Default boundaries, spaces, and priors#

This page collects the default parameter properties used by PyORBIT when the configuration file does not override them with boundaries, spaces, priors, or fixed.

The model pages explain when a parameter is activated. This page is meant as a compact lookup table for the defaults attached to the common objects and to the few model-local parameters that define their own default properties.

Important

Boundaries and priors in the YAML file must be written in the physical (or natural) parameter space. This is also true when the parameter is sampled in a logarithmic space. In that case, boundaries must be strictly positive.

In the tables below:

  • Uniform [] means a uniform prior over the listed boundaries, with no extra prior hyperparameters.

  • None in the Fixed column means that the parameter has no predefined value when fixed by the user.

  • dynamic means that the numerical boundary is computed from the dataset or from another model at initialisation time.

  • Pattern rows such as poly_c{0..9} represent all parameters in the indicated range.

Dataset systematics#

Each dataset will include one offset and one jitter parameter for each active flag in the input file. The actual parameter names are offset_0, offset_1, … and jitter_0, jitter_1, …

Parameter

Boundaries

Space

Prior

Fixed

Notes

offset_{n}

dynamic

Linear

Uniform []

[0.0, 0.0]

See subsection below.

jitter_{n}

dynamic

Linear

Uniform []

[0.0, 0.0]

See subsection below.

jitter_{n} for transit-time or transit-duration datasets

dynamic

Logarithmic

Uniform []

[0.0, 0.0]

Same boundary logic as jitter_{n}, but sampled logarithmically.

Offset boundaries#

The boundaries associated with each offset will be as large as possible to accommodate improbable or anomalous situations, such as eccentric planets or massive long-period companions with partial RV coverage.

Given x as the array with the time of the observations, y as the array with the data, and e as the corresponding error, the boundaries for the offset are determined in the following way:

x_range = np.max(x) - np.min(x)
y_range = np.max(y) - np.min(y)
y_trend = np.abs(y_range/x_range)
y_diff = np.abs(np.mean(x)-Tref) * y_trend + 1000.
offset_boundaries = [np.min(y) - 10.*y_diff, np.max(y) + 10.*y_diff]

where \(T_{\rm ref}\) is the reference time specified in the parame

Broad boundaries do not represent a problem when running an MCMC sampler, given an adequate starting point. When running pyDE+emcee, for example, you must allow a sufficiently large number of generations for the pyDE code to properly explore the parameter space; typically, 50000 generations is a good starting value.

Jitter boundaries#

The jitter boundaries are computed dynamically by taking the maximum error in the array as the reference and multiplying or dividing by 100 to set the upper or lower limits, respectively.

jitter_boundaries = [min(e)/100, 100 max(e)]

The lower boundary is intentionally set to a value other than zero to avoid problems for datasets where the jitter parameter is explored in logarithmic space. Since jitter is added in quadrature to the formal errors, a value much smaller than the error has the same effect as no jitter at all. Hence, in most cases it is not necessary to change the default lower limit to zero.

Changing the boundaries#

Offset and jitter boundaries are determined using the whole dataset, without distinction by the flag specified in the 4th and 5th columns (see Prepare a dataset file )

LEt’s take the case when a dataset is using two flags for jitter and two flags for offset, e.g., when putting together data collected with HARPS and HARPS-N but you want to use a single covariance matrix for the stellar activity. You can specify different boundaries for each distinct jitter and offset parameters:

 1inputs:
 2  RVdata:
 3    file: datasets/K2-141_RV_PyORBIT.dat
 4    kind: RV
 5    models:
 6      - radial_velocities
 7      - tinygp_quasiperiodic
 8    boundaries:
 9      jitter_0: [ 0.00,   10.0]
10      jitter_1: [ 0.00,   20.0]
11      offset_0: [ -3500.0, -3300.0]
12      offset_1: [ -4000.0, -3000.0]
----- dataset:  RVdata
jitter_0      id:  11  s:Linear      b:[      0.0000,      10.0000]   p:Uniform   []
jitter_1      id:  12  s:Linear      b:[      0.0000,      20.0000]   p:Uniform   []
offset_0      id:  13  s:Linear      b:[  -3500.0000,   -3300.0000]   p:Uniform   []
offset_1      id:  14  s:Linear      b:[  -4000.0000,   -3000.0000]   p:Uniform   []

