SampleType

SysVar SampleType

Determines the sampling method used to generate samples from probability distributions. Possible values are:

0 = Median Latin Hypercube

1 = Random Latin Hypercube

2 = Simple Monte Carlo

3 = biased Median Latin Hypercube (legacy)

4 = biased Random latin Hypercube (legacy)

5 = Sobel, limiting polynomial order as appropriate for sample size (Analytica 4.6 or higher)

6 = Sobel, allow use of high order polynomials (Analytica 4.6 or higher)

Latin Hypercube

Latin hypercube methods generate a sample of size N for a scalar uncertainty by selecting one sample from each [(i-1)/N,i/N]-fractile interval, i=1..N. For example, with a sample size of 5, Latin Hypercube would ensure that one point is in the 0 to 20th percentile range, another point between the 20th to 40th percentiles, one between the 40th to 60th percentiles, one between the 60th to 80th percentiles and in the 80th to 100th percentile range. This helps to ensure that the full range of values gets coverage an avoid random clumping that can occur with pure Monte Carlo. The points within the sample are randomly shuffled for each scalar uncertainty.

Median Latin Hypercube (MLH) selects the median percentile from each percentile range. This ensures maximal spreading of the sample points, but it also means that the set of samples is deterministic -- you'll always get the same points in the sample. The order of the points along the Run index is random, since the points are shuffled, so the sample itself (taking ordering into account) does indeed have a random component.

Random Latin Hypercube (RLH) selects the point in each percentile range at random.

Latin Hypercube methods ensure spreading of the sample points within each individual scalar dimension, but there is no coordination between separate scalar uncertainties. Hence, in a 2-D sample space, clumping and areas with minimal coverage are still possible. Latin Hypercube methods converge quadratically faster than pure Month Carlo for smooth (analytic) problems involving a single uncertainty. No theoretical guarantees exist when multiple scalar uncertainties are involved, but measurably better convergence is often observed in real-life models with as many as 40 scalar uncertainties (see Latin Hypercube vs. Monte Carlo sampling). With a large number of scalar uncertainties, convergence rates are not substantially better than Monte Carlo.

In non-smooth models, Latin Hypercube methods can on rare occasions produce artifacts that slow convergence to be worse that Monte Carlo. These situations are rare.

Monte Carlo

Pure Monte Carlo samples every point independently. It is a classical method in statistics, for which much is known. It lends itself to proof of many theoretical properties. Sampling error decreases as [math]\displaystyle{ 1/\sqrt{N} }[/math], so that to halve the sampling error, you need to quadruple the sample size.

Biased Latin Hypercube

Options 3 & 4 exist only to reproduce the same samples returned in Analytica 4.2 and earlier, but should not be used otherwise.

In these earlier versions of Analytica, there was a very small bias in the shuffling algorithm.