A Concrete Example

Let me show how this might actually function in practice, from start to finish. We'll be approxiating the same distribution PP from above. We'll assume that, a priori, I know that the distribution ranges from roughly -5 to 5, with most of the values closer to 0. (Remember, in the real world I can't look at the graph to find these values, because I don't have access to the distribution!)

  • I'll use Q(x)=N(μ=x,σ=2)Q(x) = N(\mu = x, \sigma = 2), what I used in the interactive demo above.
  • I'll generate samples from 10 different starting points. The starting points will be chosen randomly from the interval [−1,1)[-1, 1).
  • I'll generate 1100 samples in each chain and discard the first 100. This gives me 10,000 total points at the end, which should be a pretty good approximation of PP.

A Concrete Example

Let me show how this might actually function in practice, from start to finish. We'll be approxiating the same distribution PP from above. We'll assume that, a priori, I know that the distribution ranges from roughly -5 to 5, with most of the values closer to 0. (Remember, in the real world I can't look at the graph to find these values, because I don't have access to the distribution!)

  • I'll use Q(x)=N(μ=x,σ=2)Q(x) = N(\mu = x, \sigma = 2), what I used in the interactive demo above.
  • I'll generate samples from 10 different starting points. The starting points will be chosen randomly from the interval [−1,1)[-1, 1).
  • I'll generate 1100 samples in each chain and discard the first 100. This gives me 10,000 total points at the end, which should be a pretty good approximation of PP.