(parameter_defaults)=

# 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:

```python
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. 

```{code} python
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 4<sup>th</sup> and 5<sup>th</sup>  columns (see [Prepare a dataset file](prepare_dataset) ) 

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:

```{code-block} yaml
:lineno-start: 1
inputs:
  RVdata:
    file: datasets/K2-141_RV_PyORBIT.dat
    kind: RV
    models:
      - radial_velocities
      - tinygp_quasiperiodic
    boundaries:
      jitter_0: [ 0.00,   10.0]
      jitter_1: [ 0.00,   20.0]
      offset_0: [ -3500.0, -3300.0]
      offset_1: [ -4000.0, -3000.0]
```

```text
----- 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

```{code-block} yaml
:lineno-start: 8
:emphasize-lines: 2,4
    boundaries:
      #jitter_0: [ 0.00,   10.0]
      jitter_1: [ 0.00,   20.0]
      #offset_0: [ -3500.0, -3300.0]
      offset_1: [ -4000.0, -3000.0]
```

```text
----- 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:

```{code-block} yaml
:lineno-start: 8
:emphasize-lines: 2,3
    boundaries:
      jitter: [ 0.00,   10.0]
      offset: [ -3500.0, -3300.0]
```

```text
----- 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:

```{code-block} yaml
:lineno-start: 8
:emphasize-lines: 5,6
    boundaries:
      jitter: [ 0.00,   10.0]
      offset: [ -3500.0, -3300.0]
    priors:
      jitter: ['HalfGaussian', 0.00, 10.0]
      offset: ['Gaussian', -3450.0, 10.0]
```



```text
----- 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](#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`. |