Multidimensional Matern-3/2 kernel

Multidimensional Matern-3/2 kernel#

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The tinygp_multidimensional_matern32 model applies the multidimensional-GP construction to a Matern-3/2 latent process. Each dataset is modeled as a linear combination of the latent process and, optionally, its first derivative.

This model is less physically tied to stellar rotation than the quasi-periodic multidimensional GP, but it can be useful for flexible correlated-noise models shared across several time series.

Model definition and requirements#

model name: tinygp_multidimensional_matern32

Keywords#

Model-wide keywords, with the default value in boldface.

derivative

  • accepted values: mapping of dataset names to booleans

  • if False, the derivative coefficient matern32_multigp_sigma_deriv is fixed to zero for that dataset. If the keyword is not provided, derivatives are enabled for most datasets and disabled for H-alpha, S_index, Ca_HK, and FWHM.

use_shared_scale

  • accepted values: True | False

  • the Matern-3/2 scale matern32_scale is common by default in this multidimensional model.

use_activity_Prot

  • accepted values: True | False

  • replaces matern32_scale with Prot from the activity common object.

use_activity_Pdec

  • accepted values: True | False

  • replaces matern32_scale with Pdec from the activity common object.

use_stellar_rotation_period

  • accepted values: True | False

  • replaces matern32_scale with rotation_period from star_parameters.

use_stellar_activity_decay

  • accepted values: True | False

  • replaces matern32_scale with activity_decay from star_parameters.

The replacement flags are mutually exclusive because the model has only one scale parameter.

Example#

 1inputs:
 2  RVdata:
 3    file: datasets/RV_PyORBIT.dat
 4    kind: RV
 5    models:
 6      - gp_multidimensional_matern32
 7  BISdata:
 8    file: datasets/BIS_PyORBIT.dat
 9    kind: BIS
10    models:
11      - gp_multidimensional_matern32
12common:
13  activity:
14    boundaries:
15      matern32_scale: [1.0, 100.0]
16models:
17  gp_multidimensional_matern32:
18    model: tinygp_multidimensional_matern32
19    common: activity
20    RVdata:
21      boundaries:
22        matern32_multigp_sigma: [-20.0, 20.0]
23        matern32_multigp_sigma_deriv: [-20.0, 20.0]
24      derivative: True
25    BISdata:
26      boundaries:
27        matern32_multigp_sigma: [-20.0, 20.0]
28      derivative: False

Model parameters#

Name

Parameter

Common?

Definition

Notes

matern32_scale

Scale of the Matern-3/2 latent GP

common

activity

Older files may use matern32_rho

matern32_multigp_sigma

Coefficient of the latent GP

dataset

activity

matern32_multigp_sigma_deriv

Coefficient of the first derivative of the latent GP

dataset

activity

Fixed to zero when derivative: False