arXiv subjects

Daniele Imparato

Publications and source records attributed to Daniele Imparato.

3 recordsLinked to original sources

arXiv2012

Zero Variance Markov Chain Monte Carlo for Bayesian Estimators

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC estimator, based on the zero-variance principle introduced in the physics literature, is proposed. Conditions for asymptotic unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the idea is illustrated with real applications to probit, logit and GARCH Bayesian models. For all these models, a central limit theorem and unbiasedness for the zero-variance estimator are proved (see the supplementary material available on-line).

stat.CO↗

arXiv2007

A Robertson-type Uncertainty Principle and Quantum Fisher Information

Let $A_1,...,A_N$ be complex selfadjoint matrices and let $ρ$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_ρ(A_h,A_j)) \geq det (- \frac{i}{2} Tr (ρ[A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $<\cdot, \cdot >_{ρ,f}$ be the associated quantum Fisher information. In this paper we prove the inequality $$ det (Cov_ρ(A_h,A_j)) \geq det (\frac{f(0)}{2} < i[ρ, A_h],i[ρ,A_j] >_{ρ,f}) $$ that gives a non-trivial bound for any $N \in {\mathbb N}$ using the commutators $[ρ,A_h]$.

math-ph↗

arXiv2007

Inequalities for quantum Fisher information

In 2003 Luo proved an inequality relating the Wigner-Yanase information and the $SLD$-information. In this paper we prove that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.

math-ph↗