class_docstr: Sampler for Bayesian regression with a spike-and-slab prior on weights.
  
  This implementation follows the sampler described in section 3.2
  of Scott and Varian, 2013 [1]. It differs from the SpikeSlabSampler in that
  it selects the submatrix of the design matrix that is active (given by the
  sparsity pattern of the coefficients), before computing a Cholesky
  decomposition. This may provide a speedup by performing a Cholesky on a (much)
  smaller matrix, at the cost of not being able to jit compile the program, or
  to batch (since each batch element may have a different sparsity pattern, so
  the dynamically sized matrices would all be different sizes).
  
  ### Model
  
  This sampler assumes the regression model
  
  ```
  y ~ Normal(loc=matvec(design_matrix,  # `X` in [1].
                        weights),       # `beta` in `[1]`.
             scale=observation_noise_scale)  # `sigma_epsilon` in [1].
  ```
  
  where the design matrix has shape `[num_outputs, num_features]`, with a
  conjugate InverseGamma prior on the noise variance (eqn (6) of [1]):
  
  ```
  observation_noise_scale**2 ~ InverseGamma(
    concentration=observation_noise_variance_prior_concentration,
    scale=observation_noise_variance_prior_scale)
  ```
  
  and a spike-and-slab prior on the weights (eqns (5) and (6) of [1]):
  
  ```
  slab_weights ~ MultivariateNormal(
     loc=0.,  # `b` from [1].
     precision=(weights_prior_precision  # `Omega^{-1}` from [1].
                / observation_noise_scale**2))
  nonzeros ~ Bernoulli(probs=nonzero_prior_prob)  # `gamma` from [1].
  weights = slab_weights * nonzeros
  ```
  
  ### Example
  
  Constructing a sampler instance specifies the model priors:
  
  ```python
  sampler = spike_and_slab.DynamicSpikeSlabSampler(
    design_matrix=design_matrix,
    observation_noise_variance_prior_concentration=1.,
    observation_noise_variance_prior_scale=1.
    nonzero_prior_prob=0.1)
  ```
  
  The sampler instance itself is stateless, though some internal methods take
  or accept `DynamicSpikeSlabSamplerState` tuples representing posterior
  quantities maintained within a sampling pass. The sampler is
  invoked by passing the regression targets (`y`) and the initial sparsity
  pattern (`nonzeros`):
  
  ```
  (observation_noise_variance,
   weights) = sampler.sample_noise_variance_and_weights(
     targets=y, initial_nonzeros=tf.ones([num_features], dtype=tf.bool))
  ```
  
  This implements the stochastic search variable selection (SSVS) algorithm [2],
  sweeping over the features in random order to resample their sparsity
  indicators one by one. It then returns a sample from the joint posterior
  on the regression weights and the observation noise variance, conditioned
  on the resampled sparsity pattern.
  
  #### References
  
  [1] Steven L. Scott and Hal Varian. Predicting the Present with Bayesian
      Structural Time Series. __International Journal of Mathematical Modelling
      and Numerical Optimisation 5.1-2 (2014): 4-23.__
      https://people.ischool.berkeley.edu/~hal/Papers/2013/pred-present-with-bsts.pdf
  
  [2] George, E. I. and McCulloch, R. E. Approaches for Bayesian variable
      selection. __Statistica Sinica 7, 339–374 (1997)__.
docstr: Builds the joint posterior for a sparsity pattern (eqn (7) from [1]).
code: def _get_conditional_posterior(self, sampler_state):
      """Builds the joint posterior for a sparsity pattern (eqn (7) from [1])."""
      indices = ps.where(sampler_state.nonzeros)[:, 0]
      conditional_posterior_precision_chol = tf.linalg.cholesky(
          tf.gather(
              tf.gather(
                  sampler_state.weights_posterior_precision, indices
              ),
              indices,
              axis=1,
          )
      )
      conditional_weights_mean = tf.linalg.cholesky_solve(
          conditional_posterior_precision_chol,
          tf.gather(sampler_state.x_transpose_y, indices)[
              ..., tf.newaxis
          ],
      )[..., 0]
  
      @joint_distribution_auto_batched.JointDistributionCoroutineAutoBatched
      def posterior_jd():
          observation_noise_variance = yield InverseGammaWithSampleUpperBound(
              concentration=(
                  self.observation_noise_variance_posterior_concentration
              ),
              scale=sampler_state.observation_noise_variance_posterior_scale,
              upper_bound=self.observation_noise_variance_upper_bound,
              name="observation_noise_variance",
          )
  
          yield MVNPrecisionFactorHardZeros(
              loc=conditional_weights_mean,
              # Note that the posterior precision varies inversely with the
              # noise variance: in worlds with high noise we're also
              # more uncertain about the values of the weights.
              # TODO(colcarroll): Tests pass even without a square root on the
              # observation_noise_variance. Should add a test that would fail.
              precision_factor=tf.linalg.LinearOperatorLowerTriangular(
                  conditional_posterior_precision_chol
                  / tf.sqrt(
                      observation_noise_variance[
                          ..., tf.newaxis, tf.newaxis
                      ]
                  )
              ),
              nonzeros=sampler_state.nonzeros,
              name="weights",
          )
  
      return posterior_jd
  
imports: import collections
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import bernoulli
  from tensorflow_probability.python.distributions import gamma
  from tensorflow_probability.python.distributions import inverse_gamma
  from tensorflow_probability.python.distributions import joint_distribution_auto_batched
  from tensorflow_probability.python.distributions import sample
  from tensorflow_probability.python.experimental.distributions.mvn_precision_factor_linop import MultivariateNormalPrecisionFactorLinearOperator
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import vectorization_util
  from tensorflow_probability.python.mcmc.internal import util
label_desc: Use image node_id 7 for calling the DynamicSpikeSlabSampler obj's underlying member method code with example usage: obj._get_conditional_posterior(sampler_state) and returns: posterior_jd