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tfp.experimental.mcmc.PotentialScaleReductionReducer

Reducer that computes a running R-hat diagnostic statistic.

Inherits From: Reducer

PotentialScaleReductionReducer assumes that all provided chain states include samples from multiple independent Markov chains, and that all of these chains are to be included in the same calculation. PotentialScaleReductionReducer also assumes that incoming samples have shape [Ci1, Ci2,...,CiD] + A. Dimensions 0 through D - 1 index the Ci1 x ... x CiD independent chains to be tested for convergence to the same target. The remaining dimensions, A, represent the event shape and hence, can have any shape (even empty, which implies scalar samples). The number of independent chain dimensions is defined by the independent_chain_ndims parameter at initialization.

As with all reducers, PotentialScaleReductionReducer does not hold state information; rather, it stores supplied metadata. Intermediate calculations are held in a state object, which is returned via initialize and one_step method calls.

PotentialScaleReductionReducer is meant to fit into the larger Streaming MCMC framework. RunningPotentialScaleReduction in tfp.experimental.stats is better suited for more generic streaming R-hat needs. More precise algorithmic details can also be found by referencing RunningPotentialScaleReduction.

independent_chain_ndims Integer type Tensor with value >= 1 giving the number of dimensions, from dim = 1 to dim = D, holding independent chain results to be tested for convergence.
name Python str name prefixed to Ops created by this function. Default value: None (i.e., 'potential_scale_reduction_reducer').

ValueError if independent_chain_ndims < 1. This results in undefined intermediate variance calculations.

independent_chain_ndims

name

parameters

Methods

finalize

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Finalizes R-hat calculation from the final_reducer_state.

Args
final_reducer_state PotentialScaleReductionReducerState that represents the final state of the running R-hat statistic.

Returns
rhat an estimate of the R-hat.

initialize

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Initializes an empty PotentialScaleReductionReducerState.

For calculation purposes, the initial_chain_state does not count as a sample. This is a deliberate decision that ensures consistency across sampling procedures (i.e. tfp.mcmc.sample_chain follows similar semantics).

Args
initial_chain_state A (possibly nested) structure of Tensors or Python lists of Tensors representing the current state(s) of the Markov chain(s). It is used to infer the shape and dtype of future samples.
initial_kernel_results A (possibly nested) structure of Tensors representing internal calculations made in a related TransitionKernel. For streaming R-hat, this argument has no influence on the computation; hence, it is None by default. However, it's still accepted to fit the Reducer base class.

Returns
state PotentialScaleReductionReducerState with rhat_state field representing a stream of no inputs.

one_step

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Update the current_reducer_state with a new chain state.

Args
new_chain_state A (possibly nested) structure of incoming chain state(s) with shape and dtype compatible with those used to initialize the current_reducer_state.
current_reducer_state PotentialScaleReductionReducerState representing the current state of the running R-hat statistic.
previous_kernel_results A (possibly nested) structure of Tensors representing internal calculations made in a related TransitionKernel. For streaming R-hat, this argument has no influence on computation; hence, it is None by default. However, it's still accepted to fit the Reducer base class.

Returns
new_reducer_state PotentialScaleReductionReducerState with updated running statistics.