Content deleted Content added
No edit summary |
No edit summary |
||
Line 1:
This algorithm can draw samples from any [[probability distribution]] P(x), requiring only that the density can be calculated at x. The algorithm generates a set of states x<sup>t</sup> which is a [[Markov chain]] because each state x<sup>t</sup> depends only on the previous state x<sup>t-1</sup>. The algorithm depends on the creation of a ''proposal density'' Q(x<sup>t</sup>;x') which depends on the current state x<sup>t</sup> and which can generate a new proposed sample x'. For example, the proposal density could be a Gaussian centred on the current state x<sup>t</sup>
:<math>
Q( x^t; x' ) \sim N( x'-x^t, \sigma^2 I).
| |||