Base Sampler Class

Module containing base sampler for Monte Carlo sampling methods containing some basic utility methods

class monte.base_sampler.BaseSampler

Bases: object

__init__() → None

Base sampler for Monte Carlo sampling methods containing basic utility methods. Initializes the sampler with two main attributes: samples and acceptances which are saved here at each iteration

acceptance_rate()

Calculates the sampler acceptance rate

Returns:

Sampler acceptance rate

Return type:

float

property acceptances

Gets or sets acceptances property

Returns:

Acceptances property

Return type:

ndarray

credible_interval(ci=0.9)

Calculates

\[100 \times \text{ci} \%\]

credible interval for each parameter

Parameters:

ci (float, optional) – Credible interval in decimal, defaults to 0.9

Returns:

Parameter values at credible interval

Return type:

ndarray

ergodic_mean()

Calculates ergodic mean(s) for each parameter. Ergodic mean refers to the mean value until the current iteration

Returns:

Ergodic mean

Return type:

ndarray

ess()

Calculates effective sample size (for each parameter) as per Kass et al (1998) and Robert and Casella (2004; pg.500)

Returns:

Effective sample size

Return type:

ndarray

geweke(first=0.1, last=0.5)

Calculates Geweke diagnostic for a Markov chain

Parameters:

• first (float, optional) – The fraction of the chain to use for the first segment, defaults to 0.1

• last (float, optional) – The fraction of the chain to use for the last segment, defaults to 0.5

Returns:

Test Z-scores and p-values

Return type:

float, float

heidelberger_welch(alpha=0.05)

Calculates Heidelberger-Welch diagnostic for a Markov chain

Parameters:

alpha (float, optional) – Test significance level, defaults to 0.05

Returns:

Diagnostic results, including: stationarity test result, halfwidth test result, initial chain mean, updated chain start, chain end, updated chain mean

Return type:

dict

property lp

Gets or sets log-probability (lp) property

Returns:

Log-probability (lp) property

Return type:

ndarray

mean()

Estimates the expected value of the posterior by calculating the mean of the samples

Returns:

Numpy array containing posterior mean for every parameter

Return type:

ndarray

parameter_kde(figsize=(12, 8), histogram=True, bins=100, show=True, save=False, **kwargs)

Plots Kernel Density Estimation(s) (KDE) (for each parameter) of posterior. Visually estimates posterior distribution

Parameters:

• figsize (tuple, optional) – Size of the total figure (all plots together), defaults to (12, 8)

• histogram (bool, optional) – Whether to overlay histogram over KDE plots, defaults to True

• bins (int, optional) – Number of histogram bins, defaults to 100

• show (bool, optional) – Whether to show the figure at runtime, defaults to True

• save (bool, optional) – Whether to save the figure as .png file, defaults to False

plot_acf(figsize=(12, 8), show=True, save=False, **kwargs)

Plots autocorrelation function values of the parameter samples

Parameters:

• figsize (tuple, optional) – Size of the total figure (all plots together), defaults to (12, 8)

• show (bool, optional) – Whether to show the figure at runtime, defaults to True

• save (bool, optional) – Whether to save the figure as .png file, defaults to False

plot_ergodic_mean(figsize=(12, 8), show=True, save=False, **kwargs)

Plots ergodic mean(s) (for each parameter)

Parameters:

• figsize (tuple, optional) – Size of the total figure (all plots together), defaults to (12, 8)

• show (bool, optional) – Whether to show the figure at runtime, defaults to True

• save (bool, optional) – Whether to save the figure as .png file, defaults to False

plot_histogram(figsize=(12, 8), bins=100, show=True, save=False)

Plots histogram(s) (for each parameter) of posterior. Visually estimates posterior distribution

Parameters:

• figsize (tuple, optional) – Size of the total figure (all histograms together), defaults to (12, 8)

• bins (int, optional) – Number of histogram bins, defaults to 100

• show (bool, optional) – Whether to show the figure at runtime, defaults to True

• save (bool, optional) – Whether to save the figure as .png file, defaults to False

plot_histogram_fold(k=2, style='default', rcParams_update={}, show=True, save=False)

Plots histograms of k-subsets of the samples

Parameters:

• k (int, optional) – Number of subsets taken from the Markov chain for histogram plotting, defaults to 2

• style (str, optional) – matplotlib style to be used for plots. User can pass built-in matplotlib style (e.g. classic, fivethirtyeight), or a path to a custom style defined in a .mplstyle document, defaults to “default”

• rcParams_update (dict, optional) – matplotlib.rcParams to modify the style defined by style argument, defaults to {} (no modification)

• show (bool, optional) – Whether to show the plot, defaults to True

• save (bool, optional) – Whether to save the plot, defaults to False

quantiles(quantiles=array([0.25, 0.5, 0.75]))

Calculates posterior quantiles.

Parameters:

quantiles (ndarray, optional) – Quantiles, defaults to np.array([0.25, 0.5, 0.75])

Returns:

Parameter values at quantiles

Return type:

ndarray

raftery_lewis(q=0.025, r=0.005, s=0.95)

Calculates Raftery-Lewis diagnostic

Parameters:

• q (float, optional) – The quantile of interest, defaults to 0.025 for a lower tail quantile

• r (float, optional) – The accuracy required, defaults to 0.005

• s (float, optional) – The probability of achieving the specified accuracy, defaults to 0.95

Returns:

Diagnostic results and specifications, including: quantile of interest, requires samples, burn-in samples, total samples, accuracy required, probability of reaching that accuracy

Return type:

dict

property samples

Gets or sets samples property

Returns:

Samples property

Return type:

ndarray

save_samples(parameter_names=None, path=None)

Exports samples as .csv file.

Parameters:

path (str, optional) – Path where to save the .csv file. By default, it saves to the working directory, defaults to None

stationarity_test(test='adf', **kwargs)

Test for the stationarity of Markov chains

Parameters:

test (str, optional) – Statistical test used. Available are Augmented Dickey-Fuller test (adf) and Kwiatkowski–Phillips–Schmidt–Shin test (kpss), defaults to “adf”

Returns:

Test statistic, p-value

Return type:

float, float

std()

Estimates the standard deviation of the posterior

Returns:

Numpy array containing posterior standard deviation for every parameter

Return type:

ndarray

traceplots(figsize=(12, 8), show=True, save=False, **kwargs)

Plots traceplot(s) (for each parameter)

Parameters:

• figsize (tuple, optional) – Size of the total figure (all plots together), defaults to (12, 8)

• show (bool, optional) – Whether to show the figure at runtime, defaults to True

• save (bool, optional) – Whether to save the figure as .png file, defaults to False