Performs two-sample GP regression

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Description

Performs gaussian process regression for two time-series: control and case. A third null GP model is learned that assumes both data coming from same process. Various likelihood ratios between the null and individual models are estimated to distinguish when case and control processes are significantly different. Use plot.gppack to visualize the models.

Usage

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gpr2sample(x.ctrl, y.ctrl, x.case = NULL, y.case, x.targets,
  noise.ctrl = NULL, noise.case = NULL, nsnoise = TRUE, nskernel = TRUE,
  expectedmll = FALSE, params.ctrl = NULL, params.case = NULL,
  defaultparams = NULL, lbounds = NULL, ubounds = NULL,
  lockatzero = FALSE, optim.restarts = 3, derivatives = FALSE)

Arguments

x.ctrl

input points (control)

y.ctrl

output values (control)

x.case

input points (case)

y.case

output values (case)

x.targets

target points

noise.ctrl

observational noise

noise.case

observational noise

nsnoise

estimate non-stationary noise function from replicates, if available

nskernel

use non-stationary kernel (default)

expectedmll

use expected MLL optimization criteria

params.ctrl

kernel parameters (control)

params.case

kernel parameters (case)

defaultparams

initial parameters for optimization

lbounds

lower bounds for parameter optimization

ubounds

upper bounds for parameter optimization

lockatzero

estimate a pseudo-observation for time 0

optim.restarts

restarts in the gradient ascent (default=3)

derivatives

compute also GP derivatives

Details

The control and case do not need have same amount of points. The resulting gppack object contains the three learned models and the likelihood ratios along x.targets.

Value

a gppack-object that contains

ctrlmodel

the gp-object corresponding to the control data

casemodel

the gp-object corresponding to the case data

nullmodel

the gp-object corresponding to the shared null data

ratios

the log likelihood ratios between the control and case against the null model, contains..

______$mll

marginal log likelihood ratio

______$emll

expected marginal log likelihood ratio

______$pc

log posterior concentration ratio

______$npc

log noisy posterior concentration ratio

See Also

gpr1sample plot.gppack

Examples

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# read toy data
data(toydata)

## Not run: can take several minutes
 # perform two-sample regression
 res = gpr2sample(toydata$ctrl$x, toydata$ctrl$y, toydata$case$x, toydata$case$y, seq(0,22,0.1))
 print(res)
## End(Not run)

# pre-computed model for toydata
data(toygps)
print(toygps)