SCORING

• Output from Monte Carlo code is value of integrals over distribution function f:
  
  
• Consider random walk of k steps, ionized at t_k: .
• Next collision probability (density) between t and
  in constant background volume V:
  
  
• scattering (all non-ionizing processes) rate,
• Then,
  
  
• probability for particle having collision for any ,

• Sample P(t) uniformly by choosing PRN , , setting:
  
  
• Length of track t determined by first of:
  • Particle leaves V,
  • Or have a collision.
• We assume suppressed absorption
  • Explicit collisions don't include ionization,
  • Ionize gradually along track better efficiency,
  • At end of step reduce statistical weight by ,
• Monte Carlo representation of desired integral: ,
  • probability of walk ,
  • Sampled uniformly in practice .
• is estimator of function g in V.