Unbiased estimation of the Hessian for iterative feedback tuning (IFT)

Author(s):  
G. Solari ◽  
M. Gevers
Author(s):  
H.J.G. Gundersen

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.


Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-15
Author(s):  
JEAN-MICHEL MARIN ◽  
THIERRY DHORNE

2021 ◽  
Vol 11 (12) ◽  
pp. 5723
Author(s):  
Chundong Xu ◽  
Qinglin Li ◽  
Dongwen Ying

In this paper, we develop a modified adaptive combination strategy for the distributed estimation problem over diffusion networks. We still consider the online adaptive combiners estimation problem from the perspective of minimum variance unbiased estimation. In contrast with the classic adaptive combination strategy which exploits orthogonal projection technology, we formulate a non-constrained mean-square deviation (MSD) cost function by introducing Lagrange multipliers. Based on the Karush–Kuhn–Tucker (KKT) conditions, we derive the fixed-point iteration scheme of adaptive combiners. Illustrative simulations validate the improved transient and steady-state performance of the diffusion least-mean-square LMS algorithm incorporated with the proposed adaptive combination strategy.


2021 ◽  
pp. 107754632199731
Author(s):  
He Zhu ◽  
Shuai He ◽  
Zhenbang Xu ◽  
XiaoMing Wang ◽  
Chao Qin ◽  
...  

In this article, a six-degree-of-freedom (6-DOF) micro-vibration platform (6-MVP) based on the Gough–Stewart configuration is designed to reproduce the 6-DOF micro-vibration that occurs at the installation surfaces of sensitive space-based instruments such as large space optical loads and laser communications equipment. The platform’s dynamic model is simplified because of the small displacement characteristics of micro-vibrations. By considering the multifrequency line spectrum characteristics of micro-vibrations and the parameter uncertainties, an iterative feedback control strategy based on a frequency response model is designed, and the effectiveness of the proposed control strategy is verified by performing integrated simulations. Finally, micro-vibration experiments are performed with a 10 kg load on the platform. The results of these micro-vibration experiments show that after several iterations, the amplitude control errors are less than 3% and the phase control errors are less than 1°. The control strategy presented in this article offers the advantages of a simple algorithm and high precision and it can also be used to control other similar micro-vibration platforms.


2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.


2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nathanael Lapidus ◽  
Xianlong Zhou ◽  
Fabrice Carrat ◽  
Bruno Riou ◽  
Yan Zhao ◽  
...  

Abstract Background The average length of stay (LOS) in the intensive care unit (ICU_ALOS) is a helpful parameter summarizing critical bed occupancy. During the outbreak of a novel virus, estimating early a reliable ICU_ALOS estimate of infected patients is critical to accurately parameterize models examining mitigation and preparedness scenarios. Methods Two estimation methods of ICU_ALOS were compared: the average LOS of already discharged patients at the date of estimation (DPE), and a standard parametric method used for analyzing time-to-event data which fits a given distribution to observed data and includes the censored stays of patients still treated in the ICU at the date of estimation (CPE). Methods were compared on a series of all COVID-19 consecutive cases (n = 59) admitted in an ICU devoted to such patients. At the last follow-up date, 99 days after the first admission, all patients but one had been discharged. A simulation study investigated the generalizability of the methods' patterns. CPE and DPE estimates were also compared to COVID-19 estimates reported to date. Results LOS ≥ 30 days concerned 14 out of the 59 patients (24%), including 8 of the 21 deaths observed. Two months after the first admission, 38 (64%) patients had been discharged, with corresponding DPE and CPE estimates of ICU_ALOS (95% CI) at 13.0 days (10.4–15.6) and 23.1 days (18.1–29.7), respectively. Series' true ICU_ALOS was greater than 21 days, well above reported estimates to date. Conclusions Discharges of short stays are more likely observed earlier during the course of an outbreak. Cautious unbiased ICU_ALOS estimates suggest parameterizing a higher burden of ICU bed occupancy than that adopted to date in COVID-19 forecasting models. Funding Support by the National Natural Science Foundation of China (81900097 to Dr. Zhou) and the Emergency Response Project of Hubei Science and Technology Department (2020FCA023 to Pr. Zhao).


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