API¶

MCMC Results¶

The best-fit parameter vector can be accessed from the MCMC chain using the following functions of the EmceeResults object:

`EmceeResults.values`()	Convenience function to return the median values for the free parameters as an array
`EmceeResults.constrained_values`()	Convenience function to return the median values for the constrained parameters as an array
`EmceeResults.max_lnprob_values`()	Return the value of the free parameters at the iteration with the maximum probability
`EmceeResults.max_lnprob_constrained_values`()	Return the value of the constrained parameters at the iteration with the maximum probability
`EmceeResults.peak_values`()	Convenience function to return the peak values for the free parameters as an array
`EmceeResults.peak_constrained_values`()	Convenience function to return the peak values for the constrained parameters as an array

The results object can be saved and loaded from file using:

`EmceeResults.to_npz`(filename, **meta)	Save the relevant information of the class to a numpy `npz` file
`EmceeResults.from_npz`(filename)	Load a numpy `npz` file and return the corresponding `EmceeResults` object

Correlations between parameters can be analyzed using:

`EmceeResults.sorted_1d_corrs`([params, …])	Return a pandas DataFrame holding the correlation matrix, as computed from the `chains` DataFrame, for all parameters
`EmceeResults.corr`([params, labels, use_latex])	Return a pandas DataFrame holding the correlation matrix, as computed from the `chains` DataFrame, for all parameters

The results can be visualized with the following function, which take advantage of the seaborn Python plotting module:

`EmceeResults.jointplot_2d`(param1, param2[, …])	Plot the 2D traces of the given parameters, using KDE via the `seaborn.jointplot()` function.
`EmceeResults.kdeplot_2d`(param1, param2[, …])	Plot the 2D traces of the given parameters, using KDE via `seaborn.kdeplot()`
`EmceeResults.plot_correlation`([params, …])	Plot the diagonal correlation matrix, using `seaborn.heatmap`
`EmceeResults.plot_timeline`(names, *kwargs)	Plot the chain timeline for as many parameters as specified in the names tuple.
`EmceeResults.plot_triangle`(names, *kwargs)	Make a triange plot for the desired parameters using the `corner.corner()` function.

class pyRSD.rsdfit.results.EmceeResults(sampler, fit_params, burnin=None, **meta)¶

Class to hold the fitting results from an emcee MCMC run

as_dict(kind=None)¶: Return a dictionary of the values, either the median, peak, or max_lnprob

burnin¶: The number of iterations to treat as part of the “burnin” period, where the chain hasn’t stabilized yet

chains(params=[], labels={}, use_latex=False)¶

Return a pandas DataFrame holding the chains (flat traces) as columns for both the free and constrained parameters

Note that any burnin is removed from the chains.

Parameters:

params : list, {‘free’, ‘constrained’}, optional

return only a subset of the parameters

use_latex : bool, optional

If True, try to use any available latex names for the tick labels; default is False

Returns:

DataFrame :

the DataFrame holding the flat traces for all parameters

constrained_values()¶: Convenience function to return the median values for the constrained parameters as an array

copy()¶: Return a deep copy of the EmceeResults object

corr(params=[], labels={}, use_latex=False)¶

Return a pandas DataFrame holding the correlation matrix, as computed from the chains DataFrame, for all parameters

Parameters:

params : list, {‘free’, ‘constrained’}, optional

return only a subset of the parameters

use_latex : bool, optional

If True, try to use any available latex names for the tick labels; default is False

Returns:

DataFrame (Np, Np) :

the DataFrame holding the correlation between parameters

error_rescaling¶: Rescale error on parameters due to covariance matrix from mocks

classmethod from_npz(filename)¶: Load a numpy npz file and return the corresponding EmceeResults object

iterations¶: The number of iterations performed, as computed from the chain

jointplot_2d(param1, param2, thin=1, rename={}, crosshairs={}, **kwargs)¶

Plot the 2D traces of the given parameters, using KDE via the seaborn.jointplot() function.

Parameters:

param1 : str

the name of the first parameter

param2 : str

the name of the second parameter

thin : int, optional

thin the plotted array randomly by this amount

rename : dict, optional

dictionary giving a string to rename each variable; default will try to use any latex names stored

crosshairs : dict, optional

values to show as horizontal or vertical lines

**kwargs :

additional keyword arguments to pass to seaborn

Notes

Any iterations during the “burnin” period are excluded

kdeplot_2d(param1, param2, thin=1, rename={}, crosshairs={}, **kwargs)¶

Plot the 2D traces of the given parameters, using KDE via seaborn.kdeplot()

