tf.contrib.distributions.normal_conjugates_known_sigma_posterior(prior, sigma, s, n)

tf.contrib.distributions.normal_conjugates_known_sigma_posterior(prior, sigma, 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 mu (described by the Normal prior) and known variance sigma^2. The "known sigma posterior" is the distribution of the unknown mu.

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).

Returns a posterior (also Normal) distribution object, with parameters (mu', sigma'^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 sigma, 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 (mu0, sigma0).
  • 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.

Returns:

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

Raises:

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

Defined in tensorflow/contrib/distributions/python/ops/normal_conjugate_posteriors.py.