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

Home page: http://biogeme.epfl.ch

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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 16:51:48 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: | 10normalMixtureControlVariate_halton_500.html |

Sample file: | __bin_swissmetro.dat |

Number of draws for Monte-Carlo: 500

Type of draws: HALTON

01 Simulated Integral | 02 Analytical Integral | 05 Error | |
---|---|---|---|

Total | 0.638158 | 0.63785 | 0.000308626 |

Average | 0.638158 | 0.63785 | 0.000308626 |

Non zeros | 1 | 1 | 1 |

Non zeros average | 0.638158 | 0.63785 | 0.000308626 |

Minimum | 0.638158 | 0.63785 | 0.000308626 |

Maximum | 0.638158 | 0.63785 | 0.000308626 |

Row | 01 Simulated Integral | 02 Analytical Integral | 05 Error |
---|---|---|---|

1 | 0.638158 | 0.63785 | 0.000308626 |

- 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 stdcv
^{2}/stdmv^{2}, 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**

Value without correction | Value with control variate correction | Relative error | Std. dev. without correction | Std. dev. with control variate correction | Reduced number of draws | Savings | Control variate simulated | Control variate analytical | Relative error on control variate |
---|---|---|---|---|---|---|---|---|---|

0.639579 | 0.638158 | 0.222586% | 0.00773232 | 0.00109022 | 9 | 98.012% | 0.0831563 | 0.0835167 | -0.431464% |

0.639579 | 0.638158 | 0.222586% | 0.00773232 | 0.00109022 | 9 | 98.012% | 0.0831563 | 0.0835167 | -0.431464% |