`asterion`#

Fitting acoustic glitches to the mode frequencies of solar-like oscillators.

Warning

This module is a work-in-progress, use with caution.

Subpackages#

asterion.data

Submodules#

Package Contents#

class GlitchModel(nu_max, delta_nu, teff=None, epsilon=None, seed=0, window_width='full')[source]#

Bases: Model

Asteroseismic glitch model.

\[\nu_\mathrm{obs} \sim \mathcal{GP}(m(n), k(n, n') + \sigma^2\mathcal{I})\]

Where the mean function is,

\[\begin{split}m(n) &= \nu_\mathrm{bkg} + \delta_\mathrm{He} + \delta_\mathrm{CZ},\\ \nu_\mathrm{bkg} &= f_\mathrm{bkg}(n),\\ \delta_\mathrm{He} &= f_\mathrm{He}(\nu_\mathrm{bkg}),\\ \delta_\mathrm{CZ} &= f_\mathrm{CZ}(\nu_\mathrm{bkg}),\end{split}\]

and the kernel function is,

\[k(n, n') = \sigma_k^2 \exp\left( - \frac{(n' - n)^2}{l^2} \right).\]

Parameters

n (array_like) – Radial order of model observations.
nu_max (dist_like) – Prior on the frequency at maximum power.
delta_nu (dist_like) – Prior on the large frequency separation.
teff (dist_like, optional) – Prior on the effective temperature. This is used for estimating a prior on the glitch acoustic depths. If None (default), a prior of Normal(5000, 700) is assumed.
epsilon (dist_like, optional) – Prior on the asymptotic phase parameter.
num_pred (int) – The number of points in radial order for which to make predictions.
seed (int) – The seed used to generate samples from the prior on the glitch periods (acoustic depths) tau_he and tau_cz.
window_width (float) – The number of delta_nu either side of nu_max over which to average the helium glitch amplitude for the parameter ‘he_amplitude’.

n#

Radial order of model observations.

Type: numpy.ndarray

n_pred#

Radial order of model predictions.

Type: numpy.ndarray

background#

Prior on the background function.

Type: Prior

he_glitch#

Prior on the helium glitch function.

Type: Prior

cz_glitch#

Prior on the base of convective zone glitch function.

Type: Prior

window_width#

The number of delta_nu either side of nu_max over which to average the glitch amplitudes. If string, ‘full’, the window is chosen over the entire range in frequency.

Type: str or float

class GlitchModelComparison(nu_max, delta_nu, teff=None, epsilon=None, seed=0, window_width='full')[source]#

Bases: GlitchModel

Asteroseismic glitch model comparison. Compare the glitch model with a glitchless model. The frequencies are modelled using a GP with the same kernel function but different mean functions.

The glitch model is the same as GlitchModel. The glitchless model is the same except that the mean function is,

\[m_0(n) = f_\mathrm{bkg}(n),\]

The two models are compared using the Bayes’ factor,

\[K = \frac{p(\nu_\mathrm{obs} \mid \mathcal{GP}_1)} {p(\nu_\mathrm{obs} \mid \mathcal{GP}_0)}\]

where \(\mathcal{GP}_0\) is the glitchless model and \(\mathcal{GP}_1\) is the glitch model.

Parameters

n (array_like) – Radial order of model observations.
nu_max (dist_like) – Prior on the frequency at maximum power.
delta_nu (dist_like) – Prior on the large frequency separation.
teff (dist_like, optional) – Prior on the effective temperature. This is used for estimating a prior on the glitch acoustic depths. If None (default), a prior of Normal(5000, 700) is assumed.
epsilon (dist_like, optional) – Prior on the asymptotic phase parameter.
num_pred (int) – The number of points in radial order for which to make predictions.
seed (int) – The seed used to generate samples from the prior on the glitch periods (acoustic depths) tau_he and tau_cz.
window_width (float) – The number of delta_nu either side of nu_max over which to average the helium glitch amplitude for the parameter ‘he_amplitude’.

n#

Radial order of model observations.

Type: numpy.ndarray

n_pred#

Radial order of model predictions.

