Package csb :: Package statistics

Package statistics

Statistics root package.

This package contains a number of common statistical utilities. Sub-packages provide more specialized APIs, for example csb.statistics.pdf defines the probability density object model.

Submodules

csb.statistics.ars: Adaptive Rejection Sampling (ARS)
csb.statistics.maxent: A Maximum-Entropy model for backbone torsion angles.
csb.statistics.mixtures: Mixture models for multi-dimensional data.
csb.statistics.pdf: Probability density functions.
- csb.statistics.pdf.parameterized: Probability density functions with support for shared and computed parameters.
csb.statistics.rand: Random number generators
csb.statistics.samplers: Defines abstract samplers.
- csb.statistics.samplers.mc: Abstract Monte Carlo samplers.
  - csb.statistics.samplers.mc.multichain: Implements several extended-ensemble Monte Carlo sampling algorithms.
  - csb.statistics.samplers.mc.neqsteppropagator: Propagator class employing stepwise trajectories as used in the NCMC algorithm (Nilmeier et al., "Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation", PNAS 2011)
  - csb.statistics.samplers.mc.propagators: Provides various deterministic and stochastic propagators.
  - csb.statistics.samplers.mc.singlechain: Various Monte Carlo equilibrium sampling algorithms, which simulate only one Markov chain.
csb.statistics.scalemixture: Approximation of a distribution as a mixture of gaussians with a zero mean but different sigmas

Classes
	Cumulative

Functions

autocorrelation(x, n)
auto-correlation of a times series

source code

circmean(a, axis=None)
Estimate mean of a circular variable

source code

circvar(a, axis=None)
Calculate circular variance of a circular variable.

source code

density(x, nbins, normalize=True)
Histogram of univariate input data: basically calls numpy's histogram method and does a proper normalization.

source code

entropy(p)
Calculate the entropy of p.

source code

geometric_mean(x, axis=None)
Returns: geometric mean of x

source code

harmonic_mean(x, axis=None)
Returns: harmonic mean of x

source code

histogram2D(x, nbins=100, axes=None, nbatch=1000, normalize=True)
Non-greedy two-dimensional histogram.

source code

histogram_nd(x, nbins=100, axes=None, nbatch=1000, normalize=True)
Non-greedy n-dimemsional histogram.

source code

kurtosis(x, axis=None)
Returns: Sample kurtosis of x

source code

principal_coordinates(D, nd=None)
Reconstruction of a multidimensional configuration that optimally reproduces the input distance matrix.

source code

probabilistic_and(p, axis=0)
Probabilistic version of AND

source code

probabilistic_or(p, axis=0)
Probabilistic version of OR

source code

probabilistic_xor(p, axis=0)
Probabilistic version of XOR.

source code

running_average(x, w, axis=None)
Calculates a running average for given window size

source code

skewness(x, axis=None)
Returns: Sample skewness of x

source code

weighted_median(x, w)
Calculates the weighted median, that is the minimizer of argmin {\sum w_i |x_i - \mu|}

source code

Variables
	__package__ = `None` hash(x)

Function Details

autocorrelation(x, n)

source code

auto-correlation of a times series

Parameters:

x (numpy.array) - time series
n (int) - Maximal lag for which to compute the auto-correlation

circmean(a, axis=None)

source code

Estimate mean of a circular variable

Parameters:

a - input array
axis (None or integer) - axis along which mean is calculated

circvar(a, axis=None)

source code

Calculate circular variance of a circular variable.

Parameters:

a - input array
axis (None or integer) - axis along which mean is calculated

density(x, nbins, normalize=True)

source code

Histogram of univariate input data: basically calls numpy's histogram method and does a proper normalization.

Parameters:

x - input numpy array
nbins (integer) - number of bins
normalize - if true, histogram will be normalized

entropy(p)

source code

Calculate the entropy of p.

Returns:: entropy of p

geometric_mean(x, axis=None)

source code

Parameters:

x
axis - compute the geometric mean along this axis

Returns:

geometric mean of x

harmonic_mean(x, axis=None)

source code

Parameters:

x
axis - compute the harmonic mean along this axis

Returns:

harmonic mean of x

histogram2D(x, nbins=100, axes=None, nbatch=1000, normalize=True)

source code

Non-greedy two-dimensional histogram.

Parameters:

x (numpy array) - input array of rank two
nbins (integer) - number of bins
axes (tuple of two one-dimensional numpy arrays) - x- and y-axes used for binning the data (if provided this will be used instead of <nbins>)
nbatch (integer) - size of batch that is used to sort the data into the 2D grid
normalize (boolean) - specifies whether histogram should be normalized

Returns:

2-rank array storing histogram, tuple of x- and y-axis

histogram_nd(x, nbins=100, axes=None, nbatch=1000, normalize=True)

source code

Non-greedy n-dimemsional histogram.

Parameters:

x (numpy array) - input array of rank (-1,n)
nbins (integer) - number of bins
axes (tuple of two one-dimensional numpy arrays) - axes used for binning the data (if provided this will be used instead of <nbins>)
nbatch (integer) - size of batch that is used to sort the data into the nD grid
normalize (boolean) - specifies whether histogram should be normalized

Returns:

n-rank array storing histogram, tuple of axes