caribou_hi

Submodules

caribou_hi.absorption_model

absorption_model.py AbsorptionModel definition

class caribou_hi.absorption_model.AbsorptionModel(*args, **kwargs)

Bases: HIModel

Definition of the AbsorptionModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_tau_total, prior_tkin_factor])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “absorption”.

add_priors(prior_tau_total: float = 1.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_tau_totalfloat, optional: Prior distribution on total optical depth (km s-1), by default 1.0, where tau_total ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max

caribou_hi.absorption_physical_model

absorption_physical_model.py AbsorptionPhysicalModel definition

class caribou_hi.absorption_physical_model.AbsorptionPhysicalModel(*args, **kwargs)

Bases: HIPhysicalModel

Definition of the AbsorptionPhysicalModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_NHI_fwhm2_thermal, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “absorption”.

add_priors(prior_NHI_fwhm2_thermal: float = 1e+20, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_NHI_fwhm2_thermalfloat, optional: Prior distribution on column density / thermal FWHM2 (cm-2 km-2 s2), by default 1.0e20, where NHI_fwhm2_thermal ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])

caribou_hi.emission_absorption_model

emission_absorption_model.py EmissionAbsorptionModel definition

class caribou_hi.emission_absorption_model.EmissionAbsorptionModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIModel

Definition of the EmissionAbsorptionModel model. SpecData keys must be “emission” and “absorption”.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission” and “absorption”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_TB_fwhm: float = 50.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], prior_sigma_log10_NHI: float | None = None, *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_TB_fwhmfloat, optional: Prior distribution on brightness temperature x FWHM (K km s), by default 50.0, where TB_fwhm ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max
prior_sigma_log10_NHIOptional[float], optional: Shape parameter that defines the prior distribution on absorption weight / filling factor, by default None, where wt/ff ~ LogNormal(mu=-0.5*ln(10)*prior^2, sigma=prior) i.e., assuming the cloud has a log-normal column density distribution with this width If None, then the absorption weight is assumed to be 1 (i.e., same column density probed in emission and absorption)

caribou_hi.emission_absorption_physical_model

emission_absorption_physical_model.py EmissionAbsorptionPhysicalModel definition

class caribou_hi.emission_absorption_physical_model.EmissionAbsorptionPhysicalModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIPhysicalModel

Definition of the EmissionAbsorptionPhysicalModel model. SpecData keys must be “emission” and “absorption”.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission” and “absorption”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_ff_NHI: float = 1e+21, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], prior_sigma_log10_NHI: float = 0.5, *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_ff_NHIfloat, optional: Prior distribution on filling factor * column density (cm-2), by default 1.0e21, where ff_NHI ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])
prior_sigma_log10_NHIfloat, optional: Shape parameter that defines the prior distribution on absorption weight / filling factor, by default 0.5, where wt/ff ~ LogNormal(mu=-0.5*ln(10)*prior^2, sigma=prior) i.e., assuming the cloud has a log-normal column density distribution with this width

caribou_hi.emission_model

emission_model.py EmissionPhysicalModel definition

class caribou_hi.emission_model.EmissionModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIModel

Definition of the EmissionModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_TB_fwhm: float = 50.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_TB_fwhmfloat, optional: Prior distribution on brightness temperature x FWHM (K km s), by default 50.0, where TB_fwhm ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max

caribou_hi.emission_physical_model

emission_physical_model.py EmissionPhysicalModel definition

class caribou_hi.emission_physical_model.EmissionPhysicalModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIPhysicalModel

Definition of the EmissionPhysicalModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_ff_NHI: float = 1e+21, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_ff_NHIfloat, optional: Prior distribution on filling factor * column density (cm-2), by default 1.0e21, where ff_NHI ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])

caribou_hi.hi_model

hi_model.py HIModel definition

class caribou_hi.hi_model.HIModel(*args, **kwargs)

Bases: BaseModel

Definition of the HIModel model. This model is further extended by other models.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`(args, *kwargs)	Must be defined in inhereted class.
`add_priors`([prior_fwhm2, prior_log10_nHI, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_deterministics(): Add additional deterministic quantities to the model.

abstract add_likelihood(*args, **kwargs): Must be defined in inhereted class.

