### `tf.contrib.distributions.gaussian_congugates_known_sigma_predictive(prior, sigma, s, n)` {#gaussian_congugates_known_sigma_predictive}

Posterior predictive Gaussian distribution w. conjugate prior on the mean.

This model assumes that `n` observations (with sum `s`) come from a
Gaussian with unknown mean `mu` (described by the Gaussian `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 Gaussian distribution object, having parameters
`mu0` and `sigma0`, as well as known `sigma` values of the predictive
distribution(s) (also assumed Gaussian),
and statistical estimates `s` (the sum(s) of the observations) and
`n` (the number(s) of observations).

Calculates the Gaussian 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:


*  <b>`prior`</b>: `Gaussian` object of type `dtype`:
    the prior distribution having parameters `(mu0, sigma0)`.
*  <b>`sigma`</b>: tensor of type `dtype`, taking values `sigma > 0`.
    The known stddev parameter(s).
*  <b>`s`</b>: Tensor of type `dtype`.  The sum(s) of observations.
*  <b>`n`</b>: Tensor of type `int`.  The number(s) of observations.

##### Returns:

  A new Gaussian predictive distribution object.

##### Raises:


*  <b>`TypeError`</b>: if dtype of `s` does not match `dtype`, or `prior` is not a
    Gaussian object.

