chippr includes a number of modules containing helper functions.

Default Settings

defaults.check_basic_setup(params)

Sets parameter values pertaining to basic constants of simulation

Parameters:params (dict) – dictionary containing key/value pairs for simulation Returns:params – dictionary containing key/value pairs for simulation Return type:dict

defaults.check_bias_params(params)

Sets parameter values pertaining to presence of a systematic bias

Parameters:params (dict) – dictionary containing key/value pairs for simulation Returns:params – dictionary containing key/value pairs for simulation Return type:dict

defaults.check_catastrophic_outliers(params)

Sets parameter values pertaining to presence of a catastrophic outlier population

Parameters:params (dict) – dictionary containing key/value pairs for simulation Returns:params – dictionary containing key/value pairs for simulation Return type:dict

Notes

defaults.check_inf_params(params={})

Checks inference parameter dictionary for various keywords and sets to default values if not present

Parameters:params (dict, optional) – dictionary containing initial key/value pairs for inference Returns:params – dictionary containing final key/value pairs for inference Return type:dict

defaults.check_sampler_params(params)

Sets parameter values pertaining to basic constants of inference

Parameters:params (dict) – dictionary containing key/value pairs for inference Returns:params – dictionary containing key/value pairs for inference Return type:dict

defaults.check_sim_params(params={})

Checks simulation parameter dictionary for various keywords and sets to default values if not present

Parameters:params (dict, optional) – dictionary containing initial key/value pairs for simulation of catalog Returns:params – dictionary containing final key/value pairs for simulation of catalog Return type:dict

defaults.check_variable_sigmas(params)

Sets parameter values pertaining to widths of Gaussian PDF components

Parameters:params (dict) – dictionary containing key/value pairs for simulation Returns:params – dictionary containing key/value pairs for simulation Return type:dict

Notes

rms_scatter –> variable_sigmas

General Utilities

utils.ingest(in_info)

Function reading in parameter file to define functions necessary for generation of posterior probability distributions

Parameters:in_info (string or dict) – string containing path to plaintext input file or dict containing likelihood input parameters Returns:in_dict – dict containing keys and values necessary for posterior probability distributions Return type:dict

utils.safe_log(arr, threshold=4.450147717014403e-308)

Takes the natural logarithm of an array that might contain zeros.

Parameters:

• arr (ndarray, float) – array of values to be logged
• threshold (float, optional) – small, positive value to replace zeros and negative numbers

Returns:

logged – logged values, with small value replacing un-loggable values

Return type:

ndarray

Simulation Utilities

sim_utils.choice(weights)

Function sampling discrete distribution

Parameters:weights (numpy.ndarray) – relative probabilities for each category Returns:index – chosen category Return type:int

Statistics

stat_utils.acors(xtimeswalkersbins, mode='bins')

Calculates autocorrelation time for MCMC chains

Parameters:

• xtimeswalkersbins (numpy.ndarray, float) – emcee chain values of dimensions (n_iterations, n_walkers, n_parameters)
• mode (string, optional) – ‘bins’ for one autocorrelation time per parameter, ‘walkers’ for one autocorrelation time per walker

Returns:

taus – autocorrelation times by bin or by walker depending on mode

Return type:

numpy.ndarray, float

stat_utils.calculate_kld(pe, qe, vb=True)

Calculates the Kullback-Leibler Divergence between two PDFs.

Parameters:

• pe (numpy.ndarray, float) – probability distribution evaluated on a grid whose distance from q will be calculated.
• qe (numpy.ndarray, float) – probability distribution evaluated on a grid whose distance to p will be calculated.
• vb (boolean) – report on progress to stdout?

Returns:

Dpq – the value of the Kullback-Leibler Divergence from q to p

Return type:

float

stat_utils.calculate_rms(pe, qe, vb=True)

Calculates the Root Mean Square Error between two PDFs.

Parameters:

• pe (numpy.ndarray, float) – probability distribution evaluated on a grid whose distance _from_ q will be calculated.
• qe (numpy.ndarray, float) – probability distribution evaluated on a grid whose distance _to_ p will be calculated.
• vb (boolean) – report on progress to stdout?

