- Libellé inconnu,
Séminaire MODAL'X : Nicolas Chopin (ENSAE/CREST)
Publié le 24 avril 2024
–
Mis à jour le 21 mai 2024
Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations (en collaboration avec Francesca R. Crucinio et Sumeetpal S. Singh)
Date(s)
le 23 mai 2024
13h30 - 14h30
Lieu(x)
Résumé :
Given a smooth function f, we develop a general approach to turn Monte
Carlo samples with expectation m into an unbiased estimate of f(m).
Specifically, we develop estimators that are based on randomly
truncating the Taylor series expansion of f and estimating the
coefficients of the truncated series. We derive their properties and
propose a strategy to set their tuning parameters -- which depend on m
-- automatically, with a view to make the whole approach simple to
use. We develop our methods for the specific functions f(x)=logx and
f(x)=1/x, as they arise in several statistical applications such as
maximum likelihood estimation of latent variable models and Bayesian
inference for un-normalised models. Detailed numerical studies are
performed for a range of applications to determine how competitive and
reliable the proposed approach is.
Article: https://arxiv.org/abs/2403.20313
Given a smooth function f, we develop a general approach to turn Monte
Carlo samples with expectation m into an unbiased estimate of f(m).
Specifically, we develop estimators that are based on randomly
truncating the Taylor series expansion of f and estimating the
coefficients of the truncated series. We derive their properties and
propose a strategy to set their tuning parameters -- which depend on m
-- automatically, with a view to make the whole approach simple to
use. We develop our methods for the specific functions f(x)=logx and
f(x)=1/x, as they arise in several statistical applications such as
maximum likelihood estimation of latent variable models and Bayesian
inference for un-normalised models. Detailed numerical studies are
performed for a range of applications to determine how competitive and
reliable the proposed approach is.
Article: https://arxiv.org/abs/2403.20313
Mis à jour le 21 mai 2024