On the use of a Modified Latin Hypercube Sampling (MLHS) approach in the estimation of a Mixed Logit model for vehicle choice

Quasi-random number sequences have been used extensively for many years in the simulation of integrals that do not have a closed-form expression, such as Mixed Logit and Multinomial Probit choice probabilities. Halton sequences are one example of such quasi-random number sequences, and various types of Halton sequences, including standard, scrambled, and shuffled versions, have been proposed and tested in the context of travel demand modeling. In this paper, we propose an alternative to Halton sequences, based on an adapted version of Latin Hypercube Sampling. These alternative sequences, like scrambled and shuffled Halton sequences, avoid the undesirable correlation patterns that arise in standard Halton sequences. However, they are easier to create than scrambled or shuffled Halton sequences. They also provide more uniform coverage in each dimension than any of the Halton sequences. A detailed analysis, using a 16-dimensional Mixed Logit model for choice between alternative-fuelled vehicles in California, was conducted to compare the performance of the different types of draws. The analysis shows that, in this application, the Modified Latin Hypercube Sampling (MLHS) outperforms each type of Halton sequence. This greater accuracy combined with the greater simplicity make the MLHS method an appealing approach for simulation of travel demand models and simulation-based models in general

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.Comment: 41 pages, 19 figure

Corrections of the NIST Statistical Test Suite for Randomness

It is well known that the NIST statistical test suite was used for the evaluation of AES candidate algorithms. We have found that the test setting of Discrete Fourier Transform test and Lempel-Ziv test of this test suite are wrong. We give four corrections of mistakes in the test settings. This suggests that re-evaluation of the test results should be needed

Performance Estimates of the Pseudo-Random Method for Radar Detection

A performance of the pseudo-random method for the radar detection is analyzed. The radar sends a pseudo-random sequence of length $N$, and receives echo from $r$ targets. We assume the natural assumptions of uniformity on the channel and of the square root cancellation on the noise. Then for $r \leq N^{1-\delta}$, where $\delta > 0$, the following holds: (i) the probability of detection goes to one, and (ii) the expected number of false targets goes to zero, as $N$ goes to infinity.Comment: 5 pages, two figures, to appear in Proceedings of ISIT 2014 - IEEE International Symposium on Information Theory, Honolul