SHO and Matern-3/2 kernels

SHO and Matern-3/2 kernels#

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The SHO and Matern-3/2 kernels are generic GP kernels that can be used for stellar variability or correlated residuals. By default their parameters are dataset-specific. They can also share timescales across datasets or borrow the stellar rotation and activity-decay parameters from common objects.

Model definition and requirements#

model name: tinygp_sho

  • required common object: activity

  • implemented with tinygp

model name: celerite2_sho

  • required common object: activity

  • implemented with celerite2

model name: spleaf_sho

  • required common object: activity

  • implemented with S+LEAF

model name: tinygp_matern32

  • required common object: activity

  • implemented with tinygp

model name: celerite2_matern32

  • required common object: activity

  • implemented with celerite2

Keywords#

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

use_shared_hyperparameters

  • accepted values: True | False

  • moves all kernel parameters from dataset-specific to common parameters. For SHO models this includes sho_scale, sho_decay, and sho_sigma; for Matern-3/2 models this includes matern32_scale and matern32_sigma.

use_shared_scale

  • accepted values: True | False

  • makes only the kernel timescale common. For SHO models this is sho_scale; for Matern-3/2 models this is matern32_scale.

use_shared_decay

  • accepted values: True | False

  • makes only the SHO damping timescale sho_decay common.

use_activity_Prot

  • accepted values: True | False

  • replaces the kernel scale with Prot from the activity common object.

use_activity_Pdec

  • accepted values: True | False

  • replaces the kernel decay or scale with Pdec from the activity common object.

use_stellar_rotation_period

  • accepted values: True | False

  • replaces the kernel scale with rotation_period from star_parameters.

use_stellar_activity_decay

  • accepted values: True | False

  • replaces the kernel decay or scale with activity_decay from star_parameters.

For Matern-3/2 models the replacement flags are mutually exclusive because there is only one timescale.

The SHO models also support the hyperparameter-condition keywords described in the quasi-periodic plus derivative kernel. In that case the SHO scale is interpreted as Prot and the SHO decay is interpreted as Pdec for the purpose of the condition.

Examples#

Dataset-specific SHO kernel:

1models:
2  celerite2_sho:
3    model: celerite2_sho
4    boundaries:
5      sho_scale: [0.1, 100.0]
6      sho_decay: [0.1, 1000.0]
7      sho_sigma: [0.0, 1.0]

Matern-3/2 kernel with a shared timescale:

 1common:
 2  activity:
 3    boundaries:
 4      matern32_scale: [0.1, 100.0]
 5models:
 6  tinygp_matern32:
 7    model: tinygp_matern32
 8    common: activity
 9    use_shared_scale: True
10    boundaries:
11      matern32_sigma: [0.0, 1.0]

SHO kernel using stellar rotation and activity decay from star_parameters:

 1common:
 2  activity:
 3    model: activity
 4  star:
 5    star_parameters:
 6      boundaries:
 7        rotation_period: [10.0, 20.0]
 8        activity_decay: [20.0, 1000.0]
 9models:
10  spleaf_sho:
11    model: spleaf_sho
12    common:
13      - activity
14      - star_parameters
15    use_stellar_rotation_period: True
16    use_stellar_activity_decay: True
17    boundaries:
18      sho_sigma: [0.0, 1.0]

Model parameters#

SHO models#

Name

Parameter

Common?

Definition

Notes

sho_scale

SHO undamped period, or rho

dataset

activity

Common when use_shared_scale: True or use_shared_hyperparameters: True

sho_decay

SHO damping timescale, or tau

dataset

activity

Common when use_shared_decay: True or use_shared_hyperparameters: True

sho_sigma

Standard deviation of the process

dataset

activity

Common when use_shared_hyperparameters: True

Matern-3/2 models#

Name

Parameter

Common?

Definition

Notes

matern32_scale

Matern-3/2 scale, or rho

dataset

activity

Common when use_shared_scale: True or use_shared_hyperparameters: True

matern32_sigma

Standard deviation of the process

dataset

activity

Common when use_shared_hyperparameters: True

Tip

Some older result files may contain matern32_rho. The current models map it internally to matern32_scale.