nifty8.re.num.stats_distributions module#

Evaluate a function point-wise by interpolation. Can be supplied with a table_func to increase the interpolation accuracy, Best results are achieved when lambda x: table_func(func(x)) is roughly linear.

Parameters:

func (function) – Function to interpolate.
xmin (float) – The smallest value for which func will be evaluated.
xmax (float) – The largest value for which func will be evaluated.
step (float) – Distance between sampling points for linear interpolation. Either of step or num must be specified.
num (int) – The number of interpolation points. Either of step of num must be specified.
table_func (function) – Non-linear function applied to the tabulated function in order to transform the table to a more linear space.
inv_table_func (function) – Inverse of table_func.
return_inverse (bool) – Whether to also return the interpolation of the inverse of func. Only sensible if func is invertible.

invgamma_invprior(a, scale, loc=0.0, step=0.01) → Callable[source]#: Get the inverse transformation to invgamma_prior.

invgamma_prior(a, scale, loc=0.0, step=0.01) → Callable[source]#

Transform a standard normal into an inverse gamma distribution.

The pdf of the inverse gamma distribution is defined as follows using $q$ to denote the scale:

$P(x|q, a) = \frac{q^a}{\Gamma(a)}x^{-a -1} \exp \left(-\frac{q}{x}\right)$

That means that for large x the pdf falls off like $x^{(-a -1)}$ . The mean of the pdf is at $q / (a - 1)$ if $a > 1$ . The mode is $q / (a + 1)$ .

This transformation is implemented as a linear interpolation which maps a Gaussian onto an inverse gamma distribution.

Parameters:

a (float) – The shape-parameter of the inverse-gamma distribution.
scale (float) – The scale-parameter of the inverse-gamma distribution.
loc (float) – An option shift of the whole distribution.
step (float) – Distance between sampling points for linear interpolation.

laplace_prior(alpha) → Partial[source]#: Takes random normal samples and outputs samples distributed according to

lognormal_invprior(mean, std, *, _log_mean=None, _log_std=None) → Partial[source]#: Get the inverse transform to lognormal_prior.

lognormal_moments(mean, std)[source]#: Compute the cumulants a log-normal process would need to comply with the provided mean and standard-deviation std

lognormal_prior(mean, std, *, _log_mean=None, _log_std=None) → Partial[source]#

Moment-match standard normally distributed random variables to log-space

Takes random normal samples and outputs samples distributed according to

$P(xi|mu,sigma) \propto exp(mu + sigma * xi)$

such that the mean and standard deviation of the distribution matches the specified values.

normal_invprior(mean, std) → Partial[source]#: Get the inverse transform to normal_prior.

normal_prior(mean, std) → Partial[source]#: Match standard normally distributed random variables to non-standard variables.

uniform_prior(a_min=0.0, a_max=1.0) → Partial[source]#

Transform a standard normal into a uniform distribution.

Parameters:

a_min (float) – Minimum value.
a_max (float) – Maximum value.