Parameters:

param1 : str

the name of the first parameter

param2 : str

the name of the second parameter

thin : int, optional

thin the plotted array randomly by this amount

rename : dict, optional

dictionary giving a string to rename each variable; default will try to use any latex names stored

crosshairs : dict, optional

values to show as horizontal or vertical lines

**kwargs :

additional keyword arguments to pass to seaborn

Notes

Any iterations during the “burnin” period are excluded

max_lnprob¶: The value of the maximum log probability

max_lnprob_constrained_values()¶: Return the value of the constrained parameters at the iteration with the maximum probability

max_lnprob_values()¶: Return the value of the free parameters at the iteration with the maximum probability

ndim¶: The number of free parameters

peak_constrained_values()¶: Convenience function to return the peak values for the constrained parameters as an array

peak_values()¶: Convenience function to return the peak values for the free parameters as an array

plot_correlation(params=[], use_latex=True, labelsize=10)¶

Plot the diagonal correlation matrix, using seaborn.heatmap

Parameters:

params : list, {‘free’, ‘constrained’}, optional

return only a subset of the parameters

use_latex : bool, optional

If True, try to use any available latex names for the tick labels; default is True. You might want to set this to False if you are trying to use mpld3

plot_timeline(*names, **kwargs)¶

Plot the chain timeline for as many parameters as specified in the names tuple.

This plots the value of each walker as a function of iteration.

Parameters:

names : tuple

The string names of the parameters to plot

outfile : str, optional

If not None, save the resulting figure with the specified name

Returns:

fig : matplotlib.Figure

The figure object

Notes

Any iterations during the “burnin” period are excluded

plot_triangle(*names, **kwargs)¶

Make a triange plot for the desired parameters using the corner.corner() function.

Parameters:

names : tuple

The string names of the parameters to plot

thin : int, optional

The factor to thin the number of samples plotted by. Default is 1 (plot all samples)

outfile : str, optional

If not None, save the resulting figure with the specified name

Returns:

fig : matplotlib.Figure

The figure object

Notes

Any iterations during the “burnin” period are excluded

sorted_1d_corrs(params=[], use_latex=False, absval=False)¶

Return a pandas DataFrame holding the correlation matrix, as computed from the chains DataFrame, for all parameters

Parameters:

params : list, {‘free’, ‘constrained’}, optional

return only a subset of the parameters

use_latex : bool, optional

If True, try to use any available latex names for the tick labels; default is False

Returns:

DataFrame (Np, Np) :

the DataFrame holding the correlation between parameters

summarize_fit()¶: Summarize the fit, by plotting figures and outputing the relevant information

to_npz(filename, **meta)¶: Save the relevant information of the class to a numpy npz file

values()¶: Convenience function to return the median values for the free parameters as an array

verify_param_ordering(free_params, constrained_params)¶: Verify the ordering of EmceeResults.chain, making sure that the chains have the ordering specified by free_params and constrained_params

walkers¶: The number of walkers, as computed from the chain

class pyRSD.rsdfit.results.EmceeParameter(name, trace, burnin=0)¶

Class to hold the parameter fitting result

burnin¶: The number of iterations to exclude as part of the “burn-in” phase

error_rescaling¶: Rescale errors by this factor

fiducial¶: The fiducial value of the parameter

flat_trace¶: Returns the flattened chain, excluding steps that occured during the “burnin” period

mean¶: Return the average value of the chain

median¶: Return the median of the trace, i.e., the 50th percentile of the trace

one_sigma¶

Return the lower and upper one-sigma error intervals

These are computed from the percentiles, 50 - 15.86555 and 84.13445 - 50

Returns:

lower, upper

The lower and upper 1-sigma error intervals

peak¶: Return the value of the parameter that gives the peak of the posterior PDF, as determined through Gaussian kernel density estimation

stderr¶: The one-sigma standard error, averaging the lower and upper bounds

three_sigma¶

Return the lower and upper three-sigma error intervals

There are computed from the percentiles, 50 - 0.135 and 99.865 - 50

Returns:

lower, upper

The lower and upper 3-sigma error intervals

trace(niter=None)¶

Return the sample values at a specific iteration number.

shape: (nwalkers, niters)

two_sigma¶

Return the lower and upper two-sigma error intervals.

These are computed from the percentiles, 50 - 2.2775 and 97.7225 - 50

Returns:

lower, upper

The lower and upper 2-sigma error intervals

NLOPT Results¶

class pyRSD.rsdfit.results.LBFGSResults(data, fit_params)¶

Class to hold the fitting results from an scipy.optimize L-BFGS-B nonlinear optimization run.

copy()¶: Return a deep copy of the LBFGSResults object

classmethod from_npz(filename)¶: Load a numpy npz file and return the corresponding LBFGSResults object

iterations¶: The total number of iterations ran

ndim¶: The number of free parameters

summarize_fit(*args, **kwargs)¶: Summarize the fit by printing self

to_npz(filename)¶: Save the relevant information of the class to a numpy npz file

verify_param_ordering(free_params, constrained_params)¶: Verify the ordering of of parameters, making sure that the ordering specified by free_params and constrained_params is respected in the results