mcmc_sample_halton_sequence: Returns a sample from the `dim` dimensional Halton sequence.

Description

Warning: The sequence elements take values only between 0 and 1. Care must be taken to appropriately transform the domain of a function if it differs from the unit cube before evaluating integrals using Halton samples. It is also important to remember that quasi-random numbers without randomization are not a replacement for pseudo-random numbers in every context. Quasi random numbers are completely deterministic and typically have significant negative autocorrelation unless randomization is used.

Usage

mcmc_sample_halton_sequence(
  dim,
  num_results = NULL,
  sequence_indices = NULL,
  dtype = tf$float32,
  randomized = TRUE,
  seed = NULL,
  name = NULL
)

Value

halton_elements Elements of the Halton sequence. Tensor of supplied dtype and shape

[num_results, dim] if num_results was specified or shape [s, dim] where s is the size of sequence_indices if sequence_indices

were specified.

Arguments

dim: Positive integer representing each sample's event_size. Must not be greater than 1000.
num_results: (Optional) Positive scalar Tensor of dtype int32. The number of samples to generate. Either this parameter or sequence_indices must be specified but not both. If this parameter is None, then the behaviour is determined by the sequence_indices. Default value: NULL.
sequence_indices: (Optional) Tensor of dtype int32 and rank 1. The elements of the sequence to compute specified by their position in the sequence. The entries index into the Halton sequence starting with 0 and hence, must be whole numbers. For example, sequence_indices=[0, 5, 6] will produce the first, sixth and seventh elements of the sequence. If this parameter is None, then the num_results parameter must be specified which gives the number of desired samples starting from the first sample. Default value: NULL.
dtype: (Optional) The dtype of the sample. One of: float16, float32 or float64. Default value: tf$float32.
randomized: (Optional) bool indicating whether to produce a randomized Halton sequence. If TRUE, applies the randomization described in Owen (2017). Default value: TRUE.
seed: (Optional) integer to seed the random number generator. Only used if randomized is TRUE. If not supplied and randomized is TRUE, no seed is set. Default value: NULL.
name: (Optional) string describing ops managed by this function. If not supplied the name of this function is used. Default value: "sample_halton_sequence".

Details

Computes the members of the low discrepancy Halton sequence in dimension dim. The dim-dimensional sequence takes values in the unit hypercube in dim dimensions. Currently, only dimensions up to 1000 are supported. The prime base for the k-th axes is the k-th prime starting from 2. For example, if dim = 3, then the bases will be [2, 3, 5] respectively and the first element of the non-randomized sequence will be: [0.5, 0.333, 0.2]. For a more complete description of the Halton sequences see here. For low discrepancy sequences and their applications see here.

If randomized is true, this function produces a scrambled version of the Halton sequence introduced by Owen (2017). For the advantages of randomization of low discrepancy sequences see here.

The number of samples produced is controlled by the num_results and sequence_indices parameters. The user must supply either num_results or sequence_indices but not both. The former is the number of samples to produce starting from the first element. If sequence_indices is given instead, the specified elements of the sequence are generated. For example, sequence_indices=tf$range(10) is equivalent to specifying n=10.

References