| Title: | Robust Adaptive Metropolis Algorithm |
| Version: | 0.1.2 |
| Date: | 2021-10-06 |
| Description: | Function for adapting the shape of the random walk Metropolis proposal as specified by robust adaptive Metropolis algorithm by Vihola (2012) <doi:10.1007/s11222-011-9269-5>. The package also includes fast functions for rank-one Cholesky update and downdate. These functions can be used directly from R or the corresponding C++ header files can be easily linked to other R packages. |
| License: | GPL-2 |GPL-3 [expanded from: GPL (≥ 2)] |
| BugReports: | https://github.com/helske/ramcmc/issues |
| Suggests: | testthat, knitr, rmarkdown |
| Imports: | Rcpp (≥ 0.12.8) |
| LinkingTo: | Rcpp, RcppArmadillo |
| RoxygenNote: | 5.0.1 |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2021-10-06 20:50:12 UTC; jovetale |
| Author: | Jouni Helske [aut, cre] |
| Maintainer: | Jouni Helske <jouni.helske@iki.fi> |
| Repository: | CRAN |
| Date/Publication: | 2021-10-06 21:40:02 UTC |
Update the Proposal of RAM Algorithm
Description
Given the lower triangular matrix S obtained from the Cholesky decomposition of the shapeof the proposal distribution, functionadapt_S updates S according to the RAM algorithm.
Usage
adapt_S(S, u, current, n, target = 0.234, gamma = 2/3)Arguments
S | A lower triangular matrix corresponding to the Cholesky decomposition of thescale of the proposal distribution. |
u | A vector with with length matching with the dimensions of S. |
current | The current acceptance probability. |
n | Scaling parameter corresponding to the current iteration number. |
target | The target acceptance rate. Default is 0.234. |
gamma | Scaling parameter. Default is 2/3. |
Value
If the resulting matrix is positive definite, an updated value of S.Otherwise original S is returned.
Note
If the downdating would result non-positive definite matrix, no adaptation is performed.
References
Matti Vihola (2012). "Robust adaptive Metropolis algorithm with coerced acceptance rate".Statistics and Computing, 22: 997. doi:10.1007/s11222-011-9269-5
Examples
# sample from standard normal distribution# use proposals from the uniform distribution on# interval (-s, s), where we adapt sadapt_mcmc <- function(n = 10000, s) { x <- numeric(n) loglik_old <- dnorm(x[1], log = TRUE) for (i in 2:n) { u <- s * runif(1, -1, 1) prop <- x[i] + u loglik <- dnorm(prop, log = TRUE) accept_prob <- min(1, exp(loglik - loglik_old)) if (runif(1) < accept_prob) { x[i] <- prop loglik_old <- loglik } else { x[i] <- x[i - 1] } # Adapt only during the burn-in if (i < n/2) { s <- adapt_S(s, u, accept_prob, i) } } list(x = x[(n/2):n], s = s)}out <- adapt_mcmc(1e5, 2)out$shist(out$x)# acceptance rate:1 / mean(rle(out$x)$lengths)Rank-one Downdate of Cholesky Decomposition
Description
Given the lower triangular matrix L obtained from the Cholesky decomposition of A,functionchol_downdate updates L such that it corresponds to the decomposition of A - u*u'(if such decomposition exists).
Usage
chol_downdate(L, u)Arguments
L | A lower triangular matrix. Strictly upper diagonal part is not referenced. |
u | A vector with with length matching with the dimensions of L. |
Value
Updated L.
Note
The function does not check that the resulting matrix is positive semidefinite.
Rank-one Update of Cholesky Decomposition
Description
Given the lower triangular matrix L obtained from the Cholesky decomposition of A,functionchol_update updates L such that it corresponds to the decomposition of A + u*u'.
Usage
chol_update(L, u)Arguments
L | A lower triangular matrix. Strictly upper diagonal part is not referenced. |
u | A vector with with length matching with the dimensions of L. |
Value
Updated L.
Examples
L <- matrix(c(4,3,0,5), 2, 2)u <- c(1, 2)chol_update(L, u)t(chol(L %*% t(L) + u %*% t(u)))