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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Unbiased approximations of products of expectations

## Unbiased approximations of products of expectationsAdd to your list(s) Download to your calendar using vCal - Anthony Lee (University of Warwick)
- Tuesday 04 July 2017, 09:45-10:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. SINW01 - Scalable statistical inference I will describe recent work with Simone Tiberi (Zurich) and Giacomo Zanella (Bocconi), on the unbiased approximation of a product of n expectations. Such products arise, e.g., as values of the likelihood function in latent variable models, and unbiased approximations can be used in a pseudo-marginal Markov chain to facilitate inference. A straightforward, standard approach consists of approximating each term using an independent average of M i.i.d. random variables and taking the product of these approximations. While simple, this typically requires M to be O(n) so that the total number of random variables required is N = Mn = O(n^2) in order to control the relative variance of the approximation. Using all N random variables to approximate each expectation is less wasteful when producing them is costly, but produces a biased approximation. We propose an alternative to these two approximations that uses most of the N samples to approximate each expectation in such a way that the estimate of the product of expectations is unbiased. We analyze the variance of this approximation and show that it can result in N = O(n) being sufficient for the relative variance to be controlled as n increases. In situations where the cost of simulations dominates overall computational time, and fixing the relative variance, the proposed approximation is almost n times faster than the standard approach to compute. 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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