Unbiased Estimation Methods of Nonlinear Transport Models Based on Linearly Projected Data

2019 ◽  
Author(s):  
Wai Wong ◽  
S. C. Wong
Keyword(s):  
Estimation Methods ◽  
Unbiased Estimation ◽  
Nonlinear Transport ◽  
Transport Models

scholarly journals Biased and unbiased estimation of the average length of stay in intensive care units in the Covid-19 pandemic

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nathanael Lapidus ◽  
Xianlong Zhou ◽  
Fabrice Carrat ◽  
Bruno Riou ◽  
Yan Zhao ◽  
...  
Keyword(s):  
Intensive Care ◽  
Length Of Stay ◽  
Average Length ◽  
Parametric Method ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Bed Occupancy ◽  
Average Length Of Stay ◽  
Discharged Patients ◽  
First Admission

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).

scholarly journals Jaccard/Tanimoto similarity test and estimation methods for biological presence-absence data

2019 ◽  
Vol 20 (S15) ◽  
Author(s):  
Neo Christopher Chung ◽  
BłaŻej Miasojedow ◽  
Michał Startek ◽  
Anna Gambin
Keyword(s):  
Binary Data ◽  
Hypothesis Test ◽  
Similarity Coefficient ◽  
Statistical Hypothesis ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Tanimoto Coefficient ◽  
Tanimoto Similarity ◽  
Biological Studies ◽  
Wide Range

Abstract Background A survey of presences and absences of specific species across multiple biogeographic units (or bioregions) are used in a broad area of biological studies from ecology to microbiology. Using binary presence-absence data, we evaluate species co-occurrences that help elucidate relationships among organisms and environments. To summarize similarity between occurrences of species, we routinely use the Jaccard/Tanimoto coefficient, which is the ratio of their intersection to their union. It is natural, then, to identify statistically significant Jaccard/Tanimoto coefficients, which suggest non-random co-occurrences of species. However, statistical hypothesis testing using this similarity coefficient has been seldom used or studied. Results We introduce a hypothesis test for similarity for biological presence-absence data, using the Jaccard/Tanimoto coefficient. Several key improvements are presented including unbiased estimation of expectation and centered Jaccard/Tanimoto coefficients, that account for occurrence probabilities. The exact and asymptotic solutions are derived. To overcome a computational burden due to high-dimensionality, we propose the bootstrap and measurement concentration algorithms to efficiently estimate statistical significance of binary similarity. Comprehensive simulation studies demonstrate that our proposed methods produce accurate p-values and false discovery rates. The proposed estimation methods are orders of magnitude faster than the exact solution, particularly with an increasing dimensionality. We showcase their applications in evaluating co-occurrences of bird species in 28 islands of Vanuatu and fish species in 3347 freshwater habitats in France. The proposed methods are implemented in an open source R package called (https://cran.r-project.org/package=jaccard). Conclusion We introduce a suite of statistical methods for the Jaccard/Tanimoto similarity coefficient for binary data, that enable straightforward incorporation of probabilistic measures in analysis for species co-occurrences. Due to their generality, the proposed methods and implementations are applicable to a wide range of binary data arising from genomics, biochemistry, and other areas of science.

Lower Bound on the Accuracy of Parameter Estimation Methods for Linear Sensorimotor Synchronization Models

2015 ◽  
Vol 3 (1-2) ◽  
pp. 32-51 ◽  
Author(s):  
Nori Jacoby ◽  
Peter E. Keller ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Naftali Tishby
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Computational Models ◽  
Linear Models ◽  
Estimation Error ◽  
Explanatory Power ◽  
Estimation Method ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Unbiased Estimation

