## Population Monte Carlo Sampling

Practical and theoretical implementation discussion.
Zelcious
Posts: 42
Joined: Mon Jul 23, 2012 11:05 am

### Re: Population Monte Carlo Sampling

My plan is to use global importance maps to seed a MCMC algorithm. That way I can use the efficiency of those importance maps and hopefully in most cases spread the energy of the high contribution paths (generated from paths with low probability), especially if I give them extra high importance.

friedlinguini
Posts: 89
Joined: Thu Apr 11, 2013 5:15 pm

### Re: Population Monte Carlo Sampling

raider wrote:hmm... doe's it mean that any adaptive MC algorithm is hopeless in general as it introduces bias? Is it (at least theoretically) possible to have a priori bounded bias in adaptive MC?
Define "hopeless". I've heard that all adaptive MC is biased, but not an actual explanation for the claim. Heck, even non-adaptive MC renderers become biased and inconsistent as soon as tone mapping comes into the picture, especially if there are fireflies. I'm pretty sure adaptive MC is at least consistent up until the tone mapping step, which is the part I care about personally.

raider
Posts: 42
Joined: Fri Aug 03, 2012 10:36 pm
Location: Moscow, Russia.

### Re: Population Monte Carlo Sampling

friedlinguini wrote:Define "hopeless". I've heard that all adaptive MC is biased, but not an actual explanation for the claim. Heck, even non-adaptive MC renderers become biased and inconsistent as soon as tone mapping comes into the picture, especially if there are fireflies. I'm pretty sure adaptive MC is at least consistent up until the tone mapping step, which is the part I care about personally.
Ok, let me clarify a bit.

Tone mapping is another thing - it just transforms the solution of the measurement equation from one space to another (not nonlinearly). The bias I mentioned is bias of the estimator of the measurement integral (i.e. before tone mapping).

Let me explain what I meant by "hopeless".

Unbiasedness is just a nice property which means that for any number of samples N if you render the image infinitely many times your error in average will be zero. Not more, not less. In practice you will never have a chance to render infinitely many times, that means that any unbiased render will give you an image with some error (sometimes it is visible as noise, sometimes as more ugly artefacts).
A bit different thing is consistency. Consistency means that error goes to zero only when N goes to infinity. So that you can not eliminate error by averaging even infinitely high number of independent runs each with small N, instead you need to run one rendering infinitely long to get zero error. Again, to run something infinitely long is not possible. Thus you always get some level of error with consistent algorithm too.
The problem that for any unbiased algorithm you can get arbitrary big error for some particular N you set or some particular time you wait you renderer in general case.
That means that in practice unbiasedness is just a good to have, it never guarantees that you get your image without noise, artifacts within some given time and power to render.

Saying all that, I'm expressing my humble opinion that "Unbiased" is just a marketing trick in the world of rendering. It does not mean you get more realistic pictures as it depends not only on MC algorithm, but also on many other things (material models, light scattering models, spectral characteristics of lights, camera optics and so on).

Adaptive methods introduce bias, in many cases they can be even inconsistent, but if that bias or final error can be set to any desired small value (exactly or with some certainty) before rendering starts, then it will be much better than any unbiased algorithm which usually tells you nothing about the error.

By "hopeless" I mean inability of an algorithm to provide a priori estimation of error.

ingenious
Posts: 282
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Location: London, UK
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### Re: Population Monte Carlo Sampling

raider wrote:hmm... doe's it mean that any adaptive MC algorithm is hopeless in general as it introduces bias? Is it (at least theoretically) possible to have a priori bounded bias in adaptive MC?
Adaptive MC algorithms are not always biased. Most such algorithms I know are in fact unbiased, or at least the adaptivity doesn't introduce additional bias (e.g. in photon mapping based approaches).

erichocean
Posts: 3
Joined: Sat Apr 19, 2014 11:15 pm

### Re: Population Monte Carlo Sampling

Adaptive methods introduce bias, in many cases they can be even inconsistent, but if that bias or final error can be set to any desired small value (exactly or with some certainty) before rendering starts, then it will be much better than any unbiased algorithm which usually tells you nothing about the error.
Any unbiased algorithm? Or just those that do not use uniform sampling? The way I understand uniform Monte Carlo simulation, the error rate is exactly bounded by the number of samples, specifically 4x the samples reduces the absolute error by half.

Do you disagree? If this isn't true, I'd sure like to know.