Correlated datasets

Correlated datasets#

It is possible to incorporate a model for which the observed value \(Y\) at epoch \(i\) is a function of another (error-less) observable \(Z\), which I will call correlated variable:

(1)#\[Y_i = \sum_{p=0}^{d} c_p (Z_i-Z_\mathrm{ref})^p\]

\(Z_\mathrm{ref}\) is a reference value that can be either specified in the configuration file or automatically computed by PyORBIT. In the latter case, the average of all \(Z\) is taken.

Model definition and requirements#

  • model_name: local_correlation or correlation

  • required common objects: correlation

Tip

The common object correlation will be automatically grabbed by PyORBIT. Since there are no common parameters, there is no need to specify it in the common section

Keywords#

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

order

  • accepted values: any number up to 10 | 1

  • order (or degree) of the polynomial used to describe the correlation

correlated_variable

  • accepted values: any variable name | corr

  • specify which variable you want to use as correlated model. You need to declare it if you use a name different from corr for the label of your column in your dataset/ancillary file

normalization_model

  • accepted values: True | False

  • If False, the correlation model is added to the final model (which is a combination of all the other models). If True, the correlation model is multiplied to the final model (as in the case of a normalization factor).

  • If set to True, they keyword include_zero_point will be set to True as well.

use_median_xzero

  • accepted values: True | False

  • if True , automatically compute the median of the correlated variable, regardless of the value provided to the keyword use_median_xzero

x_zero

  • accepted values: any value | median of the correlated dataset

  • User value for \(Z_\mathrm{ref}\) as defined in Equation {eq} polynomial_correlation. To be valid, the keyword use_median_xzero must be set to False.

include_zero_point

  • accepted values: True | False

  • The coefficient \(c_0\) is automatically set to zero, to avoid a degeneracy between this parameter and the offset of the dataset. You can decide to fit for \(c_0\) by setting this keyword to True, but be aware of the consequences

  • Note: this keyword is set to True if normalization_model is set to True

exclude_zero_point

  • accepted values: True | False It does the opposite of the keyword include_zero_point. It must be set to True if you are using the normalization_model flag but you don’t want to fit for \(c_0\)

baseline_value

  • I’ll fix this

Warning

Not all the keywords have been implemented in version <= 9.1.12, check out if the output is consistent with your expectations.

Examples#

The input dataset follows the standard structure described in Prepare a dataset file.

# time flux flux_err jitter offset subset
    0.302929   131.510068 1.00 0  0 -1
    0.808006    58.192176 1.00 0  0 -1
    2.114672   -37.794774 1.00 0  0 -1
    ...

The ancillary dataset, specified in the ancillary keyword in the input section as in the example below, is rather simple:

# time corr
    0.302929    49.767572
    0.808006    35.340020
    2.114672    16.585392
    ...

This is an example of a basic analysis where a radial velocity model and a correlation model are used simultaneously. You can see that is not necessary to specify the correlation model in the common section, as PyORBIT will automatically grab the default boundaries, priors, and spaces from the model specification.

 1inputs:
 2  RV_data:
 3    file: dataset_dat.dat
 4    ancillary: dataset_anc.dat
 5    kind: RV
 6    models:
 7      - radial_velocities
 8      - local_correlation
 9common:
10  planets:
11    b:
12      orbit: circular
13      boundaries:
14        P: [2, 20]
15        K: [0.01, 10.0]
16  star:
17    star_parameters:
18      priors:
19        radius: ['Gaussian', 1.00, 0.02]
20        mass: ['Gaussian', 1.00, 0.02]
21models:
22  radial_velocities:
23    planets:
24      - b
25  local_correlation:
26    model: local_correlation
27    correlated_variable: corr
28    order: 1
29parameters:
30  Tref: 0.00 #BJD-2450000; istante arbitrario, più o meno centrale
31solver:
32  pyde:
33    ngen: 20000
34    npop_mult: 4
35  emcee:
36    npop_mult: 4
37    nsteps: 25000
38    nburn: 10000
39    thin: 100
40  nested_sampling:
41    nlive: 4000
42  recenter_bounds: True

New from PyORBIT version 10:

The correlated dataset can be embedded directly in the dataset file (here called dataset_dat1.dat):

# time flux flux_err jitter offset subset corr
    0.302929   131.510068 1.00 0  0 -1 49.767572
    0.808006    58.192176 1.00 0  0 -1 35.340020
    2.114672   -37.794774 1.00 0  0 -1 16.585392
    ...

In this case, it is not necessary to include the ancillary keyword anymore, but be sure to specify the correlated_variable keyword in the model section, as shown in the example above-

 1inputs:
 2  RV_data:
 3    file: dataset_dat1.dat
 4    kind: RV
 5    models:
 6      - radial_velocities
 7      - local_correlation
 8common:
 9  planets:
10    b:
11      orbit: circular
12      boundaries:
13        P: [2, 20]
14        K: [0.01, 10.0]
15  star:
16    star_parameters:
17      priors:
18        radius: ['Gaussian', 1.00, 0.02]
19        mass: ['Gaussian', 1.00, 0.02]
20models:
21  radial_velocities:
22    planets:
23      - b
24  local_correlation:
25    type: local_correlation
26    correlated_variable: corr
27    order: 1
28parameters:
29  Tref: 0.00 #BJD-2450000; istante arbitrario, più o meno centrale
30solver:
31  pyde:
32    ngen: 20000
33    npop_mult: 4
34  emcee:
35    npop_mult: 4
36    nsteps: 25000
37    nburn: 10000
38    thin: 100
39  nested_sampling:
40    nlive: 4000
41  recenter_bounds: True

Model parameters#

The following parameters will be inherited from the common model (column Common?: common) or a different value will be assigned for each dataset (column Common?: dataset)

Name

Parameter

Common?

Definition

Notes

x_zero

Constant \(Z_\mathrm{ref}\) as defined in Equation {eq} polynomial_correlation

dataset

correlation

corr_cN

Coefficient of order N

dataset

correlation