tf.contrib.distributions.normal_congugates_known_sigma_predictive(prior, sigma, s, n)
Posterior predictive Normal distribution w. conjugate prior on the mean.
This model assumes that n
observations (with sum s
) come from a Normal with unknown mean mu
(described by the Normal prior
) and known variance sigma^2
. The "known sigma predictive" is the distribution of new observations, conditioned on the existing observations and our prior.
Accepts a prior Normal distribution object, having parameters mu0
and sigma0
, as well as known sigma
values of the predictive distribution(s) (also assumed Normal), and statistical estimates s
(the sum(s) of the observations) and n
(the number(s) of observations).
Calculates the Normal distribution(s) p(x | sigma^2)
:
p(x | sigma^2) = int N(x | mu, sigma^2) N(mu | prior.mu, prior.sigma^2) dmu = N(x | prior.mu, 1/(sigma^2 + prior.sigma^2))
Returns the predictive posterior distribution object, with parameters (mu', sigma'^2)
, where:
sigma_n^2 = 1/(1/sigma0^2 + n/sigma^2), mu' = (mu0/sigma0^2 + s/sigma^2) * sigma_n^2. sigma'^2 = sigma_n^2 + sigma^2,
Distribution parameters from prior
, as well as sigma
, s
, and n
. will broadcast in the case of multidimensional sets of parameters.
Args:
-
prior
:Normal
object of typedtype
: the prior distribution having parameters(mu0, sigma0)
. -
sigma
: tensor of typedtype
, taking valuessigma > 0
. The known stddev parameter(s). -
s
: Tensor of typedtype
. The sum(s) of observations. -
n
: Tensor of typeint
. The number(s) of observations.
Returns:
A new Normal predictive distribution object.
Raises:
-
TypeError
: if dtype ofs
does not matchdtype
, orprior
is not a Normal object.
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