writing if statement using probabilities

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Answer 1

[Kaushik Lakshminarasimhan]

Assuming you already have y, ymaybe, t and s:

if t > s 
   y = ymaybe; % ymaybe becomes the new y
else
   pr = exp(-s + t);
   my_randomnumber = rand;
   if my_randomnumber < pr
      y = ymaybe; % ymaybe becomes the new y with probability exp(-s+t)
   end
end

The first part (t>s) is obvious. The second part is slightly tricky: whenever you want an event to happen with probability p, you simply draw a random number from a uniform distribution between 0 and 1 using rand function. Since the CDF of a uniform distribution U[0,1] grows linearly with unit slope, this random number will be less than p with probability p. Since you want to switch ymaybe for y with probability p, all you need to do is assign y=ymaybe if this random number is less than p. This trick can be handy in many places, so make sure you understand why this works.

[Jessie Ray]

awesome, thank you!