The mechanisms that support sensorimotor synchronization — that is, the temporal coordination of movement with an external rhythm — are often investigated using linear computational models. The main method used for estimating the parameters of this type of model was established in the seminal work of Vorberg and Schulze (2002), and is based on fitting the model to the observed auto-covariance function of asynchronies between movements and pacing events. Vorberg and Schulze also identified the problem of parameter interdependence, namely, that different sets of parameters might yield almost identical fits, and therefore the estimation method cannot determine the parameters uniquely. This problem results in a large estimation error and bias, thereby limiting the explanatory power of existing linear models of sensorimotor synchronization. We present a mathematical analysis of the parameter interdependence problem. By applying the Cramér–Rao lower bound, a general lower bound limiting the accuracy of any parameter estimation procedure, we prove that the mathematical structure of the linear models used in the literature determines that this problem cannot be resolved by any unbiased estimation method without adopting further assumptions. We then show that adding a simple and empirically justified constraint on the parameter space — assuming a relationship between the variances of the noise terms in the model — resolves the problem. In a follow-up paper in this volume, we present a novel estimation technique that uses this constraint in conjunction with matrix algebra to reliably estimate the parameters of almost all linear models used in the literature.

scholarly journals Biased and unbiased estimation of the average length of stay in intensive care units in the COVID-19 pandemic

2020 ◽  
Author(s):  
Nathanael Lapidus ◽  
Xianlong Zhou ◽  
Fabrice Carrat ◽  
Bruno Riou ◽  
Yan Zhao ◽  
...  
Keyword(s):  
Intensive Care ◽  
Length Of Stay ◽  
Average Length ◽  
Parametric Method ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Bed Occupancy ◽  
Average Length Of Stay ◽  
Discharged Patients ◽  
First Admission

BackgroundThe 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.MethodsTwo 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.FindingsLOS ≥ 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.InterpretationDischarges 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.FundingSupport 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).

scholarly journals The Estimation of Heritability of Weekly Body Weights in Japanese Quails with MINQUE(Minimum Quadratic Unbiased Estimation) Method

2016 ◽  
Vol 4 (1) ◽  
pp. 58
Author(s):  
Gökhan Tamer Kayaalp ◽  
Mikail Baylan ◽  
Sibel Canoğulları
Keyword(s):  
Variance Components ◽  
Estimation Method ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Coturnix Coturnix ◽  
Japanese Quails ◽  
Body Weights

In this study the heritability of body weights of Japanese quails (Coturnix coturnix Japanica) were estimated by using MINQUE (Minimum Quadratic Unbiased Estimation) methods. Firstly the variance components were estimated by using MINQUE method which were later estimated the heritability for weekly body weights. The estimation of heritability of body weights are following: for third week : 0.302±0.018; for fourth week: 0.70±0.15; for fifth week : 0.30±0.067

scholarly journals Linear Regression Estimation Methods for Inferring Standard Values of Snow Load in Small Sample Situations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xudong Wang ◽  
Jitao Yao
Keyword(s):  
Linear Regression ◽  
Coefficient Of Variation ◽  
Small Sample ◽  
Point Estimation ◽  
Estimation Methods ◽  
Small Samples ◽  
Unbiased Estimation ◽  
Regression Estimation ◽  
Snow Load ◽  
Standard Values

The aim of this paper is to establish a new method for inferring standard values of snow load in small sample situations. Due to the incomplete meteorological data in some areas, it is often necessary to infer the standard values of snow load in the conditions of small samples in engineering, but the point estimation methods of classical statistics adopted till now do not take into account the influences of statistical uncertainty, and the inference results are always aggressive. In order to overcome the above shortcomings, according to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distribution parameters and the tantile, using the least square method, the linear regression estimation methods for inferring standard values of snow load in small sample situations are proposed, which can take into account two cases such as parameter-free and known coefficient of variation, and the predicted formulas of snow load standard values are given, respectively. Through numerical integration and Monte Carlo numerical simulation, the numerical table of correlation coefficients is established, which is more convenient for the direct application of inferential formulas. According to the results of theoretical analysis and examples, when using the indirect point estimation methods to infer the standard values of snow load in the conditions of small samples, the inference results are always small. The linear regression estimation method is suitable for inferring standard values of snow load in the conditions of small samples, which can give more reasonable results. When using the linear regression estimation to infer standard values of snow load in practical application, even if the coefficient of variation is unknown, it can set the upper limit value of the coefficient of variation according to the experience; meanwhile, according to the parameter-free and known coefficient of variation, the estimation is carried out, respectively, and the smaller value of the two is taken as the final estimate. The method can be extended to the statistical inference of variable load standard values such as wind load and floor load.

