Importance sampling

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Monte Carlo sampling from true distribution, p(x)

The popular and effective sampling technique widely used is Monte-Carlo sampling. It helps gather samples to approximate the true distribution, p(x) of the target function, f(x). Most of the case, we do not know the distribution of the target function, f(x), and we can only sample from it. If we need to approximate the distribution, then in Monte-Carlo simulation, we randomly sample from the distribution, p(x) and approximate the distribution based on the drawn samples.

Importance sampling: approximating p(x) using q(x).

Importance sampling is effective when p(x) is hard to sample, and we need a way to estimate the property of the true distribution, p(x). In that case, we sample from another distribution, q(x), which is a simple approximation of the p(x) to approximate the properties of the true distribution, p(x).




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