Test for estimator_quantile_B
Estimation of a large quantile
Authors
- Implementation: Teddy Furon
- Science: Arnaud Guyader, Nicolas Hengartner, Eric Matzner-Lober
Contact: teddy.furon@inria.fr
Copyright INRIA 2010-2011
Licence This software and its subprograms are governed by the CeCILL license under French law and abiding by the rules of distribution of free software. See http://www.cecill.info/licences.en.html
Contents
Example
What is the quantile q such that
- x a white gaussian noise in R^20
- lies in the hypercone of axis (1,0,...,0) and angle acos(q)
- with a probability of 4.70*10^-11
Data
dim = 20; Proba = 4.7*10^-11; n = 200; % Total number of particles % real value for this problem q_true = 0.95;
Estimation
[q_est, Stat, Intern] = estimator_quantile_B(Proba,dim,'n',n,'N_sample',200);
List of all arguments of estimator_quantile_B: a: 0.9500 alpha: 0.9500 dim: 20 GENERATE: @GENERATE_INTERNAL max_iter: 40000 minheap: 0 MODIFY: @MODIFY_INTERNAL mu: 2 mu_decay: 0.0500 n: 200 N_sample: 200 P: 4.7000e-11 rate: 0.1000 SCORE: @SCORE_INTERNAL t: 10 verbose: 1 Iteration Threshold Prob mu Trials 1 5.85e-04 1.00e+00 2.00e+00 2.00e+02 200 2.01e-01 3.69e-01 2.00e+00 2.19e+03 400 3.33e-01 1.35e-01 2.00e+00 4.19e+03 600 4.41e-01 4.97e-02 2.00e+00 6.19e+03 800 5.07e-01 1.82e-02 1.71e+00 8.19e+03 1000 5.73e-01 6.69e-03 1.20e+00 1.02e+04 1200 6.31e-01 2.45e-03 1.03e+00 1.22e+04 1400 6.71e-01 9.01e-04 8.36e-01 1.42e+04 1600 7.08e-01 3.30e-04 7.94e-01 1.62e+04 1800 7.40e-01 1.21e-04 6.81e-01 1.82e+04 2000 7.70e-01 4.45e-05 6.47e-01 2.02e+04 2200 8.00e-01 1.63e-05 5.55e-01 2.22e+04 2400 8.24e-01 5.99e-06 5.01e-01 2.42e+04 2600 8.41e-01 2.20e-06 4.52e-01 2.62e+04 2800 8.57e-01 8.07e-07 4.08e-01 2.82e+04 3000 8.73e-01 2.96e-07 4.08e-01 3.02e+04 3200 8.86e-01 1.09e-07 3.87e-01 3.22e+04 3400 8.99e-01 3.99e-08 3.32e-01 3.42e+04 3600 9.09e-01 1.46e-08 3.32e-01 3.62e+04 3800 9.19e-01 5.37e-09 2.85e-01 3.82e+04 4000 9.28e-01 1.97e-09 2.57e-01 4.02e+04 4200 9.35e-01 7.23e-10 2.57e-01 4.22e+04 4400 9.42e-01 2.65e-10 2.44e-01 4.42e+04 4600 9.48e-01 9.74e-11 2.20e-01 4.62e+04 4800 9.53e-01 3.57e-11 2.20e-01 4.82e+04
Display
Print the true probability
fprintf('\nTrue quantile \t %6.2e\n\n',q_true);
True quantile 9.50e-01
Print the estimation and its confidence interval. This interval only in the asymptotic regime
fprintf('Lower bnd\t\tEstimate\t\tUpper bnd\n'); fprintf('%6.2e\t\t%6.2e\t\t%6.2e\n',Stat.interval(1),q_est,Stat.interval(2));
Lower bnd Estimate Upper bnd 9.48e-01 9.51e-01 9.55e-01
Show the last intermediate thresholds and estimated probability.
figure; semilogx([Intern(end-10:end-1,3);Proba],[Intern(end-10:end-1,2);q_est],'-+'); hold on semilogx(Proba*[1,1],[Stat.interval(1),Stat.interval(2)],'o-r'); semilogy(Proba,q_true,'^g') legend('Estimate','Confidence','True') grid on; %v = axis; v(2) =v(2)+0.01; %axis(v); hold off title('Test Estimator B') xlabel('Probability'); ylabel('Estimated quantile');
