scholarly journals Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1900
Author(s):  
Leonid Hanin
Keyword(s):  
Statistical Analysis ◽  
Upper Bound ◽  
Unbiased Estimator ◽  
Probability Distributions ◽  
Heterogeneous Population ◽  
Prevalence Studies ◽  
Population Prevalence ◽  
Statistical Assumptions ◽  
Testing Data ◽  
Asymptotically Unbiased Estimator

I formulate three basic biomedical/statistical assumptions that should ideally guide well-designed population prevalence studies of the present or past disease including COVID-19. On the basis of these assumptions alone, I compute several probability distributions required for statistical analysis of testing data collected from a sample of individuals drawn from a heterogeneous population. I also construct a consistent asymptotically unbiased estimator of the population prevalence of the disease or infection from the collected data and derive a simple upper bound for its variance. All the results are rigorously proved and valid for any test for COVID-19 or other disease provided that the sum of the test’s sensitivity and specificity is larger than 1. A few recommendations for the design of COVID-19 prevalence studies informed by the results of this work are formulated. The methodology developed in this article may prove applicable to diseases and conditions other than COVID-19 as well as in some non-epidemiological settings.

scholarly journals The Mathematics of Testing with Application to Prevalence of COVID-19

2020 ◽  
Author(s):  
Leonid Hanin
Keyword(s):  
Statistical Analysis ◽  
Study Design ◽  
Disease Prevalence ◽  
Prevalence Study ◽  
Prevalence Studies ◽  
Basic Assumptions ◽  
Testing Data ◽  
Mathematical Formulas

AbstractWe formulate three basic assumptions that should ideally guide any well-designed COVID-19 prevalence study. We provide, on the basis of these assumptions alone, a full derivation of mathematical formulas required for statistical analysis of testing data. In particular, we express the disease prevalence in a population through those for its homogeneous subpopulations. Although some of these formulas are routinely employed in prevalence studies, the study design often contravenes the assumptions upon which these formulas vitally depend. We also designed a natural prevalence estimator from the testing data and studied some of its properties. The results are equally valid for diseases other than COVID-19 as well as in non-epidemiological settings.

scholarly journals Statistical Analysis and Machine Learning Prediction of Fog-Caused Low-Visibility Events at A-8 Motor-Road in Spain

Atmosphere ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 679
Author(s):  
Sara Cornejo-Bueno ◽  
David Casillas-Pérez ◽  
Laura Cornejo-Bueno ◽  
Mihaela I. Chidean ◽  
Antonio J. Caamaño ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Probability Distributions ◽  
Pearson Correlation ◽  
Likelihood Method ◽  
Neural Network Approach ◽  
Event Duration ◽  
Full Characterization ◽  
Low Visibility ◽  
Learning Machine ◽  
The Impact

This work presents a full statistical analysis and accurate prediction of low-visibility events due to fog, at the A-8 motor-road in Mondoñedo (Galicia, Spain). The present analysis covers two years of study, considering visibility time series and exogenous variables collected in the zone affected the most by extreme low-visibility events. This paper has then a two-fold objective: first, we carry out a statistical analysis for estimating the fittest probability distributions to the fog event duration, using the Maximum Likelihood method and an alternative method known as the L-moments method. This statistical study allows association of the low-visibility depth with the event duration, showing a clear relationship, which can be modeled with distributions for extremes such as Generalized Extreme Value and Generalized Pareto distributions. Second, we apply a neural network approach, trained by means of the ELM (Extreme Learning Machine) algorithm, to predict the occurrence of low-visibility events due to fog, from atmospheric predictive variables. This study provides a full characterization of fog events at this motor-road, in which orographic fog is predominant, causing important traffic problems during all year. We also show how the ELM approach is able to obtain highly accurate low-visibility events predictions, with a Pearson correlation coefficient of 0.8, within a half-hour time horizon, enough to initialize some protocols aiming at reducing the impact of these extreme events in the traffic of the A-8 motor road.

The ellipsoidal form of clasts with practical applications to fabric and size analyses of fluvial gravels

1980 ◽  
Vol 17 (12) ◽  
pp. 1725-1739 ◽  
Author(s):  
Emlyn H. Koster ◽  
Brian R. Rust ◽  
Don J. Gendzwill
Keyword(s):  
Statistical Analysis ◽  
Flow Direction ◽  
Probability Distributions ◽  
Size Analysis ◽  
Shape Variation ◽  
Practical Applications ◽  
Flow Interactions ◽  
Typical Range ◽  
Plane Area ◽  
Key Parameter

The widespread assumption that most water-worn gravel clasts approximate ellipsoids is confirmed by a statistical analysis of available data. The analysis demonstrates a Gaussian distribution of V/Ve ratios, centred on unit ratio, where V is clast volume and Ve the volume of a symmetric ellipsoid with equivalent triaxial dimensions. For internally isotropic and unbroken clasts, ellipsoidal form evolves as the rounding due to abrasion reaches its final stages. There appears to be no other major control on the tendency towards ellipsoidal geometry. The ellipsoidal tendency assists the interpretation of fluvial gravel deposits, which depends greatly on accurate description of clast size and fabric.Firstly, it facilitates calculation of Ap, the plane area projected upstream by clasts, a key parameter in bed–flow interactions such as preferred fabric. Formulae are derived to calculate Ap for ellipsoidal clasts with any configuration relative to flow direction. Viewing fabric in terms of the Ap variable supports and explains earlier conclusions concerning the controls on variability of imbrication angle.Secondly, an investigation of the relative merits of six size measures as descriptors of areal trends and predictors of nominal diameter, dn, concludes that (abc)1/3(the formula for dn of an ellipsoid) is superior. Other measures, namely, a, b, c, (a + c)/2, and (a + b + c)/3, are all subject to error in proportion to the degree of shape variation. Also, since downstream fining is typically accompanied by a changing proportion of oblate, bladed, prolate, and equant forms, dn is subject to inconsistent levels of under- or overestimation. The commonly used b dimension is endorsed as an acceptable predictor of dn, but a severely overestimates dn and should be abandoned. Information on errors in size analysis is presented as nomograms in the form of contoured c/b versus b/a plots and as probability distributions based on the typical range of shape variation in fluvial gravel.

CP VIOLATION IN THE B SYSTEM—A STATISTICAL ANALYSIS

1990 ◽  
Vol 05 (05) ◽  
pp. 337-347
Author(s):  
DAVID LONDON
Keyword(s):  
Statistical Analysis ◽  
Cp Violation ◽  
Standard Model ◽  
Probability Distributions ◽  
New Physics ◽  
Hadronic Decay ◽  
System A ◽  
The Standard Model ◽  
Model Predictions ◽  
Cp Asymmetries

The standard model predictions for CP violating hadronic decay asymmetries are presented in the form of probability distributions. From these distributions, it can be easily seen what the most likely values of these quantities are, which measurements would clearly be signs of new physics, and which values of the CP asymmetries would most constrain the parameters of the standard model.

Probability distributions for the strength of fibrous materials under local load sharing I: Two-level failure and edge effects

1982 ◽  
Vol 14 (01) ◽  
pp. 68-94 ◽  
Author(s):  
D. Gary Harlow ◽  
S. Leigh Phoenix
Keyword(s):  
Edge Effects ◽  
Upper Bound ◽  
Fiber Strength ◽  
Probability Distributions ◽  
Probability Model ◽  
Load Sharing ◽  
Local Load ◽  
Material Strength ◽  
Fibrous Materials ◽  
Fiber Element

The focus of this paper is on obtaining a conservative but tight bound on the probability distribution for the strength of a fibrous material. The model is the chain-of-bundles probability model, and local load sharing is assumed for the fiber elements in each bundle. The bound is based upon the occurrence of two or more adjacent broken fiber elements in a bundle. This event is necessary but not sufficient for failure of the material. The bound is far superior to a simple weakest link bound based upon the failure of the weakest fiber element. For large materials, the upper bound is a Weibull distribution, which is consistent with experimental observations. The upper bound is always conservative, but its tightness depends upon the variability in fiber element strength and the volume of the material. In cases where the volume of material and the variability in fiber strength are both small, the bound is believed to be virtually the same as the true distribution function for material strength. Regarding edge effects on composite strength, only when the number of fibers is very small is a correction necessary to reflect the load-sharing irregularities at the edges of the bundle.

scholarly journals Effect of sodium metabisulfite gel on the bond strength of dentin of bleached teeth

