Prior distributions

Each free parameter of a retrieval calculations needs to have an associated prior distribution. The prior distribution describes any prior knowledge that is available about the parameter. The number and type of the free parameters depend on the chosen forward model and user-specified configuration options.

BeAR supports the following types of distributions:

  • delta - a delta distribution with a fixed value

  • uniform - a uniform distribution with a lower and upper bound

  • log_uniform - a log-uniform distribution with a lower and upper bound

  • gaussian - a Gaussian distribution with a mean and standard deviation

  • linked - links this prior to that of another parameter

A special case is the linked distribution. This distribution links the prior distribution of one parameter to that of another. Thus, these two parameters will always have the same value during a retrieval calculation.

Prior distributions units

BeAR also supports units for its prior distributions. The following units are currently taken into account:

  • Rs or Rsun - the solar radius

  • Rj or Rjupiter - Jupiter’s radius

  • Re or Rearth - Earth’s radius

  • pc - distance in parsec

  • ly - distance in light years

Priors without units are assumed to be in cgs units.

Prior distributions file

The priors.config file contains the information on the prior distributions of the free parameters. The file has the following structure:

delta         log_g           2.99     
uniform       r_planet        1.6    2.3    Rj
gaussian      r_star          1.57   0.07   Rs
log_uniform   H2O             1e-12  1e-1
log_uniform   TiO             1e-12  1e-3
log_uniform   VO              1e-12  1e-3
log_uniform   K               1e-12  1e-3
uniform       temperature     500    1600

The first column lists the distribution type of the prior, the second column the model parameter name, and the remaining columns the parameters of the distribution, while the optional, last column is the unit of the parameter.

The type, order and number of these parameters in prior distributions file is determined by chosen forward model.

A special case is the linked distribution. This distribution links the prior distribution of one parameter to that of another. The config parameter for this distribution is the line number of the parameter distribution that it should be linked to. An example of this is shown below:

uniform       log_g           4.0     6.0        
uniform       scaling_factor  0.1     5.0        
gaussian      distance        5.8819  0.0029  pc
log_uniform   mr_h2o          1e-12   0.01  
log_uniform   mr_ch4          1e-12   0.01  
log_uniform   mr_nh3          1e-12   0.01
log_uniform   mr_k            1e-12   0.01
log_uniform   mr_h2s          1e-12   0.01
linked        mr_co2          5
uniform       temperature1    5000    1000      
uniform       temperature2    0.3     0.95       
uniform       temperature3    0.3     0.95       
uniform       temperature4    0.4     0.95       
uniform       temperature5    0.5     0.95

Here, the prior for the CO2 mixing ratios is linked to the fifth parameter, which is the mixing ratio of CH4 in this example. Thus, CO2 will always have the same mixing ratio as methane for this retrieval setup. It is important to note that BeAR cannot check the consistency of the linked parameters. For example, if the linked parameter is a temperature, the resulting mixing ratios of CO2 would make no sense. It is the user’s responsibility to ensure that the linked parameters are consistent.

Order of prior distributions

The order of the prior distributions in the priors.config file is very important. In general they have to appear in the following order:

  • general forward model parameters, as discussed in the section on forward models

  • priors for the chosen chemistry models, as discussed in the section on chemistry models

  • temperature profile priors, as discussed in this section

  • cloud model priors as discussed in the section on cloud models

  • priors for optional modules that can be used for a specific forward model

  • observational offset priors as discussed in the section on observations

A general prior configuration file, therefore has the following structure:

uniform       forward_model_param1   0.0     10.0
uniform       forward_model_param2   0.0     10.0
uniform       forward_model_param3   0.0     10.0
log_uniform   chemistry_param1       1e-12   0.01  
log_uniform   chemistry_param2       1e-12   0.01
log_uniform   chemistry_param3       1e-12   0.01
log_uniform   chemistry_param4       1e-12   0.01
log_uniform   chemistry_param5       1e-12   0.01
uniform       temperature_param1     5000    1000      
uniform       temperature_param2     0.3     0.95       
uniform       temperature_param3     0.3     0.95       
uniform       temperature_param4     0.4     0.95       
uniform       temperature_param5     0.5     0.95
log_uniform   cloud_param1           0.0     10.0
log_uniform   cloud_param2           0.0     10.0
log_uniform   cloud_param3           0.0     10.0
uniform       module_param1          0.0     1.00       
uniform       module_param2          0.0     1.00       
uniform       module_param3          0.0     1.00
gaussian      observation_offset1    100     0.4
gaussian      observation_offset2    100     0.4