/draw-from-pyramid

Draw ages for existing population from a population pyramid

Primary LanguageJupyter NotebookMIT LicenseMIT

draw-from-pyramid

Draw ages for existing population from a population pyramid.

Context: I have an agent based model of disease transmission which is initialized with a number of living agents. I need to initialize these agents with age according to an existing population pyramid (potentially ignoring sex, potentially considering sex). We will use Vose's algorithm for aliasing to setup for efficient sampling from the population age distribution.

See pyramid_alias.py for the code.

See explore.ipynb for an example and the result of sampling from the distribution.

Note: this pseudo-code uses probabilities. The implementation in pyramid_alias.py depends on the integer counts in each bin (which, helpfully, avoids floating point accuracy issues).

Initialization:

  • Create arrays Alias and Prob, each of size n
  • Create two worklists, Small and Large
  • Multiply each probability by n
  • For each scaled probability pi
    • If pi < 1, add i to Small
    • Otherwise (pi ≥ 1), add i to Large
  • While Small is not empty:
    • Remove the first element from Small; call it l
    • Remove the first element from Large; call it g
    • Set Prob[l] = pl
    • Set Alias[l] = g
    • Set pg = pg − (1 − pl)
    • If pg < 1, add g to Small
    • Otherwise (pg ≥ 1), add g to Large
  • While Large is not empty:
    • Remove the first element from Large; call it g
    • Set Prob[g] = 1

Generation:

  • Generate a fair die roll from an n-sided die; call the side i
  • Flip a biased coin that comes up heads with probability Prob[i]
  • If the coin comes up "heads," return i
  • Otherwise, return Alias[i]

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