add_priors(prior_fwhm2: float = 200.0, prior_log10_nHI: Iterable[float] = [0.0, 1.5], prior_velocity: Iterable[float] = [-10.0, 10.0], prior_log10_n_alpha: Iterable[float] = [-6.0, 1.0], prior_fwhm_L: float | None = None, prior_baseline_coeffs: dict[str, Iterable[float]] | None = None)

Add priors and deterministics to the model

Parameters:

prior_fwhm2float, optional: Prior distribution on FWHM^2 (km2 s-2), by default 200.0, where fwhm2 ~ prior * ChiSquared(nu=1) i.e., half-normal on FWHM
prior_log10_nHIIterable[float], optional: Prior distribution on log10 volume density (cm-3), by default [0.0, 1.5], where log10_nHI ~ Normal(mu=prior[0], sigma=prior[1])
prior_velocityIterable[float], optional: Prior distribution on centroid velocity (km s-1), by default [-10.0, 10.0], where velocity_norm ~ Beta(alpha=2.0, beta=2.0) velocity ~ prior[0] + (prior[1] - prior[0]) * velocity_norm
prior_log10_n_alphaIterable[float], optional: Prior distribution on log10 Lyman alpha photon density (cm-3), by default [-6.0, 1.0], where log10_n_alpha ~ Normal(mu=prior[0], sigma=prior[1])
prior_fwhm_LOptional[float], optional: Prior distribution on the pseudo-Voight Lorentzian profile line width (km/s), by default None, where fwhm_L ~ HalfNormal(sigma=prior_fwhm_L) If None, the line profile is assumed Gaussian.
prior_baseline_coeffsOptional[dict[str, Iterable[float]]], optional: Width of normal prior distribution on the normalized baseline polynomial coefficients. Keys are dataset names and values are lists of length baseline_degree+1. If None, use [1.0]*(baseline_degree+1) for each dataset, by default None

caribou_hi.hi_physical_model

hi_physical_model.py HIPhysicalModel definition

class caribou_hi.hi_physical_model.HIPhysicalModel(*args, **kwargs)

Bases: BaseModel

Definition of the HIPhysicalModel model. This model is further extended by other models.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`(args, *kwargs)	Must be defined in inhereted class.
`add_priors`([prior_fwhm2, prior_velocity, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_deterministics(): Add deterministic quantities to the model.

abstract add_likelihood(*args, **kwargs): Must be defined in inhereted class.

add_priors(prior_fwhm2: float = 200.0, prior_velocity: Iterable[float] = [-10.0, 10.0], prior_log10_n_alpha: Iterable[float] = [-6.0, 1.0], prior_nth_fwhm_1pc: Iterable[float] = [1.75, 0.25], prior_depth_nth_fwhm_power: Iterable[float] = [0.3, 0.1], prior_fwhm_L: float | None = None, prior_baseline_coeffs: dict[str, Iterable[float]] | None = None)

Add priors and deterministics to the model

Parameters:

prior_fwhm2float, optional: Prior distribution on FWHM^2 (km2 s-2), by default 200.0, where fwhm2 ~ prior * ChiSquared(nu=1) i.e., half-normal on FWHM
prior_velocityIterable[float], optional: Prior distribution on centroid velocity (km s-1), by default [-10.0, 10.0], where velocity_norm ~ Beta(alpha=2.0, beta=2.0) velocity ~ prior[0] + (prior[1] - prior[0]) * velocity_norm
prior_log10_n_alphaIterable[float], optional: Prior distribution on log10 Lyman alpha photon density (cm-3), by default [-6.0, 1.0], where log10_n_alpha ~ Normal(mu=prior[0], sigma=prior[1])
prior_nth_fwhm_1pcfloat, optional: Prior distribution on non-thermal line width at 1 pc (km/s), by default [1.75, 0.25], where nth_fwhm_1pc ~ TruncatedNormal(mu=prior[0], sigma=prior[1], lower=0.0)
prior_depth_nth_fwhm_powerfloat, optional: Prior distribution on non-thermal line width vs. depth power law index, by default [0.3, 0.1], where depth_nth_fwhm_power ~ InverseGamma(mu=prior[0], sigma=prior[1])
prior_fwhm_LOptional[float], optional: Prior distribution on the pseudo-Voight Lorentzian profile line width (km/s), by default None, where fwhm_L ~ HalfNormal(sigma=prior_fwhm_L) If None, the line profile is assumed Gaussian.
prior_baseline_coeffsOptional[dict[str, Iterable[float]]], optional: Width of normal prior distribution on the normalized baseline polynomial coefficients. Keys are dataset names and values are lists of length baseline_degree+1. If None, use [1.0]*(baseline_degree+1) for each dataset, by default None

