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Posterior Normal distribution with conjugate prior on the mean.
tfp.experimental.substrates.jax.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
and known variance
scale**2. The "known scale posterior" is
the distribution of the unknown
Accepts a prior Normal distribution object, having parameters
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
will broadcast in the case of multidimensional sets of parameters.
Normalobject of type
dtype: the prior distribution having parameters
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.
A new Normal posterior distribution object for the unknown observation
TypeError: if dtype of
sdoes not match
prioris not a Normal object.