Logic tree sampling strategies

Stating from version 3.10, the OpenQuake engine suppports 4 different strategies for sampling the logic tree. They are called, respectively, early_weights, late_weights, early_latin, late_latin. Here we will discuss how they work.

First of all, we must point out that logic tree sampling is controlled by three parameters in the job.ini:

• number_of_logic_tree_samples (default 0, no sampling)
• sampling_method (default early_weights)
• random_seed (default 42)

When sampling is enabled number_of_logic_tree_samples is a positive number, equal to the number of branches to be randomly extracted from full logic tree of the calculation. The precise why the random extraction works depends on the sampling method.

early_weights

We this sampling method, the engine randomly choose branches depending on the weights in the logic tree; having done that, the hazard curve statistics (mean and quantiles) are computed with equal weights.

late_weights

We this sampling method, the engine randomly choose branches ignoring the weights in the logic tree; however, the hazard curve statistics are computed by taking into account the weights.

early_latin

We this sampling method, the engine randomly choose branches depending on the weights in the logic tree by using an hypercube latin sampling; having done that, the hazard curve statistics are computed with equal weights.

late_latin

We this sampling method, the engine randomly choose branches ignoring the weights in the logic tree, but still using an hypercube sampling; then, the hazard curve statistics are computed by taking into account the weights.

More precisely, the engine calls something like the function

``openquake.hazardlib.lt.random_sample(

branchsets, num_samples, seed, sampling_method)``

You are invited to play with it; in general the latin sampling produces samples much closer to the expected weights even with few samples. Here in an example with two branchsets with weights [.4, .6] and [.2, .3, .5] respectively.

>>> bsets = [[('X', .4), ('Y', .6)], [('A', .2), ('B', .3), ('C', .5)]]

With 100 samples one would expect to get the path XA 8 times, XB 12 times, XC 20 times, YA 12 times, YB 18 times, YC 30 times. Instead we get:

>>> paths = random_sample(bsets, 100, 42, 'early_weights')
>>> collections.Counter(paths)
Counter({'YC': 26, 'XC': 24, 'YB': 17, 'XA': 13, 'YA': 10, 'XB': 10})

>>> paths = random_sample(bsets, 100, 42, 'late_weights')
>>> collections.Counter(paths)
Counter({'XA': 20, 'YA': 18, 'XB': 17, 'XC': 15, 'YB': 15, 'YC': 15})

>>> paths = random_sample(bsets, 100, 42, 'early_latin')
>>> collections.Counter(paths)
Counter({'YC': 31, 'XC': 19, 'YB': 17, 'XB': 13, 'YA': 12, 'XA': 8})

>>> paths = random_sample(bsets, 100, 45, 'late_latin')
>>> collections.Counter(paths)
Counter({'YC': 18, 'XA': 18, 'XC': 16, 'YA': 16, 'XB': 16, 'YB': 16})