A Cosine Distribution Sampler

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• Questions?
• Cosine Sampler
  • Requirements
    • x = sampleCosine()
    • p = cosinePDF( x )
  • Precompute samples
    • A cosine sampler becomes a struct that holds the precomputed samples and some other information
      
  • Computing product terms for normalization constant without loops
    

    if mod(a,2) == 1
        numeratorValues = 2 : 2 : a-1;
        denominatorValues = 3 : 2 : a;
    else
        numeratorValues = [ 3 : 2 : a-1, pi/4 ];
        denominatorValues = 4 : 2 : a;
    end
    
    n = prod( denominatorValues ) / prod( numeratorValues );

  • Rejection sampling
    

    for i = 1 : nSamples
        while samples(i) > coinFlip
            samples(i) = rand * pi/2
            p = ...
            coinFlip = rand * n

    • Or you can combine the loops:
      

      nSamples = 509;
      samples = zeros( 1, nSamples );
      i = 1;                              % Index of sample being generated
      
      while i <= nSamples                 % Rejection sample until list full
          
          x = rand * pi / 2;
          if rand < cos(x)^a
              samples(i) = x;
              i = i + 1;
          end
          
      end

  • Notice how sampleCosine uses the precomputed samples and the “next sample” value:
    

    x = sampler.samples( sampler.next );
    sampler.next = mod( sampler.next, sampler.maxSamples ) + 1;

• Next
  • Start working with my old code
  • Be sure you have a copy of it!

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