Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Design of Computer Experiments  QuasiMonte Carlo sampling
This keyword is related to the topics:
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required (Choose One)  sequence type (Group 1)  halton  Generate samples from a Halton sequence  
hammersley  Use Hammersley sequences  
Optional  latinize  Adjust samples to improve the discrepancy of the marginal distributions  
Optional  quality_metrics  Calculate metrics to assess the quality of quasiMonte Carlo samples  
Optional  variance_based_decomp  Activates global sensitivity analysis based on decomposition of response variance into contributions from variables  
Optional  samples  Number of samples for samplingbased methods  
Optional  fixed_sequence  Reuse the same sequence and samples for multiple sampling sets  
Optional  sequence_start  Choose where to start sampling the sequence  
Optional  sequence_leap  Specify how often the sequence is sampled  
Optional  prime_base  The prime numbers used to generate the sequence  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  model_pointer  Identifier for model block to be used by a method 
QuasiMonte Carlo methods produce low discrepancy sequences, especially if one is interested in the uniformity of projections of the point sets onto lower dimensional faces of the hypercube (usually 1D: how well do the marginal distributions approximate a uniform?)
This method generates sets of uniform random variables on the interval [0,1]. If the user specifies lower and upper bounds for a variable, the [0,1] samples are mapped to the [lower, upper] interval.
The user must first choose the sequence type:
halton
or hammersley
Then three keywords are used to define the sequence and how it is sampled:
prime_base
sequence_start
sequence_leap
Each of these has defaults, so specification is optional.
The quasiMonte Carlo sequences of Halton and Hammersley are deterministic sequences determined by a set of prime bases. Generally, we recommend that the user leave the default setting for the bases, which are the lowest primes. Thus, if one wants to generate a sample set for 3 random variables, the default bases used are 2, 3, and 5 in the Halton sequence. To give an example of how these sequences look, the Halton sequence in base 2 starts with points 0.5, 0.25, 0.75, 0.125, 0.625, etc. The first few points in a Halton base 3 sequence are 0.33333, 0.66667, 0.11111, 0.44444, 0.77777, etc. Notice that the Halton sequence tends to alternate back and forth, generating a point closer to zero then a point closer to one. An individual sequence is based on a radix inverse function defined on a prime base. The prime base determines how quickly the [0,1] interval is filled in. Generally, the lowest primes are recommended.
The Hammersley sequence is the same as the Halton sequence, except the values for the first random variable are equal to 1/N, where N is the number of samples. Thus, if one wants to generate a sample set of 100 samples for 3 random variables, the first random variable has values 1/100, 2/100, 3/100, etc. and the second and third variables are generated according to a Halton sequence with bases 2 and 3, respectively.
For more information about these sequences, see[43], [42], and [56].
These keywords may also be of interest: