priors#

This is the API for the priors module.

coPsi.priors.beta_prior(val, alphas=[1.12, 0.1], betas=[3.09, 0.3])#

Beta prior.

\[f (x;a,b) = \frac{\Gamma (a + b) x^{a-1} (1-x)^{b-1}}{\Gamma (a) \Gamma (b)} \, , \ \mathrm{for} \ 0 \leq x \leq 1, \ a > 0, b > 0 \, ,\]

where \(\Gamma\) is the gamma function (scipy.stats.gamma)

Parameters:

val (float) – \(x\).
alphas (list) – \(a\) is drawn from a normal distribution with \(\mu=\) alphas[0] and \(\sigma=\) alphas[1]. Default [1.12,0.1].
betas (list) – \(b\) is drawn from a normal distribution with \(\mu=\) betas[0] and \(\sigma=\) betas[1]. Default [3.09,0.3].

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.beta_prior_dis(alphas=[1.12, 0.1], betas=[3.09, 0.3])#

Beta prior distribution.

See beta_prior().

Parameters:

alphas (list) – \(a\) is drawn from a normal distribution with \(\mu=\) alphas[0] and \(\sigma=\) alphas[1]. Default [1.12,0.1].
betas (list) – \(b\) is drawn from a normal distribution with \(\mu=\) betas[0] and \(\sigma=\) betas[1]. Default [3.09,0.3].

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.flat_prior(val, xmin, xmax)#

Uniform prior.

\[f(x) = \frac{1}{b-a}, \, \ \mathrm{for} \ a \leq x \leq b,\ \mathrm{else} \, f(x) = 0 \, .\]

Parameters:

val (float) – \(x\).
xmin (float) – \(a\).
xmax (float) – \(b\).

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.flat_prior_dis(val, xmin, xmax)#

Flat distribution.

See flat_prior().

Parameters:

val (float) – \(x\).
xmin (float) – \(a\).
xmax (float) – \(b\).

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.gauss_prior(val, xmid, xwid)#

Gaussian prior.

\[f (x) = \frac{1}{\sqrt{2 \pi}\sigma} \exp \left (-\frac{(x - \mu)^2}{2 \sigma^2} \right) \, .\]

Parameters:

val (float) – \(x\).
xmid (float) – \(\mu\).
xwid (float) – \(\sigma\).

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.gauss_prior_dis(mu, sigma)#

Gaussian distribution.

See gauss_prior().

Parameters:

xmid (float) – \(\mu\).
xwid (float) – \(\sigma\).

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.jeff_prior(val, xmin, xmax)#: Jeffrey’s prior.

coPsi.priors.tgauss_prior(val, xmid, xwid, xmin, xmax)#

Truncated Gaussian prior.

\[f (x; \mu, \sigma, a, b) = \frac{1}{\sigma} \frac{g(x)}{\Phi(\frac{b-\mu}{\sigma}) - \Phi(\frac{a-\mu}{\sigma})} \, ,\]

where \(g(x)\) is the Gaussian from gauss_prior() and \(\Phi\) is the (Gauss) error function (scipy.special.erf ).

Parameters:

val (float) – \(x\).
xmid (float) – \(\mu\).
xwid (float) – \(\sigma\).
xmin (float) – \(a\).
xmax (float) – \(b\).

Returns:

\(f(x)\)

Return type:

float

coPsi.priors.tgauss_prior_dis(mu, sigma, xmin, xmax)#

Truncated Gaussian distribution.

See tgauss_prior().

Parameters:

xmid (float) – \(\mu\).
xwid (float) – \(\sigma\).
xmin (float) – \(a\).
xmax (float) – \(b\).

Returns:

\(f(x)\)

Return type:

float