Presented by:
Andrew Duncan
Date:
Tuesday 18th July 2017 - 15:40 to 16:20
Venue:
INI Seminar Room 1
Abstract:
In many applications one
often wishes to quantify the discrepancy between a sample and a target
probability distribution. This has become particularly relevant for
Markov Chain Monte Carlo methods, where practitioners are now turning to biased
methods which trade off asymptotic exactness for computational speed.
While a reduction in variance due to more rapid sampling can outweigh the
bias introduced, the inexactness creates new challenges for parameter
selection. The natural metric in which to quantify this discrepancy is
the Wasserstein or Kantorovich metric. However, the computational
difficulties in computing this quantity has typically dissuaded practitioners.
To address this, we introduce a new computable quality
measure based on Stein's method that quantifies the maximum discrepancy between
sample and target expectations over a large class of test functions. We
demonstrate this tool by comparing exact, biased, and deterministic sample
sequences and illustrate applications to hyperparameter selection, convergence
rate assessment, and quantifying bias-variance tradeoffs in posterior
inference.
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