dd>vector of size K specifying the variance of each components (default: rep(1,K)).</dd>


<dt>sigma</dt>
<dd>The standard deviation of the Gaussian noise added to each observation points.</dd>


<dt>basisType</dt>
<dd>string specifying the basis type used; possible options are: 'sin', 'cos' and 'fourier' (default: 'cos') (See code of 'CreateBasis' for implementation details.)</dd>


<dt>CovFun</dt>
<dd>an alternative specification of the covariance structure.</dd>

</dl>

Create a sparse Functional Data sample for a Gaussian Process

MakeSparseGP: Create a sparse Functional Data sample for a Gaussian Process

Description

Usage

Value

Arguments