Hi,(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have N iid samples from a distribution q, and I want to estimate another distributin, p, using those samples (Importance Sampling).

By "standard importance sampling", I mean the case where samples (prior samples. i.e. samples from q) have equal weights ([tex] w_i = 1/N [/tex]).

In the case of "standard importance sampling", I should perform these steps:

1) compute (unnormalized) weights for those sample according to [tex]p(s_i)/q(s_i)[/tex] ([tex]s_{i}[/tex] is the i'th sample from q)

2) normalize those weights

3) then an estimate of p would be this:

[tex] \hat{p} = \sum_{i=1}^N w_{i} \delta(i) [/tex]

(w_i are normalized weights computed at step 2. delta(i) is the Dirac delta function at s_i)

Now consider the case where samples (prior samples, i.e. samples from q) are weighted (differnt weights, and normalized. for example [tex] u_i [/tex]).

Is it enough (justified) to change the (unnormalized) weights (computed at step 1) to [tex]p(s_i)u_{i}/q(s_i)[/tex]?

(multiplying prior weights and "standard importance sampling" weights together?)

Thanks in advance.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on Importance Sampling (Monte Carlo method)

Loading...

Similar Threads - Question Importance Sampling | Date |
---|---|

I Question about simplifying Sigma notation | Feb 11, 2018 |

I Shopping List Game: Probability Question | Dec 10, 2017 |

I A simple question about probability theory | Aug 2, 2017 |

B Correlation question | Jun 20, 2017 |

I Existential Import paper by Corcoran and Massoud | Jan 7, 2017 |

**Physics Forums - The Fusion of Science and Community**