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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Optimal Confidence for Monte Carlo Integration of Smooth Functions

## Optimal Confidence for Monte Carlo Integration of Smooth FunctionsAdd to your list(s) Download to your calendar using vCal - Robert J. Kunsch (UniversitÃ¤t OsnabrÃ¼ck)
- Thursday 21 February 2019, 13:40-14:15
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation We study the complexity $n(\varepsilon,\delta)$ of approximating the integral of smooth functions at absolute precision $\varepsilon > 0$ with confidence level $1 – \delta \in (0,1)$ using function evaluations as information within randomized algorithms. Methods that achieve optimal rates in terms of the root mean square error (RMSE) are not always optimal in terms of error at confidence, usually we need some non-linearity in order to suppress outliers. Besides, there are numerical problems which can be solved in terms of error at confidence but no algorithm can guarantee a finite RMSE , see [1]. Hence, the new error criterion seems to be more general than the classical RMSE . The sharp order for multivariate functions from classical isotropic Sobolev spaces $W_p 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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