If you don’t specify the boundaries for one of the parameters, the automa

 8    boundaries:
 9      #jitter_0: [ 0.00,   10.0]
10      jitter_1: [ 0.00,   20.0]
11      #offset_0: [ -3500.0, -3300.0]
12      offset_1: [ -4000.0, -3000.0]
----- dataset:  RVdata
jitter_0      id:  11  s:Linear      b:[      0.0120,    1088.3783]   p:Uniform   []
jitter_1      id:  12  s:Linear      b:[      0.0000,      20.0000]   p:Uniform   []
offset_0      id:  13  s:Linear      b:[ -13430.6237,    6632.5000]   p:Uniform   []
offset_1      id:  14  s:Linear      b:[  -4000.0000,   -3000.0000]   p:Uniform   []

To apply the same boundaries:

 8    boundaries:
 9      jitter: [ 0.00,   10.0]
10      offset: [ -3500.0, -3300.0]
----- dataset:  RVdata
jitter_0      id:  11  s:Linear      b:[      0.0000,      10.0000]   p:Uniform   []
jitter_1      id:  12  s:Linear      b:[      0.0000,      10.0000]   p:Uniform   []
offset_0      id:  13  s:Linear      b:[  -3500.0000,   -3300.0000]   p:Uniform   []
offset_1      id:  14  s:Linear      b:[  -3500.0000,   -3300.0000]   p:Uniform   []

The same considerations above applies also to spaces and priors, for example:

 8    boundaries:
 9      jitter: [ 0.00,   10.0]
10      offset: [ -3500.0, -3300.0]
11    priors:
12      jitter: ['HalfGaussian', 0.00, 10.0]
13      offset: ['Gaussian', -3450.0, 10.0]
----- dataset:  RVdata
jitter_0      id:  11  s:Linear      b:[      0.0000,      10.0000]   p:HalfGaussian   [ 0. 10.]
jitter_1      id:  12  s:Linear      b:[      0.0000,      10.0000]   p:HalfGaussian   [ 0. 10.]
offset_0      id:  13  s:Linear      b:[  -3500.0000,   -3300.0000]   p:Gaussian   [-3450.    10.]
offset_1      id:  14  s:Linear      b:[  -3500.0000,   -3300.0000]   p:Gaussian   [-3450.    10.]

Planets#

Common object: common: planets.

Parameter

Boundaries

Space

Prior

Fixed

P

[0.4, 100000.0]

Log_Base2

Uniform []

None

K

[0.001, 2000.0]

Log_Base2

Uniform []

None

Tc

[0.0, 1000.0]

Linear

Uniform []

None

Tc_Tref

[0.0, 1000.0]

Linear

Uniform []

None

mean_long

[0.0, 360.0]

Linear

Uniform []

0.0

e_coso

[-1.0, 1.0]

Linear

Uniform []

0.0

e_sino

[-1.0, 1.0]

Linear

Uniform []

0.0

sre_coso

[-1.0, 1.0]

Linear

Uniform []

0.0

sre_sino

[-1.0, 1.0]

Linear

Uniform []

0.0

e

[0.0, 1.0]

Linear

Uniform []

0.0

omega

[0.0, 360.0]

Linear

Uniform []

90.0

M_Me

[0.05, 1000.0]

Log_Base2

Uniform []

None

M_Ms

[1e-09, 0.5]

Log_Base2

Uniform []

None

Me_Ms

[0.1, 2000.0]

Log_Base2

Uniform []

None

i

[0.0, 180.0]

Linear

Uniform []

90.0

Omega

[0.0, 360.0]

Linear

Uniform []

180.0

R_Rs

[1e-05, 0.5]

Linear

Uniform []

0.05

a_Rs

[1e-05, 500.0]

Linear

Uniform []

1.0

b

[0.0, 2.0]

Linear

Uniform []

0.0

lambda

[-180.0, 180.0]

Linear

Uniform []

0.0

phase_amp

[0.0, 0.5]

Linear

Uniform []

0.0

delta_occ

[0.0, 0.5]

Linear

Uniform []

0.0

phase_off

[-180.0, 180.0]

Linear

Uniform []

0.0

albedo

[0.0, 1.0]

Linear

Uniform []

0.0

redist

[0.0, 1.0]

Linear

Uniform []

0.0

insol

[0.0, 1000000000.0]

Log_Base2

Uniform []

1.0

apo_center

dynamic

Linear

Uniform []

None

apo_timescale

[10.0, 100000.0]

Log_Base10

Uniform []

None

Star Parameters#

Common object: common: star: star_parameters.

