In the above displayed formulae p ( y k | ξ ξ k i ) stands for the likelihood function x k ↦ ↦ p ( y k | x k ) evaluated at x k = ξ ξ k i , and p ( x k + 1 | ξ ξ ^ ^ k i ) stands for the conditional density p ( x k + 1 | x k ) evaluated at x k = ξ ξ ^ ^ k i .