Type: numpy.ndarray

background#

Prior on the background function.

Type: Prior

he_glitch#

Prior on the helium glitch function.

Type: Prior

cz_glitch#

Prior on the base of convective zone glitch function.

Type: Prior

window_width#

The number of delta_nu either side of nu_max over which to average the helium glitch amplitude for the parameter ‘he_amplitude’.

Type: float

class Inference(model, *, n, nu, nu_err=None, seed=0)[source]#

Perform inference on a given model.

Parameters

model (Model) – Model which predicts the asteroseismic mode frequencies.
nu (array_like) – Asteroseismic mode frequencies.
nu_err (array_like, optional) – Observational uncertainty on the asteroseismic mode frequencies.
seed (int) – Seed for pseudo-random number generation.

Example

from asterion import Model, Inference

n = [9, 10, 11, 12, 13]
nu = [111.1, 122.2, 133.3, 144.4, 155.5]
nu_err = 0.01
model = Model(...)  # Construct the model here
infer = Inference(model, n=n, nu=nu, nu_err=nu_err, seed=42)
# Sample from prior predictive
infer.prior_predictive(num_samples=2000)
# Sample from posterior
infer.sample()
# Sample from posterior predictive
infer.posterior_predictive()
# Get data from inference
data = infer.get_data()
# Save data
data.to_netcdf('inference_data.nc')

model#

Model with which to perform inference.

Type: Model

nu#

Observed mode frequencies.

Type: numpy.ndarray

nu_err#

Uncertainty on observed mode frequencies.

Type: numpy.ndarray, optional

samples#

Posterior samples.

Type: dict, optional

weighted_samples#

Posterior weighted samples.

Type: dict, optional

sample_stats#

Posterior sample statistics.

Type: dict, optional

prior_predictive_samples#

Prior predictive samples.

Type: dict, optional

predictive_samples#

Posterior predictive samples.

Type: dict, optional

sample_method#

Posterior sampling method.

Type: str, optional

find_map(self, num_steps=10000, handlers=None, reparam='auto', svi_kwargs={})[source]#

EXPERIMENTAL: find MAP.

Parameters

num_steps (int) – [description]. Defaults to 10000.
handlers (list, optional) – [description]. Defaults to None.
reparam (str, or numpyro.handlers.reparam) – [description]. Defaults to ‘auto’.
svi_kwargs (dict) – [description]. Defaults to {}.

get_circ_var_names(self)[source]#

[summary]

Returns: Circular variable names in the model.
Return type: list

get_data(self)[source]#

Get inference data.

Returns: Inference data.
Return type: arviz.InferenceData

get_trace(self, pred=False)[source]#

[summary]

Parameters: pred (bool) – Whether to trace the predictive model or not. Default is False.
Returns: Model trace.
Return type: OrderedDict

init_mcmc(self, model, num_warmup=1000, num_samples=1000, num_chains=1, sampler='NUTS', sampler_kwargs={}, **kwargs)[source]#

Initialises the MCMC sampler.

Parameters

model (callable) – [desc]
num_warmup (int) – [description]. Defaults to 1000.
num_samples (int) – [description]. Defaults to 1000.
num_chains (int) – [description]. Defaults to 1.
sampler (str, or numpyro.infer.mcmc.MCMCKernel) – Choose one of [‘NUTS’], or pass a numpyro mcmc kernel.
sampler_kwargs (dict) – Keyword arguments to pass to the chosen sampler.
**kwargs – Keyword arguments to pass to mcmc instance.

init_nested(self, model, num_live_points=50, max_samples=50000, sampler='multi_ellipsoid', **kwargs)[source]#

[summary]

Parameters

model (Model) – [description]
num_live_points (int) – [description]. Defaults to 50.
max_samples (int) – [description]. Defaults to 50000.
sampler (str) – [description]. Defaults to “multi_ellipsoid”.
**kwargs – Keyword arguments to pass to nested sampler instance.

Returns

[description]

Return type

numpyro.contrib.nested_sampling.NestedSampler

map_predictive(self, **kwargs)[source]#

EXPERIMENTAL: Get predictive from MAP.

