A Tighter Bayesian CramÉR-rao Bound

Bacharach, Lucien; Fritsche, Carsten; Orguner, Umut; Chaumette, Éric

doi:10.1109/icassp.2019.8683614

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…In this section, we provide simulation results that illustrate the theoretical ones from the previous sections. these results appeared in [22], and are given here for sake of completeness.…”

Section: E Numerical Resultsmentioning

confidence: 80%

“…The main contributions of the present paper with respect to previous work [21], [22] are threefold. First, we introduce a more general proof of the covariance inequality leading to the tighter form of BLBs, that encompass the case of vector parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

“…However, this study was limited to the case of scalar parameter estimation. The precision gain of the tighter BLBs had not been assessed until our recent conference paper [22], which focused on the case of the BCRB and showed promising results: the tighter BCRB (TBCRB) was shown to be asymptotically tight by simulation, but this was not formally proved.…”

Section: Introductionmentioning

confidence: 99%

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Some Results on Tighter Bayesian Lower Bounds on the Mean-Square Error

Bacharach,

Fritsche,

Orguner

et al. 2019

Preprint

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In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we study alternative forms of BLBs obtained from a covariance inequality, where the inner product is based on the a posteriori instead of the joint probability density function. We hence obtain a family of BLBs, which is shown to form a counterpart at least as tight as the well-known Weiss-Weinstein family of BLBs, and we extend it to the general case of vector parameter estimation. Conditions for equality between these two families are provided. Focusing on the Bayesian Cramér-Rao bound (BCRB), a definition of efficiency is proposed relatively to its tighter form, and efficient estimators are described for various types of common estimation problems, e.g., scalar, exponential family model parameter estimation. Finally, an example is provided, for which the classical BCRB is known to not be tight, while we show its tighter form is, based on formal proofs of asymptotic efficiency of Bayesian estimators. This analysis is finally corroborated by numerical results.

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Section: E Numerical Resultsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some Results on Tighter Bayesian Lower Bounds on the Mean-Square Error

Bacharach,

Fritsche,

Orguner

et al. 2019

Preprint

Self Cite

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show abstract

“…Evaluating the TBCRB is in general no less demanding than computing the EMSD, and our reason for starting with the TBCRB is that it comes with a condition for when it is tight. Often it is more convenient to consider the Bayesian Cramér-Rao bound (BCRB), which is obtained via an application of Jensen's inequality [26,45]…”

Section: G Bayesian Cramér-rao Boundsmentioning

confidence: 99%

Bayesian quantum thermometry based on thermodynamic length

Jørgensen,

Kołodyński,

Mehboudi

et al. 2021

Preprint

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In this work, we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a well-defined measure of estimation precision becomes non-trivial, and furthermore the construction of a suitable criterion for optimal measurement design must be re-examined to account for the prior uncertainty. We propose a fully Bayesian approach to temperature estimation based on the concept of thermodynamic length, which solves both these problems. As an illustration of this framework, we consider thermal spin-1/2 particles and investigate the fundamental difference between two cases; on the one hand, when the spins are probing the temperature of a heat reservoir and, on the other, when the spins themselves constitute the sample.

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“…Needless to say, the VTSB is not the unique Bayesian lower bound of interest. Research concerning alternative, and possibly tighter, bounds is also active [122]. A compilation of several works concerned with Bayesian bounds can be found in Ref.…”

Section: Bayesian Estimatorsmentioning

confidence: 99%

Estimação Bayesiana para termometria colisional e computação quântica não-holonômica em tempo ótimo

Alves

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A Tighter Bayesian CramÉR-rao Bound

Cited by 7 publications

References 27 publications

Some Results on Tighter Bayesian Lower Bounds on the Mean-Square Error

Some Results on Tighter Bayesian Lower Bounds on the Mean-Square Error

Bayesian quantum thermometry based on thermodynamic length

Estimação Bayesiana para termometria colisional e computação quântica não-holonômica em tempo ótimo

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