We now define some proposal distribution QxQ_x that defines some distribution centered around whatever xx we give. A standard example would be a normal distribution centered around xx with some constant standard deviation.

Generally, we want this proposal distribution to be symmetric, meaning that Qy(x)=Qx(y)Q_y(x) = Q_x(y) for any x,yx, y. That is, QQ isn't biased in any particular direction: it's not putting its thumb on the scale and unduly affecting the list of samples we will obtain.1

  1. It's not that hard to correct for cases where the proposal isn't symmetric, but we are trying (with limited success!) to keep the math simple.↩
plot

We now define some proposal distribution QxQ_x that defines some distribution centered around whatever xx we give. A standard example would be a normal distribution centered around xx with some constant standard deviation.

Generally, we want this proposal distribution to be symmetric, meaning that Qy(x)=Qx(y)Q_y(x) = Q_x(y) for any x,yx, y. That is, QQ isn't biased in any particular direction: it's not putting its thumb on the scale and unduly affecting the list of samples we will obtain.1

  1. It's not that hard to correct for cases where the proposal isn't symmetric, but we are trying (with limited success!) to keep the math simple.↩
plot