×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.
Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

Efficiency of reversible MCMC methods: elementary derivations and applications to composite methods

Click here to flash read.

arXiv:2305.18268v2 Announce Type: replace
Abstract: We review criteria for comparing the efficiency of Markov chain Monte Carlo (MCMC) methods with respect to the asymptotic variance of estimates of expectations of functions of state, and show how such criteria can justify ways of combining improvements to MCMC methods. We say that a chain on a finite state space with transition matrix $P$ efficiency-dominates one with transition matrix $Q$ if for every function of state it has lower (or equal) asymptotic variance. We give elementary proofs of some previous results regarding efficiency dominance, leading to a self-contained demonstration that a reversible chain with transition matrix $P$ efficiency-dominates a reversible chain with transition matrix $Q$ if and only if none of the eigenvalues of $Q-P$ are negative. This allows us to conclude that modifying a reversible MCMC method to improve its efficiency will also improve the efficiency of a method that randomly chooses either this or some other reversible method, and to conclude that improving the efficiency of a reversible update for one component of state (as in Gibbs sampling) will improve the overall efficiency of a reversible method that combines this and other updates. It also explains how antithetic MCMC can be more efficient than i.i.d. sampling. We also establish conditions that can guarantee that a method is not efficiency-dominated by any other method.

Click here to read this post out
ID: 809184; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: March 29, 2024, 7:33 a.m. Changes:
/u/anonymous
Dictionaries:
Words:
Spaces:
Views: 16
CC:
No creative common's license
Comments: