DÉMONSTRATIONS AU PROGRAMME POUR LE BAC S
Yvan Monka – Académie de Strasbourg – www.maths-?et-?tiques.fr. 1. DÉMONSTRATIONS AU PROGRAMME POUR LE BAC S. SUITES. Propriété : Si q > 1 alors lim.
ROC : Restitution organisées des connaissances
Jun 21 2015 ROC : Restitution organisées des ... Bien lire les pré-requis dans les questions ROC
Toutes les questions de cours et R.O.C. au bac de T.S.
TOUTES LES R.O.C. DU BAC S. Exercice no 7. Restitution organisée de connaissances [Spécialité] (Amérique du Nord 27 mai 2011).
Démonstrations exigibles au bac
On a montré par récurrence que pour tout entier naturel n (1 + a)n ? 1 + na. http ://www.maths-france.fr. 1 c Jean-Louis Rouget
Optimal ROC Curves from Score Variable Threshold Tests
Dec 15 2020 variable are typically based on a mathematical model for the ... LRT's to generate ROC curves
trinROC: Statistical Tests for Assessing Trinormal ROC Data
Jun 29 2021 URL https://git.math.uzh.ch/reinhard.furrer/trinROC ... Class3
La courbe ROC (receiver operating characteristic) : principes et
de la courbe ROC et ses applications en biologie clinique. L'objectif étant d'effectuer une Chaque seuil possède des valeurs de sensibilité et de spé-.
Terminale S Les ROC danalyse à connaître. Vous trouverez ici les
Restitution Organisée de Connaissance (ROC d'analyse). Sujets de Bac. 2. ROC sur les fonctions : théorème des gendarmes. Définition : On dit que la fonction
ROC CURVE ESTIMATION: AN OVERVIEW
rsilva@math.tecnico.ulisboa.pt. Patricia de Zea Bermudez The Receiver Operating Characteristic (ROC) curve was developed by en-.
Sensitivity Specificity
Associated Confidence Interval
Oak Ridge Leadership Computing Facility – The OLCF was
Oak Ridge Leadership Computing Facility – The OLCF was
An introduction to ROC analysis - CCRMA
receiver operating characteristics (ROC) graph is atechnique for visualizing organizing and selecting classi?-ers based on their performance ROC graphs have longbeen used in signal detection theory to depict the tradeo?between hit rates and false alarm rates of classi?ers (Egan1975; Swets et al 2000)
Estimation receiver operating characteristic curve and ideal
We are proposing a general framework the estimationROC curve (EROC) for the evaluation of observers onmore general combined detection and estimation tasks We de?ne the EROC curve for the detection of a signaland the estimation of a set of signal parameters Thiscurve is a straightforward generalization of the LROCcurve
Chapter 0706 Integrating Discrete Functions - MATH FOR COLLEGE
Dec 23 2009 · 07 06 4 Chapter 07 06 and applying the trapezoidal rule over each of the above integrals gives
Which two points in ROC space have the same performance?
Two pointsin ROC space, (FP1,TP1) and (FP2,TP2), have the sameperformance if This equation de?nes the slope of an iso-performance line.All classi?ers corresponding to points on a line of slopemhave the same expected cost. Each set of class and cost dis-tributions de?nes a family of iso-performance lines.
How ROC analysis is used in med algorithm 4?
ROC analysis is commonly employed in med- Algorithm 4.TThreshold averaging of ROC curvesInputs: samples, the number of threshold samples;nrocs,the number of ROC curves to be sampled;ROCS[nrocs], anarray ofnrocsROC curves sorted by score;npts[m], thenumber of points in ROC curvem.
How to generate ROC points?
Algorithm 1.E?cient method for generating ROC pointsInputs: L, the set of test examples;f(i), the probabilisticclassi?ers estimate that exampleiis positive;PandN, thenumber of positive and negative examples. Fig. 6. The optimistic, pessimistic and expected ROC segments resultingfrom a sequence of 10 equally scored instances.
What is a ROC curve?
An ROC curve is a two-dimensional depiction of classi-?er performance. To compare classi?ers we may want toreduce ROC performance to a single scalar value represent-ing expected performance. A common method is to calcu-late the area under the ROC curve, abbreviated AUC (Bradley, 1997; Hanley and McNeil, 1982). Since the
07.06.1
Chapter 07.06
Integrating Discrete Functions
After reading this chapter, you should be able to: 1. integrate discrete functions by several methods, 2. derive the formula for trapezoidal rule with unequal segments, and 3. solve examples of finding integrals of discrete functions.What is integration?
Integration is the process of m
easuring the area under a function plotted on a graph. Why would we want to integrate a function? Among the most common examples are finding the velocity of a body from an acceleration function, and displacement of a body from a velocity function. Throughout many engineering fields, there are (what sometimes seems like) countless applications for integral calculus. You can read about a few of these applications in different engineering majors in Chapters 07.00A-07.00G. Sometimes, the function to be integrated is given at discrete data points, and the area under the curve is needed to be approximated. Here, we will discuss the integration of such discrete functions, b a dxxfI where )(xf is called the integrand and is given at discrete value of x, a lower limit of integration b upper limit of integration07.06.2 Chapter 07.06
Figure 1 Integration of a function
Integrating discrete functions
Multiple methods of integrating discrete functions are shown below using an example.Example 1
The upward velocity of a rocket is given as a function of tim e in Table 1.Table 1 Velocity as a function of time.
(s)t )m/s()(tv 0 010 227.04
15 362.78
20 517.35
22.5 602.97
30 901.67
Determine the distance,
,s covered by the rocket from 11t to 16t using the velocity data provided and use any applicable numerical technique.Solution
Method 1: Average Velocity Method
The velocity of the rocket is not provided at
11t and ,16t so we will have to use an
interval that includes16,11 to find the average velocity of the rocket within that range. In
this case, the interval20,10 will suffice.
04.227)10(v
78.362)15(v
35.517)20(v
Integrating Discrete Functions 07.06.3
3)20()15()10(vvvVelocityAverage
335.51778.36204.227
m/s06.369 Figure 1 Velocity vs. time data for the rocket example Using ,tvs we get m3.1845)1116)(06.369(sMethod 2: Trapezoidal Rule
If we were finding the distance traveled between times in the data table, we would simply find the area of the trapezoids with the corner points given as the velocity and time data points. For example 20 10 )(dttv 20 151510 )()(dttvdttv and applying the trapezoidal rule over each of the above integrals gives 20 10 )(dttv )]20()15([21520)]15()10([21015vvvv The values of )10(v, )15(v and )20(v are given in Table 1.
However, we are interested in finding
16 11 )(dttv 16 151511 )()(dttvdttv
07.06.4 Chapter 07.06
and applying the trapezoidal rule over each of the above integrals gives 16 11 )(dttv)]16()15([21516)]15()11([21115vvvv ))16(78.362(21516)78.362)11((21115vv How do we find )11(v and )16(v? We use linear interpolation. To find )11(v, ,10148.2704.227)(ttv 1510t1011148.2704.227)11(v
m/s19.254 and to find )16(v ,15913.3078.362)(ttv 2015t1516913.3078.362)16(v
m/s69.393 Then 16 11 )69.39378.362(21516)78.36219.254(21115 m2.1612 Method 3: Polynomial interpolation to find the velocity profile Because we are finding the area under the curve from ,20,10 we must use three points, ,10 t ,15t and ,20t to fit a quadratic polynomial through the data. Using polynomial interpolation, our resulting velocity function is (refer to notes on direct method of interpolation) .2010,3766.0733.1705.12 2 ttttv Now, we simply take the integral of the quadratic within our limits, giving us 16 11 23766.0733.1705.12dttts
16 113233766.0
2733.1705.12
ttt 3322111633766.011162733.17111605.12
m3.1604 Method 4: Spline interpolation to find the velocity profile Fitting quadratic splines (refer to notes on spline method of interpolation) through the data results in the following set of quadratics ,704.22)(ttv 100t,88.88928.48888.0 2 tt 1510t
Integrating Discrete Functions 07.06.5
,61.14166.351356.0 2 tt 2015t ,55.554956.336048.1 2 tt 5.2220t ,13.15286.2820889.0 2 tt 305.22tThe value of the integral would then simply be
16 151511 )()(dttvdttvs 16 15 2 15 11 2 16
1523151123
61.141266.35
31356.088.882928.4
38888.0
tttttt111588.8811152928.4111538888.0
2233151661.1411516266.35151631356.0
232233
m9.1595
Example 2
What is the absolute relative true error for each of the four methods used in Example 1 if the data in Table 1 was actually obtained from the velocity profile of tttv8.92100140000140000ln2000)(, where v is given in m/s and t in s.Solution
The distance covered between 11tand 16t is
16 118.92100140000140000ln2000dttts
m9.1604Method 1
The approximate value obtained using average velocity method was m3.1845. Hence, the absolute relative true error, t , is %1009.16043.18459.1604 t %976.14Method 2:
The approximate value obtained using the trapezoidal rule was m2.1612. Hence, the absolute relative true error, t , is07.06.6 Chapter 07.06
%1009.16042.16129.1604 t %451.0Method 3:
The approximate value obtained using the direct polynomial was 1604.3 m. Hence, the absolute relative true error, t , is %1009.16043.16049.1604 t %037.0Method 4:
The approximate value obtained using the spline interpolation was 1595.9 m, hence, the absolute relative true error, t , is %1009.16049.15959.1604 t %564.0 Table 2 Comparison of discrete function methods of numerical integrationMethod
Approximate
Value tAverage Velocity 1845.3 14.976%
Trapezoidal Rule 1612.2 0.451%
Polynomial Interpolation 1604.3 0.037%
Spline Interpolation 1595.9 0.564%
Trapezoidal Rule for Discrete Functions with Unequal Segments For a general case of a function given at ndata points 11 ,xfx,quotesdbs_dbs16.pdfusesText_22[PDF] rattrapage maths spécialité
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