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# tf.contrib.distributions.normal_conjugates_known_scale_posterior

Posterior Normal distribution with conjugate prior on the mean.

``````tf.contrib.distributions.normal_conjugates_known_scale_posterior(
prior,
scale,
s,
n
)
``````

This model assumes that `n` observations (with sum `s`) come from a Normal with unknown mean `loc` (described by the Normal `prior`) and known variance `scale**2`. The "known scale posterior" is the distribution of the unknown `loc`.

Accepts a prior Normal distribution object, having parameters `loc0` and `scale0`, as well as known `scale` 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).

Returns a posterior (also Normal) distribution object, with parameters `(loc', scale'**2)`, where:

``````mu ~ N(mu', sigma'**2)
sigma'**2 = 1/(1/sigma0**2 + n/sigma**2),
mu' = (mu0/sigma0**2 + s/sigma**2) * sigma'**2.
``````

Distribution parameters from `prior`, as well as `scale`, `s`, and `n`. will broadcast in the case of multidimensional sets of parameters.

#### Args:

• `prior`: `Normal` object of type `dtype`: the prior distribution having parameters `(loc0, scale0)`.
• `scale`: tensor of type `dtype`, taking values `scale > 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.

#### Returns:

A new Normal posterior distribution object for the unknown observation mean `loc`.

#### Raises:

• `TypeError`: if dtype of `s` does not match `dtype`, or `prior` is not a Normal object.