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

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 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 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).

Calculates the Normal distribution(s) p(x | sigma^2):

  p(x | sigma^2) = int N(x | mu, sigma^2) N(mu |, prior.sigma^2) dmu
                 = N(x |, 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.


  • 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.


A new Normal predictive distribution object.


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

Defined in tensorflow/contrib/distributions/python/ops/