2018 ◽  
Vol 12 (02) ◽  
pp. 163-170
Author(s):  
Henrique Heringer Vieira ◽  
Josè Carlos Toledo ◽  
Anderson Catelan ◽  
Thayla Hellen Nunes Gouveia ◽  
Flávio Henrique Baggio Aguiar ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Data Analysis ◽  
Statistical Analysis ◽  
Bond Strength ◽  
Deleterious Effect ◽  
Statistical Difference ◽  
Dental Composites ◽  
Sodium Metabisulfite ◽  
Application Time ◽  
Testing Data

ABSTRACT Objective: This study aimed to evaluate the effect of the application of sodium metabisulfite (SMB) on the bond strength of bleached teeth. Materials and Methods: The study was divided into two parts. The first part evaluated the application of various concentrations of SMB for 1 h prior to the completion of bonding procedures. Fifty blocks were divided into five groups (n = 10): control; bleaching with 35% hydrogen peroxide (HP); HP + 5% SMB; HP + 12.5% SMB; and HP + 25% SMB. The second part evaluated the application of 25% gel SMB to either enamel or dentin, including the application time. Sixty blocks were divided into six groups (n = 10): control; bleaching with 35% HP; HP + 25% SMB for 1 h in enamel; HP + 25% SMB for 1 h in dentin; HP + 25% SMB for 10 min in enamel; and HP + 25% SMB for 10 min in dentin. Statistical Analysis: Following the completion of microshear bond testing, data were analyzed using one-way analysis of variance as well as Tukey's and Dunnett's tests. Results: In part 1, data analysis revealed statistical differences (P < 0.0001) between HP and HP + 5% SMB. No statistical differences were found between the control and both HP + 12.5% SMB and HP + 25% SMB. Part 2 revealed a statistical difference (P = 0.001359) only between the bleached group and others. Conclusions: The use of 25% SMB gel immediately after bleaching was able to reverse the deleterious effect of bleaching on the bond strength of dental composites to dentin.

BOUNDS ON EXTROPY WITH VARIATIONAL DISTANCE CONSTRAINT

2018 ◽  
Vol 33 (2) ◽  
pp. 186-204 ◽  
Author(s):  
Jianping Yang ◽  
Wanwan Xia ◽  
Taizhong Hu
Keyword(s):  
Probability Distribution ◽  
Confidence Interval ◽  
Upper Bound ◽  
Probability Distributions ◽  
Analytic Formula ◽  
Distance Constraint ◽  
Variation Distance ◽  
The Difference ◽  
Variational Distance

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].

scholarly journals Statistical deprojection of galaxy pairs

2018 ◽  
Vol 614 ◽  
pp. A45 ◽  
Author(s):  
Laurent Nottale ◽  
Pierre Chamaraux
Keyword(s):  
Statistical Analysis ◽  
Probability Distribution ◽  
Physical Properties ◽  
Previous Analysis ◽  
Probability Distributions ◽  
Second Step ◽  
Line Of Sight ◽  
Mass Determination ◽  
Dynamical Parameters

Aims. The purpose of the present paper is to provide methods of statistical analysis of the physical properties of galaxy pairs. We perform this study to apply it later to catalogs of isolated pairs of galaxies, especially two new catalogs we recently constructed that contain ≈1000 and ≈13 000 pairs, respectively. We are particularly interested by the dynamics of those pairs, including the determination of their masses. Methods. We could not compute the dynamical parameters directly since the necessary data are incomplete. Indeed, we only have at our disposal one component of the intervelocity between the members, namely along the line of sight, and two components of their interdistance, i.e., the projection on the sky-plane. Moreover, we know only one point of each galaxy orbit. Hence we need statistical methods to find the probability distribution of 3D interdistances and 3D intervelocities from their projections; we designed those methods under the term deprojection. Results. We proceed in two steps to determine and use the deprojection methods. First we derive the probability distributions expected for the various relevant projected quantities, namely intervelocity vz, interdistance rp, their ratio, and the product $r_p v_z^2$, which is involved in mass determination. In a second step, we propose various methods of deprojection of those parameters based on the previous analysis. We start from a histogram of the projected data and we apply inversion formulae to obtain the deprojected distributions; lastly, we test the methods by numerical simulations, which also allow us to determine the uncertainties involved.

Sign in / Sign up

Export Citation Format

Share Document