scholarly journals Improved spatial soliton theory on the example of photorefractive gallium arsenide

2021 ◽  
Vol 127 (9) ◽  
Author(s):  
Marek Wichtowski ◽  
Andrzej Ziółkowski
Keyword(s):  
Spatial Soliton ◽  
Standard Theory ◽  
Nonlinear Transport ◽  
Transport Models ◽  
Soliton Theory ◽  
Dark Solitons ◽  
Material Equations ◽  
Standard Solution ◽  
Index Changes ◽  
Screening Solitons

AbstractThis article presents a critical look at the standard theory of bright and dark photorefractive screening solitons. We pay attention to the commonly overlooked fact of the inconsistency of the theory in the context of the accordance of soliton solution with the microscopic band transport models. Taking into account the material equations for the semi-insulating semiconductor (SI-GaAs) and including the nonlinear transport of hot electrons, a simple differential equation has been developed to determine the distribution of refractive index changes in the material for a localized optical beam. An amendment to the standard solution of (1 + 1)D solitons has been proposed, which particularly should be used for dark solitons to obtain the plausible self-consistent solutions

scholarly journals Estimation of density and distribution functions of a Burr X distribution

2018 ◽  
Vol 52 (1) ◽  
pp. 43-59
Author(s):  
AMULYA KUMAR MAHTO ◽  
YOGESH MANI TRIPATH ◽  
SANKU DEY
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Distribution Functions ◽  
Least Square ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Least Square Estimation ◽  
Data Set

Burr type X distribution is one of the members of the Burr family which was originally derived by Burr (1942) and can be used quite effectively in modelling strength data and also general lifetime data. In this article, we consider efficient estimation of the probability density function (PDF) and cumulative distribution function (CDF) of Burr X distribution. Eight different estimation methods namely maximum likelihood estimation, uniformly minimum variance unbiased estimation, least square estimation, weighted least square estimation, percentile estimation, maximum product estimation, Cremer-von-Mises estimation and Anderson-Darling estimation are considered. Analytic expressions for bias and mean squared error are derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.

scholarly journals A new biased estimation method based on Neumann series for solving ill-posed problems

2019 ◽  
Vol 16 (4) ◽  
pp. 172988141987205 ◽  
Author(s):  
QW Yang
Keyword(s):  
Estimation Method ◽  
Neumann Series ◽  
High Order ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Biased Estimation ◽  
Ridge Estimation ◽  
Rank Defect ◽  
Ill Posed ◽  
Neumann Series Expansion

The ill-posed least squares problems often arise in many engineering applications such as machine learning, intelligent navigation algorithms, surveying and mapping adjustment model, and linear regression model. A new biased estimation (BE) method based on Neumann series is proposed in this article to solve the ill-posed problems more effectively. Using Neumann series expansion, the unbiased estimate can be expressed as the sum of infinite items. When all the high-order items are omitted, the proposed method degenerates into the ridge estimation or generalized ridge estimation method, whereas a series of new biased estimates can be acquired by including some high-order items. Using the comparative analysis, the optimal biased estimate can be found out with less computation. The developed theory establishes the essential relationship between BE and unbiased estimation and can unify the existing unbiased and biased estimate formulas. Moreover, the proposed algorithm suits for not only ill-conditioned equations but also rank-defect equations. Numerical results show that the proposed BE method has improved accuracy over the existing robust estimation methods to a certain extent.

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