Why do we use rejection sampling in statistics?
The idea of rejection sampling is that although we cannot easily sample from ff, there exists another density gg, like a Normal distribution or perhaps a tt -distribution, from which it is easy for us to sample (because there’s a built in function or someone else wrote a nice function).
Which is a property of the rejection sampling algorithm?
In most cases, this will not be a problem. One property of the rejection sampling algorithm is that the number of draws we need to take from the candidate density gg before we accept a candidate is a geometric random variable with success probability 1 / c1/c.
What is the rejection sampling range for t2t2?
From the picture, there are samples in the range of 44 – 66. In order to transform the t2t2 samples into N(0, 1)N (0,1) samples, we will need to reject many of the samples out in the tail.
How to calculate the distribution of rejection values?
We can now show that the distribution of the accepted values from the rejection sampling algorithm above follows the target density ff. We can do this by calculating the distribution function of the accepted values and show that this is equal to F(t) = ∫t − ∞f(x)dxF (t) = ∫t −∞ f (x)dx.
Can a rejection sampling algorithm produce uniform random variables?
While running the rejection sampling algorithm in this way to produce Uniform random variables will still work, it will be very inefficient. We can now show that the distribution of the accepted values from the rejection sampling algorithm above follows the target density ff.
Which is the target density in rejection sampling?
The density gg will be referred to as the “candidate density” and ff will be the “target density”. In order to use the rejections sampling algorithm, we must first ensure that the support of ff is a subset of the support of gg. If XfX f is the support of ff and XgX g is the support of gg, then we must have Xf ⊂ XgX f ⊂ X g.