Returns:

rms – the value of the RMS error between q and p

Return type:

float

stat_utils.cf(xtimes)

Helper function to calculate autocorrelation time for chain of MCMC samples

Parameters:xtimes (numpy.ndarray, float) – single parameter values for a single walker over all iterations Returns:cf – autocorrelation time over all time lags for one parameter of one walker Return type:numpy.ndarray, float

stat_utils.cfs(x, mode)

Helper function for calculating autocorrelation time for MCMC chains

Parameters:

• x (numpy.ndarray, float) – input parameter values of length number of iterations by number of walkers if mode=’walkers’ or dimension of parameters if mode=’bins’
• mode (string) – ‘bins’ for one autocorrelation time per parameter, ‘walkers’ for one autocorrelation time per walker

Returns:

cfs – autocorrelation times for all walkers if mode=’walkers’ or all parameters if mode=’bins’

Return type:

numpy.ndarray, float

stat_utils.cft(xtimes, lag)

Helper function to calculate autocorrelation time for chain of MCMC samples

Parameters:

• xtimes (numpy.ndarray, float) – single parameter values for a single walker over all iterations
• lag (int) – maximum lag time in number of iterations

Returns:

ans – autocorrelation time for one time lag for one parameter of one walker

Return type:

numpy.ndarray, float

stat_utils.gr_test(sample, threshold=1.2)

Performs the Gelman-Rubin test of convergence of an MCMC chain

Parameters:

• sample (numpy.ndarray, float) – chain output
• threshold (float, optional) – Gelman-Rubin test statistic criterion (usually around 1)

Returns:

test_result – True if burning in, False if post-burn in

Return type:

boolean

stat_utils.mean(population)

Calculates the mean of a population

Parameters:population (np.array, float) – population over which to calculate the mean Returns:mean – mean value over population Return type:np.array, float

stat_utils.multi_parameter_gr_stat(sample)

Calculates the Gelman-Rubin test statistic of convergence of an MCMC chain over multiple parameters

Parameters:sample (numpy.ndarray, float) – multi-parameter chain output Returns:Rs – vector of the potential scale reduction factors Return type:numpy.ndarray, float

stat_utils.norm_fit(population)

Calculates the mean and standard deviation of a population

Parameters:population (np.array, float) – population over which to calculate the mean Returns:norm_stats – mean and standard deviation over population Return type:tuple, list, float

stat_utils.single_parameter_gr_stat(chain)

Calculates the Gelman-Rubin test statistic of convergence of an MCMC chain over one parameter

Parameters:chain (numpy.ndarray, float) – single-parameter chain Returns:R_hat – potential scale reduction factor Return type:float

Plotting Utilities

plot_utils.plot_h(sub_plot, bin_ends, to_plot, s='--', c='k', a=1, w=1, d=[(0, (1, 0.0001))], l=None, r=False)

Helper function to plot horizontal lines of a step function

Parameters:

• sub_plot (matplotlib.pyplot subplot object) – subplot into which step function is drawn
• bin_ends (list or ndarray) – list or array of endpoints of bins
• to_plot (list or ndarray) – list or array of values within each bin
• s (string, optional) – matplotlib.pyplot linestyle
• c (string, optional) – matplotlib.pyplot color
• a (int or float, [0., 1.], optional) – matplotlib.pyplot alpha (transparency)
• w (int or float, optional) – matplotlib.pyplot linewidth
• d (list of tuple, optional) – matplotlib.pyplot dash style, of form [(start_point, (points_on, points_off, …))]
• l (string, optional) – label for function
• r (boolean, optional) – True for rasterized, False for vectorized

plot_utils.plot_step(sub_plot, bin_ends, to_plot, s='--', c='k', a=1, w=1, d=[(0, (1, 0.0001))], l=None, r=False)

Plots a step function

Parameters:

• sub_plot (matplotlib.pyplot subplot object) – subplot into which step function is drawn
• bin_ends (list or ndarray) – list or array of endpoints of bins
• to_plot (list or ndarray) – list or array of values within each bin
• s (string, optional) – matplotlib.pyplot linestyle
• c (string, optional) – matplotlib.pyplot color
• a (int or float, [0., 1.], optional) – matplotlib.pyplot alpha (transparency)
• w (int or float, optional) – matplotlib.pyplot linewidth
• d (list of tuple, optional) – matplotlib.pyplot dash style, of form [(start_point, (points_on, points_off, …))]
• l (string, optional) – label for function
• r (boolean, optional) – True for rasterized, False for vectorized

Notes

Make this not need a subplot

plot_utils.plot_v(sub_plot, bin_ends, to_plot, s='--', c='k', a=1, w=1, d=[(0, (1, 0.0001))], r=False)

Helper function to plot vertical lines of a step function

Parameters:

• sub_plot (matplotlib.pyplot subplot object) – subplot into which step function is drawn
• bin_ends (list or ndarray) – list or array of endpoints of bins
• to_plot (list or ndarray) – list or array of values within each bin
• s (string, optional) – matplotlib.pyplot linestyle
• c (string, optional) – matplotlib.pyplot color
• a (int or float, [0., 1.], optional) – matplotlib.pyplot alpha (transparency)
• w (int or float, optional) – matplotlib.pyplot linewidth
• d (list of tuple, optional) – matplotlib.pyplot dash style, of form [(start_point, (points_on, points_off, …))]
• r (boolean, optional) – True for rasterized, False for vectorized

plot_utils.set_up_plot()

Sets up plots to look decent