Useful and little-known applications of the Least Square Method and some consequences of covariances

Helene, O.; Mariano, Leandro; Guimarães-Filho, Z. O.

doi:10.1016/j.nima.2016.06.126

Cited by 8 publications

(5 citation statements)

References 17 publications

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“…The calculations of the effect size (dz) were performed by G*Power version 3.1.9.7 [30]. All the fitting procedures were carried out using the least square method [31], where the best fit parameters correspond to the minimum χ 2 , defined as:…”

Section: E Variables Statistical Analyses and Fitting Proceduresmentioning

confidence: 99%

“…The 95% confidence intervals of the fitted functions were assumed as ∼ 2σ f . In some model estimates, standard uncertainty propagation techniques were also applied [31].…”

Section: E Variables Statistical Analyses and Fitting Proceduresmentioning

confidence: 99%

“…The dasheddotted red and green lines represent, respectively, the upper and lower limits considering a 95% confidence interval (CI). The fitting was performed using the least square method [31] and the confidence intervals were obtained using uncertainty propagation techniques and the covariance matrix of the best-fit parameters, as similarly described elsewhere [32]. It is verified that < EM C > drops more significantly for 1 < N N S 5 and N N S 10.…”

Section: Average Minimum Sf Effectiveness Versus Nnsmentioning

confidence: 99%

See 2 more Smart Citations

Evaluating the root causes of fatigue and associated risk factors in the Brazilian regular aviation industry

Rodrigues¹,

Fischer²,

Helene³

et al. 2022

Preprint

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Section: E Variables Statistical Analyses and Fitting Proceduresmentioning

confidence: 99%

“…The 95% confidence intervals of the fitted functions were assumed as ∼ 2σ f . In some model estimates, standard uncertainty propagation techniques were also applied [31].…”

Section: E Variables Statistical Analyses and Fitting Proceduresmentioning

confidence: 99%

Section: Average Minimum Sf Effectiveness Versus Nnsmentioning

confidence: 99%

See 1 more Smart Citation

Evaluating the root causes of fatigue and associated risk factors in the Brazilian regular aviation industry

Rodrigues¹,

Fischer²,

Helene³

et al. 2022

Preprint

Self Cite

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“…Finally, there is a vast literature in statistics applied to physics on the problem of aggregating correlated measures of the same quantity to reduce the noise [13,15,25,26]. In particular, the method called BLUE is equivalent to the model-aware benchmark that we present in Section 3.2 [21,22].…”

Section: Introductionmentioning

confidence: 99%

Aggregating Correlated Estimations with (Almost) no Training

Delemazure,

Durand,

Mathieu

2023

Frontiers in Artificial Intelligence and Applications

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Many choice problems cannot be solved exactly and use several estimation algorithms that assign scores to the different available options. The estimation errors can have various correlations, from low (e.g. between two very different approaches) to high (e.g. when using a given algorithm with different hyperparameters). Most aggregation rules would suffer from this diversity of correlations. In this article, we introduce Embedded Voting (EV), an aggregation rule designed to take correlations into account, and we compare it to other aggregation rules in various experiments based on synthetic data. Our results show that when sufficient information about the correlations between errors is available, a maximum likelihood aggregation should be preferred. Otherwise, typically with limited training data, EV outperforms the other approaches.

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“…where k max = 1 for Mexico and Russia, 2 for Brazil, UK and India and 3 for USA. The propagation of the uncertainties of the best fit parameters to the reconstructed infection curve took into account the full co-variance matrix V b, as similarly described in [37], with the vector G ′ m being defined as:…”

mentioning

confidence: 99%

A Monte Carlo approach to model COVID-19 deaths and infections using Gompertz functions

Rodrigues,

Helene

2020

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This study provides a phenomenological method to describe the exponential growth, saturation and decay of coronavirus disease 2019 (COVID-19) deaths and infections via a Monte Carlo approach. The calculations connect Gompertz-type trial distributions of infected people per day with the distribution of deaths adopting two gamma distributions to account for the elapsed time that encompass the incubation and symptom onset to death periods. The analyses include death's data from United States of America (USA), Brazil, Mexico, United Kingdom (UK), India and Russia, which comprise the four countries with the highest number of deaths and the four countries with the highest number of confirmed cases, as of Aug 07, 2020, according to the World Health Organization webpage: https://covid19.who.int/table. The Gompertz functions were fitted to the data of weekly averaged confirmed deaths per day by mapping the χ 2 values. The uncertainties, variances and covariances of the model parameters were calculated by propagation, taking into account the standard deviations of the data for each epidemiological week. The fitted functions for the average deaths per day for USA and India have an upward trend, with the former having a higher growth rate and quite huge uncertainties. For Mexico, UK and Russia, the fits are consistent with a slope down pattern. For Brazil we found a subtle trend down, but with significant uncertainties. The USA, UK and India data shown a first peak with a higher growth rate when compared to the second one (typically 2.7 to 3.7 times higher), demonstrating the benefits of non-pharmaceutical interventions of sanitary measures and social distance flattening the curves of the pandemic. For the case of USA, however, a third peak seems quite plausible, most likely related with the recent relaxation policies. Brazil's data are satisfactorily described by two highly overlapped Gompertz functions with similar growth rates, suggesting a two-steps process for the pandemic spreading. For the case of Mexico and Russia single peaks with smoother slopes fitted the data satisfactorily. The 95% confidence intervals for the total number of deaths (×10 3 ) predicted by the model for Aug 31, 2020 are 160 to 220, 110 to 130, 59 to 62, 46.6 to 47.3, 54 to 63 and 16.0 to 16.7 for USA, Brazil, Mexico, UK, India and Russia, respectively. Our estimates for the prevalences of infections are in reasonable agreement with some preliminary reports from serological studies carried out in USA and Brazil. The prevalences and 95% confidence intervals for Aug 1, 2020 were estimated to be 8.

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Useful and little-known applications of the Least Square Method and some consequences of covariances

Cited by 8 publications

References 17 publications

Evaluating the root causes of fatigue and associated risk factors in the Brazilian regular aviation industry

Evaluating the root causes of fatigue and associated risk factors in the Brazilian regular aviation industry

Aggregating Correlated Estimations with (Almost) no Training

A Monte Carlo approach to model COVID-19 deaths and infections using Gompertz functions

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