Parameter

Boundaries

Space

Prior

Fixed

radius

[0.0, 2.0]

Linear

Uniform []

1.0

mass

[0.0, 2.0]

Linear

Uniform []

1.0

density

[0.0, 5.0]

Linear

Uniform []

1.0

i_star

[0.0, 180.0]

Linear

Uniform []

90.0

cosi_star

[0.0, 1.0]

Linear

Uniform []

1.0

v_sini

[0.0, 200.0]

Linear

Uniform []

1.6

rotation_period

[1.0, 1000.0]

Linear

Uniform []

27.0

activity_decay

[10.0, 10000.0]

Linear

Uniform []

1000.0

temperature

[2000.0, 11000.0]

Linear

Uniform []

5777.0

line_contrast

[0.0, 100.0]

Linear

Uniform []

50.0

line_fwhm

[0.0, 12.0]

Linear

Uniform []

6.0

rv_center

[-300.0, 300.0]

Linear

Uniform []

0.0

veq_star

[0.0, 70.0]

Linear

Uniform []

1.6

alpha_rotation

[0.0, 1.0]

Linear

Uniform []

0.6

convective_c1

[0.0, 5.0]

Linear

Uniform []

0.0

convective_c2

[-5.0, 0.0]

Linear

Uniform []

0.0

convective_c3

[-5.0, 5.0]

Linear

Uniform []

0.0

Stellar Activity#

Common object: common: activity.

Parameter

Boundaries

Space

Prior

Fixed

Prot

[1.0, 1000.0]

Linear

Uniform []

None

Pdec

[1.0, 1000.0]

Linear

Uniform []

None

Pcyc

[50.0, 10000.0]

Linear

Uniform []

None

Oamp

[0.0001, 2.0]

Log_Base2

Uniform []

None

Hamp

[1e-08, 1000000.0]

Linear

Uniform []

None

Camp

[1e-08, 1000000.0]

Linear

Uniform []

None

sho_scale

[1.0, 1000.0]

Linear

Uniform []

None

sho_decay

[1e-08, 1000000.0]

Log_Base2

Uniform []

None

sho_sigma

[1e-08, 1000000.0]

Log_Base2

Uniform []

None

grn_period

[1.0, 1000.0]

Linear

Uniform []

None

grn_sigma

[1e-08, 1000000.0]

Log_Base2

Uniform []

None

rot_sigma

[1e-08, 1000000.0]

Log_Base2

Uniform []

None

rot_fmix

[0.001, 1.0]

Linear

Uniform []

None

rot_Q0

[1e-08, 1000000.0]

Log_Base10

Uniform []

None

rot_deltaQ

[1e-08, 1000000.0]

Log_Base10

Uniform []

None

Vc

[-500.0, 500.0]

Linear

Uniform []

None

Vr

[-500.0, 500.0]

Linear

Uniform []

None

Lc

[-500.0, 500.0]

Linear

Uniform []

None

Bc

[-500.0, 500.0]

Linear

Uniform []

None

Br

[-500.0, 500.0]

Linear

Uniform []

None

rot_amp

[-500.0, 500.0]

Linear

Uniform []

None

con_amp

[-500.0, 500.0]

Linear

Uniform []

None

cos_amp

[-500.0, 500.0]

Linear

Uniform []

None

cos_der

[-500.0, 500.0]

Linear

Uniform []

None

cyc_amp

[-500.0, 500.0]

Linear

Uniform []

None

cyc_der

[-500.0, 500.0]

Linear

Uniform []

None

matern32_sigma

[1e-06, 1000000.0]

Log_Base10

Uniform []

None

matern32_scale

[0.001, 1000.0]

Log_Base10

Uniform []

None

matern32_multigp_sigma

[-10000.0, 1000.0]

Linear

Uniform []

None

matern32_multigp_sigma_deriv

[-10000.0, 1000.0]

Linear

Uniform []

None

sin_P

[1.0, 1000.0]

Log_Base2

Uniform []

None

sin_K

[0.001, 2000.0]

Log_Base2

Uniform []

None

sin_f

[1.0, 1000.0]

Log_Base2

Uniform []

None

grn_k{0..9}_period

[1e-08, 100.0]

Linear

Uniform []

0.0

grn_k{0..9}_sigma

[1e-08, 100.0]

Log_Base2

Uniform []

None

osc_k{0..9}_period

[1e-08, 100.0]

Linear

Uniform []

0.0

osc_k{0..9}_sigma

[1e-08, 100.0]

Log_Base2

Uniform []

None

osc_k{0..9}_Q0

[1.0, 1000.0]

Log_Base10

Uniform []

None

Limb Darkening#

Common objects: ld_linear, ld_quadratic, ld_square-root, ld_logarithmic, ld_exponential, ld_power2, and ld_nonlinear.

