biogeme 2.4 [Mar 4 aoû 2015 12:14:44 EDT]

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

This file has automatically been generated on Tue Aug 4 21:59:02 2015

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Simulation report

Number of draws for Monte-Carlo: 500

Type of draws: HALTON

Aggregate values

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.

Savings

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: 500