caribou_hi.physics

physics.py Physics utilities

caribou_hi.physics.calc_depth_nonthermal(fwhm_nonthermal: float, nth_fwhm_1pc: float, depth_nth_fwhm_power: float) → float

Calculate the line-of-sight depth from the non-thermal line broadening. This is the inverse of calc_nonthermal_fwhm.

Parameters:

fwhm_nonthermalfloat: Non-thermal FWHM line width (km s-1)
nth_fwhm_1pcfloat: Non-thermal line width at 1 pc(km s-1)
depth_nth_fwhm_powerfloat: Depth vs. non-thermal line width power law index

Returns:

float: Line-of-sight depth (pc)

caribou_hi.physics.calc_kinetic_temp(thermal_fwhm2: float) → float

Calculate the kinetic temperature from the thermal line broadening. This is the inverse of calc_thermal_fwhm. (Condon & Ransom eq. 7.35)

Parameters:

thermal_fwhm2float: Thermal FWHM^2 (km2 s-2)

Returns:

float: Kinetic temperature (K)

caribou_hi.physics.calc_log10_column_density(tau_total: float, spin_temp: float) → float

Calculate the column density.

Parameters:

tau_totalfloat: Total optical depth
spin_tempfloat: Spin temperature (K)

Returns:

float: log10 column density (cm-2)

caribou_hi.physics.calc_log10_density(log10_column_density: float, log10_depth: float)

Calculate the density.

Parameters:

log10_column_densityfloat: log10 column density (cm-2)
log10_depthfloat: log10 depth (pc)

Returns:

float: log10 volume density (cm-3)

caribou_hi.physics.calc_log10_nonthermal_pressure(log10_density, fwhm2_nonthermal)

Calculate the non-thermal pressure.

Parameters:

log10_column_densityfloat: log10 column density (cm-2)
fwhm2_nonthermalfloat: Non-thermal FWHM^2 (km2 s-2)

Returns:

float: log10 non-thermal pressure (K cm-3)

caribou_hi.physics.calc_nonthermal_fwhm(depth: float, nth_fwhm_1pc: float, depth_nth_fwhm_power: float) → float

Calculate the non-thermal line broadening assuming a size-linewidth relationship

Parameters:

depthfloat: Line-of-sight depth (pc)
nth_fwhm_1pcfloat: Non-thermal line width at 1 pc(km s-1)
depth_nth_fwhm_powerfloat: Depth vs. non-thermal line width power law index

Returns:

float: Non-thermal FWHM line width (km s-1)

caribou_hi.physics.calc_pseudo_voigt(velo_axis: Iterable[float], velocity: Iterable[float], fwhm2: Iterable[float], fwhm_L: float) → Iterable[float]

Evaluate a pseudo Voight profile in order to aid in posterior exploration of the parameter space. This parameterization includes a latent variable fwhm_L, which can be conditioned on zero to analyze the posterior. We also consider the spectral channelization. We do not perform a full boxcar convolution, rather we approximate the convolution by assuming an equivalent FWHM for the boxcar kernel of 4 ln(2) / pi * channel_width ~= 0.88 * channel_width

Parameters:

velo_axisIterable[float]: Observed velocity axis (km s-1; length S)
velocityIterable[float]: Cloud center velocity (km s-1; length N)
fwhm2Iterable[float]: Cloud FWHM^2 line widths (km2 s-2; length N)
fwhm_Lfloat: Latent pseudo-Voigt profile Lorentzian FWHM (km s-1)

Returns:

Iterable[float]: Line profile (MHz-1; shape S x N)

caribou_hi.physics.calc_spin_temp(kinetic_temp: float, density: float, n_alpha: float) → float

Calculate the spin temperature following Kim et al. (2014) eq. 4

Parameters:

kinetic_tempfloat: Kinetic temperature (K)
densityfloat: HI volume density (cm-3)
n_alphafloat: Lyman alpha photon density (cm-3)

Returns:

float: Spin temperature (K)

caribou_hi.physics.calc_tau_total(column_density: float, spin_temp: float) → float

Calculate the total optical depth.