Parameters

model_args (tuple) – [description]. Defaults to ().
model_kwargs (dict) – [description]. Defaults to {}.

Returns

[description]

Return type

xarray.Dataset

posterior_predictive(self, **kwargs)[source]#

[summary]

Parameters: **kwargs – Keyword arguments to pass to Predictive instance.

predictive(self, n, nu=None, nu_err=None, n_pred=None, **kwargs)[source]#

[summary]

Parameters

model_args (tuple) – Positional arguments to pass to the model callable.
model_kwargs (dict) – Keyword arguments to pass to the model callable.
**kwargs – Kwargs to pass to Predictive.

Returns

[description]

Return type

dict

prior_predictive(self, num_samples=1000, **kwargs)[source]#

[summary]

Parameters

num_samples (int) – Number of samples to take from the prior.
**kwargs – Keyword arguments to pass to Predictive instance.

run_mcmc(self, model, num_warmup=1000, num_samples=1000, num_chains=1, sampler='NUTS', sampler_kwargs={}, extra_fields=(), init_params=None, **kwargs)[source]#

Runs MCMC for a given set of model arguments.

Parameters

model (callable) – [desc]
num_warmup (int) – [description]. Defaults to 1000.
num_samples (int) – [description]. Defaults to 1000.
num_chains (int) – [description]. Defaults to 1.
sampler (str) – Choose one of [‘NUTS’]
sampler_kwargs (dict) – Keyword arguments to pass to the chosen sampler.
extra_fields (tuple) – Extra fields to report in sample_stats. Defaults to ().
init_params (dict) – Initial parameter values prior to sampling. Defaults to None.
**kwargs – Keyword arguments to pass to mcmc instance.

Returns

[description]

Return type

tuple

run_nested(self, model, num_live_points=50, num_samples=1000, max_samples=50000, sampler='multi_ellipsoid', **kwargs)[source]#

[summary]

Parameters

model (Model) – [description]
num_live_points (int) – [description]. Defaults to 100.
num_samples (int) – [description]. Defaults to 1000.
max_samples (int) – [description]. Defaults to 100000.
sampler (str) – [description]. Defaults to “multi_ellipsoid”.
**kwargs – Keyword arguments to pass to nested sampler instance.

sample(self, num_samples=1000, method='nested', handlers=None, reparam='auto', **kwargs)[source]#

[summary]

Parameters

num_samples (int) – Number of samples after warmup.
method (str) – Sampling method, choose from [‘mcmc’, ‘nested’].
handlers (list, optional) – Handlers to apply to the model during inference.
reparam (str, or numpyro.infer.reparam.Reparam) – Default is ‘auto’ will automatically reparameterise the model to improve sampling during MCMC.
**kwargs – Keyword arguments to pass to the sampling method.

get_dims(data, group='posterior')[source]#

Get available dimension groups for a given inference data group.

Parameters

data (arviz.InferenceData) – Inference data object.
group (str) – Inference data group.

Returns

[description]

Return type

list[tuple]

get_labeller(data, group='posterior', var_names=None)[source]#

Get labeller for use with arviz plotting. This automatically searches variable metadata (contained in their attrs dictionary) for its ‘symbol’ and ‘unit’ if available.

Parameters

data (arviz.InferenceData) – Inference data object.
group (str) – Inference data group for which to map labels.
var_names (list[str], optional) – Variable names for which to map labels.

Returns

Label map.

Return type

arviz.labels.MapLabeller

get_summary(data, group='posterior', var_names=None, **kwargs)[source]#

Get a summary of the inference data for a chosen group.

Parameters

data (arviz.InferenceData) – Inference data object.
group (str) – [description]. Defaults to ‘posterior’.
var_names (list, optional) – [description]. Defaults to None (all variable names)
**kwargs – Keyword arguments to pass to arviz.summary().

Returns

Summary of inference data.

Return type

xarray.Dataset, or pandas.DataFrame

asterion#

Subpackages#

Submodules#

Package Contents#

`asterion`#