On nonnegative unbiased estimators
By Pierre E. Jacob, Alexandre Hoang Thiery. 2013
72 citations recorded by the source corpus.
We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm yielding almost surely nonnegative unbiased estimators of $f(\lambda)\in\mathbb{R}^+$. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow "exact inference" in intractable models, in the sense that integrals with respect to a target distribution can be estimated without any systematic error, even though the associated probability density function cannot be evaluated pointwise. We discuss the consequences of our results on the applicability of pseudo-marginal algorithms and thus on the possibility of exact inference in intractable models. We illustrate our study with particular choices of functions $f$ corresponding to known challenges in statistics, such as exact simulation of diffusions, inference in large datasets and doubly intractable distributions.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fe88ae72b0a9100137e8cebd77653f79609c09b7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Jianfeng Lu
- Deborshee Sen
- David B. Dunson
- Matthias Sachs
- Qiang Yang
- Yu Zhang
- Lawrence Carin
- Paul Fearnhead
In Statistics and Probability
- Jianfeng Lu
- Deborshee Sen
- David B. Dunson
- Matthias Sachs
- Daniel M. McNeish
- Christopher Nemeth
- Paul Fearnhead
- Lawrence Carin
Citations in the corpus
- Efficient posterior sampling for high-dimensional imbalanced logistic regression. (2019, background): “While the pseudo-marginal approach of [3] provides a potential solution, it is generally impossible to obtain the required unbiased estimators of likelihoods using sub-samples [19].”
- Posterior Computation with the Gibbs Zig-Zag Sampler (2020, background): “The pseudo-marginal approach of Andrieu and Roberts (2009) offers a potential solution, but it is generally impossible to obtain the required unbiased estimators of likelihoods using data sub-samples (Jacob and Thiery, 2015).”