Parameters:

column_densityfloat: Column density (cm-2)
spin_tempfloat: Spin temperature (K)

Returns:

float: total optical depth

caribou_hi.physics.calc_thermal_fwhm2(kinetic_temp: float) → float

Calculate the thermal line broadening assuming a Maxwellian velocity distribution (Condon & Ransom eq. 7.35)

Parameters:

kinetic_tempfloat: Kinetic temperature (K)

Returns:

float: Thermal FWHM^2 line width (km2 s-2)

caribou_hi.physics.gaussian(x: float, center: float, fwhm: float) → float

Evaluate a normalized Gaussian function

Parameters:

xfloat: Position at which to evaluate
centerfloat: Gaussian centroid
fwhmfloat: Gaussian FWHM line width

Returns:

float: Gaussian evaluated at x

caribou_hi.physics.lorentzian(x: float, center: float, fwhm: float) → float

Evaluate a normalized Lorentzian function

Parameters:

xfloat: Position at which to evaluate
centerfloat: Centroid
fwhmfloat: FWHM

Returns:

float: Lorentzian evaluated at x

caribou_hi.physics.radiative_transfer(tau: Iterable[float], tspin: Iterable[float], filling_factor: Iterable[float], bg_temp: float) → Iterable[float]

Evaluate the radiative transfer to predict the emission spectrum. The emission spectrum is ON - OFF, where ON includes the attenuated emission of the background and the clouds, and the OFF is the emission of the background. Order of N clouds is assumed to be [nearest, …, farthest]. The contribution of each cloud is diluted by the filling factor, a number between zero and one.

Parameters:

tauIterable[float]: Optical depth spectra (shape S x N)
tspinIterable[float]: Spin temperatures (K) (shape N)
filling_factorIterable[float]: Filling factor (between zero and one) (shape N)
bg_tempfloat: Assumed background temperature

Returns:

Iterable[float]: Predicted emission brightness temperature spectrum (K) (length S)

Module contents

class caribou_hi.AbsorptionModel(*args, **kwargs)

Bases: HIModel

Definition of the AbsorptionModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_tau_total, prior_tkin_factor])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “absorption”.

add_priors(prior_tau_total: float = 1.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_tau_totalfloat, optional: Prior distribution on total optical depth (km s-1), by default 1.0, where tau_total ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max

class caribou_hi.AbsorptionPhysicalModel(*args, **kwargs)

Bases: HIPhysicalModel

Definition of the AbsorptionPhysicalModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_NHI_fwhm2_thermal, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “absorption”.

add_priors(prior_NHI_fwhm2_thermal: float = 1e+20, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_NHI_fwhm2_thermalfloat, optional: Prior distribution on column density / thermal FWHM2 (cm-2 km-2 s2), by default 1.0e20, where NHI_fwhm2_thermal ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])

class caribou_hi.EmissionAbsorptionModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIModel

Definition of the EmissionAbsorptionModel model. SpecData keys must be “emission” and “absorption”.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission” and “absorption”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_TB_fwhm: float = 50.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], prior_sigma_log10_NHI: float | None = None, *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_TB_fwhmfloat, optional: Prior distribution on brightness temperature x FWHM (K km s), by default 50.0, where TB_fwhm ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max
prior_sigma_log10_NHIOptional[float], optional: Shape parameter that defines the prior distribution on absorption weight / filling factor, by default None, where wt/ff ~ LogNormal(mu=-0.5*ln(10)*prior^2, sigma=prior) i.e., assuming the cloud has a log-normal column density distribution with this width If None, then the absorption weight is assumed to be 1 (i.e., same column density probed in emission and absorption)

class caribou_hi.EmissionAbsorptionPhysicalModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIPhysicalModel

