Likelihood (mesmer.likelihood)

This module contains the main likelihood object of the package. mesmer.likelihood.LogProb. This object is initialized by providing a set of observed data and its covariance, and specifying a model.

class mesmer.likelihood.LogProb(data=None, covariance=None, frequencies=None, model=None)

Bases: object

Class calculating the marginalize posterior of spectral parameters given some observed data, its covariance, and a model for the emission of different components. This class links together the functions required to calculate the terms in Equation (A7) of 1608.00551.

The setup of this class requires the observed multifrequency sky maps, their pixel covariance (assumed diagonal in pixel space), the SED matrix (instance of mesmer.FMatrix), a dictionary containing the fixed parameter and their values, and a set of priors, which tell the likelihood which parameters are to be let vary.

Parameters

data: ndarray

Array of shape (Nfreq, Npol, Npix) containing the observed multi-frequency data.

covariance: ndarray

Array of shape (Nfreq, Npol, Npix) containing the pixel covariance of the array data.

fmatrix: object, :class:`mesmer.FMatrix`

Instance of mesmer.FMatrix that defines the component scaling in the fitted sky model.

fixed_parameters: dict

Dictionary, where key, value pairs correspond to parameter names and values to be fixed.

priors: dict

Dictionary, where key, value pairs correpsond to which parameters are allowed to vary, and the corresponding mean and standard deviation of the Gaussian prior.

get_amplitdue_covariance(theta, component=None)

Convenience function to return the component covariances, N_T_inv, for a given set of spectral parameters.

get_amplitude_expectation(theta, component=None)

Convenience function to return the component-separated expected amplitudes, T_bar, taking care of the relevant reshaping.

load_data_from_hdf5(fpath, mc=0)

Method to instantiate data attributes using data saved in an HDF5 archive.

Parameters

fpath: str, Path

Path to the hdf5 archive.

record: str

Record in which the data is stored. This could be the name of the group in which the datasets are saved.

classmethod load_data_from_hdf5_batch(fpath, model=None)

Method to instantiate data attrib utes using data saved in an HDF5 archive. Note that a simpler structure for this method would place the for loop within a single opening of the hdf5 file. However, this hogs the resource, and we want to be able to write to this file from other processes.

Parameters

fpath: str, Path

Path to the hdf5 archive.

model: Path (optional, default=None)

If specified, this is a path to a yaml file containing an SED model specification.

Returns

mesmer.likelihood.LogProb

Instantiated mesmer.likelihood.LogProb object.

classmethod load_model_from_yaml(fpath)

Method to load a model configuration from a yaml file.

model_setup(model)

Function to parse the model definition dictionary.

The first level of the dictionary has keys corresponding to the different components, and must match one of the functions in mesmer.seds. The values of the keys are dictionaries with fixed and varied keywords. These contain further dictionaries with fixed parameter name / value pairs, and free parameter prior name / pairs.

Parameters

model: dict

Dictionary defining model.

theta_0(npoints=None, seed=7837)

Function to generate a starting guess for optimization or sampling by drawing a random point from the prior.

Parameters

npoints: int (optional, default=None)

If npoints is not None, function returns an array of draws from the prior of dimension (npoints, ndim). This can be useful for initializing a set of optimization runs, or samplers.

seed: int (optional, default=7837)

Seed for the PRNG key used by jax. jax has a subtly different approach to random number generation to numpy. Worth reading about this before setting this number.

Returns

ndarray

Array of length the number of free parameters.