Extended multidimensional kernels

Extended multidimensional kernels#

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The standard multidimensional quasi-periodic model uses one latent quasi-periodic GP and, optionally, its first derivative. PyORBIT also includes tinygp multidimensional kernels that add a second latent component: either a cosine term or a squared-exponential term.

These models are useful when the data show an activity signal that is not fully described by a single quasi-periodic latent process.

Model definition and requirements#

model name: tinygp_multidimensional_quasiperiodiccosine

required common object: activity
aliases: tinygp_multidimensional_quasiperiodic_cosine
adds a cosine latent component to the quasi-periodic latent GP

model name: tinygp_multidimensional_quasiperiodicsquaredexponential

required common object: activity
aliases: tinygp_multidimensional_quasiperiodic_squaredexponential
adds a squared-exponential latent component with timescale Pcyc

model name: tinygp_multiquasiperiodic_trainedsquaredexponential

required common object: activity
aliases: tinygp_multiquasiperiodictrainedsquaredexponential
adds a squared-exponential component trained independently within each dataset, while the quasi-periodic component remains multidimensional

All three models require tinygp; read Caveats on the use of tinyGP carefully.

Keywords#

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

hyperparameters_condition

accepted values: True | False
activates the quasi-periodic hyperparameter condition described in the quasi-periodic kernel.

rotation_decay_condition

accepted values: True | False
if activated, requires Pdec > 2 Prot.

use_stellar_rotation_period

accepted values: True | False
replaces Prot with rotation_period from star_parameters.

use_stellar_activity_decay

accepted values: True | False
replaces Pdec with activity_decay from star_parameters.

derivative

accepted values: mapping of dataset names to booleans
sets the default derivative use for each dataset. If not provided, derivatives are enabled for most datasets and disabled for H-alpha, S_index, Ca_HK, and FWHM.

derivative_quasiperiodic

accepted values: mapping of dataset names to booleans
overrides the derivative switch for the quasi-periodic component. If False, rot_amp is fixed to zero for that dataset.

derivative_cosine

accepted values: mapping of dataset names to booleans
used by tinygp_multidimensional_quasiperiodiccosine. If False, cos_der is fixed to zero for that dataset.

derivative_squaredexponential

accepted values: mapping of dataset names to booleans
used by tinygp_multidimensional_quasiperiodicsquaredexponential. If False, cyc_der is fixed to zero for that dataset.

Examples#

Quasi-periodic plus cosine:

models:
  gp_multidimensional:
    model: tinygp_multidimensional_quasiperiodiccosine
    common: activity
    hyperparameters_condition: True
    rotation_decay_condition: True
    RVdata:
      boundaries:
        rot_amp: [0.0, 20.0]
        con_amp: [-20.0, 20.0]
        cos_amp: [-20.0, 20.0]
        cos_der: [-20.0, 20.0]
      derivative_quasiperiodic: True
      derivative_cosine: True
    Sdata:
      boundaries:
        con_amp: [-1.0, 1.0]
        cos_amp: [-1.0, 1.0]
      derivative_quasiperiodic: False
      derivative_cosine: False

Quasi-periodic plus squared-exponential:

common:
  activity:
    boundaries:
      Prot: [10.0, 20.0]
      Pdec: [20.0, 1000.0]
      Pcyc: [100.0, 5000.0]
      Oamp: [0.001, 1.0]
models:
  gp_multidimensional:
    model: tinygp_multidimensional_quasiperiodicsquaredexponential
    common: activity
    RVdata:
      boundaries:
        rot_amp: [0.0, 20.0]
        con_amp: [-20.0, 20.0]
        cyc_amp: [-20.0, 20.0]
        cyc_der: [-20.0, 20.0]
      derivative_quasiperiodic: True
      derivative_squaredexponential: True

Trained squared-exponential component:

models:
  gp_multidimensional:
    model: tinygp_multiquasiperiodic_trainedsquaredexponential
    common: activity
    RVdata:
      boundaries:
        rot_amp: [0.0, 20.0]
        con_amp: [-20.0, 20.0]
        cyc_amp: [0.0, 20.0]
      derivative_quasiperiodic: True

Model parameters#

Quasi-periodic plus cosine#

Name	Parameter	Common?	Definition	Notes
`Prot`	Rotational period of the star	common	`activity`
`Pdec`	Decay timescale of active regions	common	`activity`
`Oamp`	Coherence scale	common	`activity`
`con_amp`	Coefficient of the quasi-periodic latent GP	dataset	`activity`
`rot_amp`	Coefficient of the quasi-periodic derivative	dataset	`activity`	Fixed to zero when `derivative_quasiperiodic: False`
`cos_amp`	Coefficient of the cosine latent component	dataset	`activity`
`cos_der`	Coefficient of the derivative of the cosine component	dataset	`activity`	Fixed to zero when `derivative_cosine: False`

Quasi-periodic plus squared-exponential#

Name	Parameter	Common?	Definition	Notes
`Prot`	Rotational period of the star	common	`activity`
`Pdec`	Decay timescale of active regions	common	`activity`
`Pcyc`	Timescale of the squared-exponential component	common	`activity`
`Oamp`	Coherence scale	common	`activity`
`con_amp`	Coefficient of the quasi-periodic latent GP	dataset	`activity`
`rot_amp`	Coefficient of the quasi-periodic derivative	dataset	`activity`	Fixed to zero when `derivative_quasiperiodic: False`
`cyc_amp`	Coefficient of the squared-exponential component	dataset	`activity`
`cyc_der`	Coefficient of the derivative of the squared-exponential component	dataset	`activity`	Fixed to zero when `derivative_squaredexponential: False`

Multidimensional quasi-periodic plus trained squared-exponential#

Name	Parameter	Common?	Definition	Notes
`Prot`	Rotational period of the star	common	`activity`
`Pdec`	Decay timescale of active regions	common	`activity`
`Pcyc`	Timescale of the trained squared-exponential component	common	`activity`
`Oamp`	Coherence scale	common	`activity`
`con_amp`	Coefficient of the quasi-periodic latent GP	dataset	`activity`
`rot_amp`	Coefficient of the quasi-periodic derivative	dataset	`activity`	Fixed to zero when `derivative_quasiperiodic: False`
`cyc_amp`	Amplitude coefficient of the dataset-local squared-exponential component	dataset	`activity`