Common object

Parameter

Boundaries

Space

Prior

Fixed

ld_linear

ld_c1

[0.0, 1.0]

Linear

Uniform []

None

two-coefficient laws

ld_c1

[0.0, 1.0]

Linear

Uniform []

None

two-coefficient laws

ld_c2

[-1.0, 1.0]

Linear

Uniform []

None

two-coefficient laws

ld_q1

[0.0, 1.0]

Linear

Uniform []

None

two-coefficient laws

ld_q2

[0.0, 1.0]

Linear

Uniform []

None

ld_nonlinear

ld_c1

[0.0, 1.0]

Linear

Uniform []

None

ld_nonlinear

ld_c2

[0.0, 1.0]

Linear

Uniform []

None

ld_nonlinear

ld_c3

[0.0, 1.0]

Linear

Uniform []

None

ld_nonlinear

ld_c4

[0.0, 1.0]

Linear

Uniform []

None

The two-coefficient laws are ld_quadratic, ld_square-root, ld_logarithmic, ld_exponential, and ld_power2.

Normalization, Dilution, Offset, and Jitter#

Common object

Parameter

Boundaries

Space

Prior

Fixed

normalization_factor

n_factor

[1e-06, 1000000.0]

Log_Base2

Uniform []

0.0

dilution_factor

d_factor

[0.0, 1.0]

Linear

Uniform []

0.0

common_offset

offset

dynamic

Linear

Uniform []

0.0

common_jitter

jitter

dynamic

Linear

Uniform []

0.0

common_offset and common_jitter inherit their numerical boundaries from the datasets that use them. If more than one dataset shares the same common parameter, the boundary is expanded to include all relevant datasets.

Polynomial and Detrending Models#

Common objects: polynomial_trend, detrending, and lightcurve_detrending.

Common object

Parameter

Boundaries

Space

Prior

Fixed

polynomial_trend

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

polynomial_trend

x_offset

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

polynomial_trend

poly_factor

[-100.0, 100.0]

Linear

Uniform []

0.0

polynomial_trend

poly_c{0..9}

[-10.0, 10.0]

Linear

Uniform []

0.0

detrending

det_linear

[-10.0, 10.0]

Linear

Uniform []

0.0

detrending

det_poly

[-1.0, 1.0]

Linear

Uniform []

0.0

detrending

det_c{0..9}

[-100.0, 100.0]

Linear

Uniform []

0.0

detrending

det_m32_sigma

[1e-06, 1000000.0]

Log_Base10

Uniform []

None

detrending

det_m32_rho

[1e-06, 1000000.0]

Log_Base10

Uniform []

None

detrending

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

lightcurve_detrending

coeff_linear

[-10.0, 10.0]

Linear

Uniform []

0.0

lightcurve_detrending

coeff_poly

[-10.0, 10.0]

Linear

Uniform []

0.0

lightcurve_detrending

coeff_c0

[-100000.0, 100000.0]

Linear

Uniform []

0.0

lightcurve_detrending

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

lightcurve_detrending

poly_c{0..9}

[-1000000.0, 1000000.0]

Linear

Uniform []

0.0

Correlation Models#

Common objects: correlation and complex_correlation.

Model or common object

Parameter

Boundaries

Space

Prior

Fixed

correlation

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

correlation

corr_c{0..10}

[-100000.0, 1000000.0]

Linear

Uniform []

0.0

complex_correlation

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

complex_correlation

corr_c{0..10}

[-100000.0, 1000000.0]

Linear

Uniform []

0.0

local_correlated_jitter

x_zero

[-100000.0, 100000.0]

Linear

Uniform []

None

local_correlated_jitter

c{1..order}

[0.0, 1000000.0]

Linear

Uniform []

None

The local_correlated_jitter coefficients are model-local rather than common object parameters. Their highest order is set by the model keyword order.

Harmonics and Sinusoids#

Common objects: harmonics and sinusoid.

