stats

class aims3.stats.Likelihood(obs, sigma)

An object to setup and evaluate a likelihood function for fitting models to observations.

Calling the object evaluates the likelihood, i.e. –χ²/2.

chi2(model, a=None)

Return χ² of the given model using surface correction parameters a.

chi2_seismic(model, a=None)

Return the seismic χ² of the given model using surface correction parameters a.

chi2_nonseismic(model)

Return the non-seismic χ² of the given model.

extend_frequency_function(names, num_rows, den_rows=None)

A utility function to extend the frequency function by appending the names of the new components, their numerator matrix num_rows and, if present, denominator matrix den_rows.

setup_frequency_function(function_names=[])

Set up the frequency function using the list of options in function_names (e.g. ['avg_dnu1', 'r02']). Current options (see The frequency function) are:

  • nu<l>: the individual frequencies

  • nu_min<i>: use the i-th lowest radial mode frequency

  • r02: the r₀₂ separation ratios

  • r13: the r₁₃ separation ratios

  • r01: the r₀₁ separation ratios

  • r10: the r₁₀ separation ratios

  • d2nu: the second frequency differences \(\Delta_2\nu_{l,n}=\nu_{l,n-1}-2\nu_{l,n}+\nu_{l,n+1}\)

  • dnu<l>: the first frequency differences \(\Delta\nu_{l,n}=\nu_{l,n}-\nu_{l,n-1}\)

  • avg_dnu<l>: the average large separation \(\langle\Delta\nu_l\rangle\) (found by linear regression)

<l> indicates an optional angular degree. If omitted, all available angular degrees will be used. avg_dnu gives a single large separation fit by regression using all the modes.

frequency_function(freqs)

Evaluate the frequency function using the frequencies in array freqs, which must have already been selected to match the observations.

set_chi2_weights(weight_option, seismic_weight_factor=1.0, nonseismic_weight_factor=1.0)

Assigns the relative weights for the log-likelihoods of the seismic and non-seismic parts (\(w_\mathrm{seismic}\) and \(w_\mathrm{non-seismic}\)) of the likelihood function depending on the number of terms in each. e.g. Given \(T_\mathrm{eff}\), [Fe/H] and four frequency separation ratios, we have two non-seismic terms and four seismic terms, i.e. \(n_\mathrm{non-seismic}=2\) and \(n_\mathrm{seismic}=4\).

Parameters

  • weight_option (str) –

    For each option, the non-seismic and seismic weights are, respectively:

    • None or '': both 1, ignoring the extra weight factors.

    • 'absolute': both 1, multiplied by the extra weight factors.

    • 'relative': 1 and \(n_\mathrm{non-seismic}/n_\mathrm{seismic}\)

    • 'reduced': both \(1/(n_\mathrm{non-seismic}+n_\mathrm{seismic}-1)\)

    • 'reduced_bis': \(1/(n_\mathrm{non-seismic}-1)\) and \(1/(n_\mathrm{seismic}-1)\)

  • seismic_weight_factor (float) – Additional absolute weight by which to multiply the seismic component.

  • nonseismic_weight_factor (float) – Additional absolute weight by which to multiply the non-seismic component.

get_optimal_surface_correction(model, name=None, obs=None, sigma=None, fixed=None, maxiter=20)

Calculates the optimal surface correction parameters for model relative to some observations. By default, this uses the data stored in the Likelihood object (i.e. self) but you can pass keyword arguments to override these with other values.

Parameters

  • model (AIMS3 Model) – model for which to compute optimal surface correction parameters

  • name (str, optional) –

    name of the surface correction, options are

    • None: don’t use any surface corrections

    • 'Ball2014': use one-term (or cubic) correction by Ball & Gizon (2014)

    • 'Ball2014_2': use two-term (or combined) correction by Ball & Gizon (2014)

    • 'Kjeldsen2008': use power-law correction by Kjeldsen et al. (2008) with power fixed[0] and free amplitude

    • 'Kjeldsen2008_scaling': like Kjeldsen2008 but the power is based on the scaling relation by Sonoi et al. (2015), as implemented in b_Kjeldsen2008

    • 'Kjeldsen2008_2' or 'PowerLaw': like Kjeldsen2008 but both the amplitude and power are free

    • 'Sonoi2015': use the modified Lorentzian by Sonoi et al. (2015) with power fixed[0] and free amplitude

    • 'Sonoi2015_scaling': like Sonoi2015 but the power is based on the scaling relation by Sonoi et al. (2015), as implemented in beta_Sonoi2015

    • 'Sonoi2015_2': like Sonoi2015 but both the amplitude and power are free

  • obs (array, optional) – observed frequencies

  • sigma (array, optional) – uncertainties on observed frequencies

  • fixed (iterable of floats) – fixed parameters for surface correction

  • maxiter (int) – maximum number of iterations for Newton’s method when optimising a surface correction with non-linear parameters

Returns

free – optimal free parameters of the surface correction

Return type

array