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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Measuring Sample Discrepancy with Diffusions

## Measuring Sample Discrepancy with DiffusionsAdd to your list(s) Download to your calendar using vCal - Andrew Duncan (University of Sussex; The Alan Turing Institute)
- Tuesday 18 July 2017, 15:40-16:20
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. SIN - Scalable inference; statistical, algorithmic, computational aspects 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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