Common object

Parameter

Boundaries

Space

Prior

Fixed

harmonics

P

[0.5, 1000.0]

Log_Base2

Uniform []

None

harmonics

T0

[-100.0, 100.0]

Linear

Uniform []

0.0

harmonics

phase

[0.0, 360.0]

Linear

Uniform []

0.0

harmonics

amp_S{1..5}

[1e-06, 1000000.0]

Log_Base2

Uniform []

0.0

harmonics

amp_C{1..5}

[1e-06, 1000000.0]

Log_Base2

Uniform []

0.0

harmonics

pha_S{n}

[0.0, 360.0/n]

Linear

Uniform []

0.0

harmonics

pha_C{n}

[0.0, 360.0/n]

Linear

Uniform []

0.0

sinusoid

sine_period

[0.4, 100000.0]

Log_Base2

Uniform []

None

sinusoid

sine_amp

[-1000000000.0, 1000000000.0]

Linear

Uniform []

None

sinusoid

sine_phase

[0.0, 360.0]

Linear

Uniform []

0.0

sinusoid

sine_offset

[0.0, 360.0]

Linear

Uniform []

0.0

sinusoid

x_zero

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

sinusoid

x_offset

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

sinusoid

poly_factor

[-1000000000.0, 1000000000.0]

Linear

Uniform []

0.0

sinusoid

poly_c{0..9}

[-1000000.0, 1000000.0]

Linear

Uniform []

0.0

CHEOPS and CCF Parameters#

Common objects: cheops_modelling and ccf_parameters.

Common object

Parameter

Boundaries

Space

Prior

Fixed

cheops_modelling

scale_factor

[-5.0, 20.0]

Linear

Uniform []

1.0

cheops_modelling

ramp

[-100.0, 100.0]

Linear

Uniform []

0.0

cheops_modelling

dfdt

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

d2fdt2

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdbg

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdcontam

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdsmear

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdx

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdy

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

d2fdx2

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

d2fdxdy

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

d2fdy2

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdsinphi

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdcosphi

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdcos2phi

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdsin2phi

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdcos3phi

[-1.0, 1.0]

Linear

Uniform []

0.0

cheops_modelling

dfdsin3phi

[-1.0, 1.0]

Linear

Uniform []

0.0

ccf_parameters

contrast_m

[-10.0, 10.0]

Linear

Uniform []

0.0

ccf_parameters

contrast_q

[0.0, 1.0]

Linear

Uniform []

0.0

ccf_parameters

fwhm_m

[-10.0, 10.0]

Linear

Uniform []

0.0

ccf_parameters

fwhm_q

[0.0, 70.0]

Linear

Uniform []

0.0

ccf_parameters

rv_offset

[-10.0, 10.0]

Linear

Uniform []

0.0

Model Families#

Most entries in the models section do not define new boundaries directly. They select which common-object parameters are sampled and whether those parameters are shared among datasets or local to a dataset.

Model family

Parameter defaults used

radial_velocities, rv_planets, planetary_velocities

planets; optionally star_parameters when planet mass parametrizations are used.

transit_times, Tc_planets

planets; TTV variants can create dataset-local Tc parameters whose default boundaries are the time span of each transit subset unless overridden.

batman_transit, pytransit_transit, pytransit_dynamical, and their TTV/subset variants

planets, star_parameters, and a limb-darkening common object.

batman_transit_eclipse_phasecurve, spiderman_thermal

planets, plus eclipse and phase-curve parameters from the planets table.

gp_quasiperiodic, gp_quasiperiodic_alternative, gp_quasiperiodic_derivative, gp_quasiperiodic_cosine, gp_pyaneti_quasiperiodic, gp_framework_quasiperiodic

activity; optionally star_parameters for shared rotation_period or activity_decay.

tinygp_*, celerite2_*, spleaf_* Gaussian-process models

activity; optionally star_parameters for shared stellar activity hyperparameters.

Multidimensional GP models

activity; coefficients such as rot_amp, con_amp, cos_amp, cyc_amp, and Matern-3/2 multidimensional coefficients are often dataset-local.

polynomial_trend, shared_polynomial_trend, local_polynomial_trend, subset_polynomial_trend

polynomial_trend.

detrending, full_detrending, polynomial_detrending, exponential_detrending, detrending_matern32

detrending.

correlation, complex_correlation

correlation or complex_correlation.

local_correlated_jitter

The model-local parameters listed in Correlation Models.

common_offset, common_jitter

common_offset and common_jitter, with dynamic boundaries from the datasets.

dilution_factor, local_dilution_factor

dilution_factor.

normalization_factor, local_normalization_factor, subset_normalization_factor

normalization_factor.

harmonics

harmonics.

sinusoid, local_sinusoid, sinusoid_common_period, sinusoid_polynomial_modulation

sinusoid.

cheops_detrending, cheops_factormodel

cheops_modelling.

spectral_rotation and subset variants

star_parameters and, when requested, ccf_parameters.

rossitermclaughlin_* models

planets, star_parameters, limb darkening, and in some implementations ccf_parameters.