tf.contrib.distributions.normal_conjugates_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
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
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
will broadcast in the case of multidimensional sets of parameters.
Normalobject of type
dtype: the prior distribution having parameters
sigma: tensor of type
dtype, taking values
sigma > 0. The known stddev parameter(s).
s: Tensor of type
dtype. The sum(s) of observations.
n: Tensor of type
int. The number(s) of observations.
A new Normal predictive distribution object.
TypeError: if dtype of
sdoes not match
prioris not a Normal object.