biogeme 2.6a [Mon Apr 17 15:33:55 CEST 2017]

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Michel Bierlaire, Transport and Mobility Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL)

This file has automatically been generated on Tue Apr 18 16:51:44 2017

If you drag this HTML file into the Calc application of OpenOffice, or the spreadsheet of LibreOffice, you will be able to perform additional calculations.

Report file: 03controlVariate_halton.html
Sample file: __bin_swissmetro.dat

Simulation report

Number of draws for Monte-Carlo: 20000

Type of draws: HALTON

Aggregate values

01_Simulated Integral02_Analytical Integral05_Error
Non zeros111
Non zeros average1.718281.71828-2.84647e-06

Detailed records

Row01_Simulated Integral02_Analytical Integral05_Error

Precision of Monte-Carlo simulation for integrals

Value without correction
Output of the Monte-Carlo simulation (vmc).
Value with control variate correction
Output of the Monte-Carlo simulation after the application of the control variate method (vcv). Value used by Biogeme.
Relative error
100 (vmc - vcv) / vcv
Std. dev. without correction
Calculated as the square root of the variance of the original draws, divided by the square root of the number of draws (stdmc).
Std. dev. with control variate correction
Calculated as the square root of the variance of the corrected draws, divided by the square root of the number of draws (stdcv).
Reduced number of draws
Rcv = R stdcv2/stdmv2, where R is the current number of draws. This is the number of draws that are sufficient (when the correction is applied) to achieve the same precision as the method without correction.
100 * (R-Rcv) / R
Control variate simulated
Value of the integral used for control variate using Monte-Carlo simulation (simulated).
Control variate analytical
Value of the analytical integral used for control variate (analytical).
Relative error on control variate
100 (simulated - analytical) / analytical. If this value is more than 1% (in absolute value), the row is displayed in red, emphasizing that either the number of draws for the original Monte-Carlo is insufficient, or the analytical value of the integral is wrong.

Number of draws: 20000

Value without correctionValue with control variate correctionRelative errorStd. dev. without correctionStd. dev. with control variate correctionReduced number of drawsSavingsControl variate simulatedControl variate analyticalRelative error on control variate