Definition of the EmissionAbsorptionPhysicalModel model. SpecData keys must be “emission” and “absorption”.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission” and “absorption”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_ff_NHI: float = 1e+21, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], prior_sigma_log10_NHI: float = 0.5, *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_ff_NHIfloat, optional: Prior distribution on filling factor * column density (cm-2), by default 1.0e21, where ff_NHI ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])
prior_sigma_log10_NHIfloat, optional: Shape parameter that defines the prior distribution on absorption weight / filling factor, by default 0.5, where wt/ff ~ LogNormal(mu=-0.5*ln(10)*prior^2, sigma=prior) i.e., assuming the cloud has a log-normal column density distribution with this width

class caribou_hi.EmissionModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIModel

Definition of the EmissionModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add additional deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_TB_fwhm: float = 50.0, prior_tkin_factor: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_TB_fwhmfloat, optional: Prior distribution on brightness temperature x FWHM (K km s), by default 50.0, where TB_fwhm ~ HalfNormal(sigma=prior)
prior_tkin_factorIterable[float], optional: Prior distribution on kinetic temperature factor, by default [2.0, 2.0], where tkin_factor ~ Beta(alpha=prior[0], beta=prior[1]) tkin = tkin_factor * tkin_max

class caribou_hi.EmissionPhysicalModel(*args, bg_temp: float = 3.77, **kwargs)

Bases: HIPhysicalModel

Definition of the EmissionPhysicalModel model.

Attributes:

baseline_deterministics: Get the deterministic baseline parameter names.
baseline_freeRVs: Get the free baseline parameter names.
cloud_deterministics: Get the deterministic cloud parameter names.
cloud_freeRVs: Get the free cloud parameter names.
hyper_deterministics: Get the deterministic hyper parameter names.
hyper_freeRVs: Get the free hyper parameter names.
labeller: Get the arviz labeller.
unique_solution: Check if posterior samples suggest a unique solution.

Methods

`add_baseline_priors`([prior_baseline_coeffs])	Add baseline priors to the model.
`add_deterministics`()	Add deterministic quantities to the model.
`add_likelihood`()	Add likelihood to the model.
`add_priors`([prior_filling_factor, ...])	Add priors and deterministics to the model
`bic`([chain, solution])	Calculate the Bayesian information criterion at the mean point estimate.
`fit`([n, draws, rel_tolerance, ...])	Approximate posterior distribution using Variational Inference (VI).
`graph`()	Generate visualization of the model graph.
`mean_lnlike`([chain, solution])	Evaluate mean log-likelihood over posterior samples.
`null_bic`()	Evaluate the Bayesian Information Criterion for the null hypothesis (baseline only, no clouds)
`predict_baseline`([baseline_params])	Predict the un-normalized baseline model.
`reset_results`()	Reset results and convergence checks.
`sample`([init, n_init, chains, init_kwargs, ...])	Sample posterior distribution using MCMC.
`sample_posterior_predictive`([solution, thin])	Generate posterior predictive samples
`sample_prior_predictive`([samples])	Generate prior predictive samples
`sample_smc`(**kwargs)	Sample posterior distribution using Sequential Monte Carlo.
`solve`(**kwargs)	Identify unique solutions and break the labeling degeneracy.

add_likelihood(): Add likelihood to the model. SpecData key must be “emission”.

add_priors(prior_filling_factor: Iterable[float] = [2.0, 1.0], prior_ff_NHI: float = 1e+21, prior_fwhm2_thermal_fraction: Iterable[float] = [2.0, 2.0], *args, **kwargs)

Add priors and deterministics to the model

Parameters:

prior_filling_factorIterable[float], optional: Prior distribution on filling factor, by default [2.0, 1.0], where filling_factor ~ Beta(alpha=prior[0], beta=prior[1])
prior_ff_NHIfloat, optional: Prior distribution on filling factor * column density (cm-2), by default 1.0e21, where ff_NHI ~ HalfNormal(sigma=prior)
prior_fwhm2_thermal_fractionIterable[float], optional: Prior distribution on thermal FWHM^2 / total FWHM^2, by default [2.0, 2.0], where fwhm2_thermal_fraction ~ Beta(alpha=prior[0], beta=prior[1])