fsu_quasi_mc
Design of Computer Experiments  QuasiMonte Carlo sampling
Topics
package_fsudace, design_and_analysis_of_computer_experiments
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
Sequence Type 
Generate samples from a Halton sequence 

Use Hammersley sequences 

Optional 
Adjust samples to improve the discrepancy of the marginal distributions 

Optional 
Calculate metrics to assess the quality of quasiMonte Carlo samples 

Optional 
Activates global sensitivity analysis based on decomposition of response variance into contributions from variables 

Optional 
Number of samples for samplingbased methods 

Optional 
Reuse the same sequence and samples for multiple sampling sets 

Optional 
Choose where to start sampling the sequence 

Optional 
Specify how often the sequence is sampled 

Optional 
The prime numbers used to generate the sequence 

Optional 
Number of iterations allowed for optimizers and adaptive UQ methods 

Optional 
Identifier for model block to be used by a method 
Description
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
orhammersley
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.
Theory
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 [Hal60], [HS64], and [KW97].