tensorflow_probability/python/distributions/normal_conjugate_posteriors.py
def normal_conjugates_known_scale_posterior(prior, scale, s, n):
  """Posterior Normal distribution with conjugate prior on the mean.

  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.
  """
  if not isinstance(prior, normal.Normal):
    raise TypeError("Expected prior to be an instance of type Normal")

  if s.dtype != prior.dtype:
    raise TypeError(
        "Observation sum s.dtype does not match prior dtype: %s vs. %s"
        % (s.dtype, prior.dtype))

  n = tf.cast(n, prior.dtype)
  scale0_2 = tf.square(prior.scale)
  scale_2 = tf.square(scale)
  scalep_2 = 1.0/(1/scale0_2 + n/scale_2)
  return normal.Normal(
      loc=(prior.loc / scale0_2 + s / scale_2) * scalep_2,
      scale=tf.sqrt(scalep_2))
def normal_conjugates_known_scale_posterior(prior, scale, s, n):
  """Posterior Normal distribution with conjugate prior on the mean.

  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.
  """
  if not isinstance(prior, normal.Normal):
    raise TypeError("Expected prior to be an instance of type Normal")

  if s.dtype != prior.dtype:
    raise TypeError(
        "Observation sum s.dtype does not match prior dtype: %s vs. %s"
        % (s.dtype, prior.dtype))

  n = tf.cast(n, prior.dtype)
  scale0_2 = tf.square(prior.scale)
  scale_2 = tf.square(scale)
  scalep_2 = 1.0/(1/scale0_2 + n/scale_2)
  return normal.Normal(
      loc=(prior.loc / scale0_2 + s / scale_2) * scalep_2,
      scale=tf.sqrt(scalep_2))
Posterior Normal distribution with conjugate prior on the mean.

  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.