4 ms·
>The idea is to approximate the density of P(x) while trying to reject as little as possible. Hence less wasteful. The idea is to approximate P(x) period. Rej
by coherentpony 14y ago
>The idea is to approximate the density of P(x) while trying to reject as little as possible. Hence less wasteful.
The idea is to approximate P(x) period. Rejecting as little as possible means nothing other than one's choice of proposal was poor. There are published works stating the optimal acceptance probability in high dimensions is 23.4% (see the work of Roberts et al (1997)). I think if one wanted to reject as little as possible one would have, albeit naïvely, tuned to a much higher acceptance rate.
- Dn_Ab 14y agoYou misconstrued. Reject as little as possible (<> reject little) was the motivation with respect to more naive random walks which suffer at dimensionality. I was not talking about leniency of proposal, where you are of course correct.
- coherentpony 14y ago>You misconstrued. Reject as little as possible (<> reject little) was the motivation with respect to more naive random walks which suffer at dimensionality. Misunderstanding on my part; apologies. Can you clarify the statement on dimensionality? Moment calculations converge at a sharp rate of 1/sqrt(n). Riemann sums as approximations to integrals (moments) suffer from the curse of dimensionality.