kernel_adapt | R Documentation |
Implementation of Haario et al. (2001)'s Adaptive Metropolis.
kernel_adapt(
mu = 0,
bw = 0L,
lb = -.Machine$double.xmax,
ub = .Machine$double.xmax,
freq = 1L,
warmup = 500L,
Sigma = NULL,
Sd = NULL,
eps = 1e-04,
fixed = FALSE,
until = Inf
)
kernel_am(
mu = 0,
bw = 0L,
lb = -.Machine$double.xmax,
ub = .Machine$double.xmax,
freq = 1L,
warmup = 500L,
Sigma = NULL,
Sd = NULL,
eps = 1e-04,
fixed = FALSE,
until = Inf
)
mu |
Either a numeric vector or a scalar. Proposal mean. If scalar, values are recycled to match the number of parameters in the objective function. |
bw |
Integer scalar. The bandwidth, is the number of observations to include in the computation of the variance-covariance matrix. |
lb, ub |
Either a numeric vector or a scalar. Lower and upper bounds for bounded kernels. When of length 1, the values are recycled to match the number of parameters in the objective function. |
freq |
Integer scalar. Frequency of updates. How often the variance-covariance matrix is updated. The implementation is different from that described in the original paper (see details). |
warmup |
Integer scalar. The number of iterations that the algorithm has to wait before starting to do the updates. |
Sigma |
The variance-covariance matrix. By default this will be an identity matrix during the warmup period. |
Sd |
Overall scale for the algorithm. By default, the variance-covariance
is scaled to |
eps |
Double scalar. Default size of the initial step (see details). |
fixed |
Logical scalar or vector of length |
until |
Integer scalar. Last step at which adaptation takes place (see details). |
While it has been shown that under regular conditions this transition kernel generates ergodic chains even when the adaptation does not stop, some practitioners may want to stop adaptation at some point.
kernel_adapt
Implements the adaptive Metropolis (AM) algorithm of Haario
et al. (2001). If the value of bw is greater than zero, then the algorithm
folds back AP, a previous version which is known to have ergodicity problems.
The parameter eps
has two functions. The first one is to set the initial
scale for the multivariate normal kernel, which is replaced after warmup
steps with the actual variance-covariance computed by the main algorithm.
The second usage is in the equation that ensures that the variance-covariance
is greater than zero, this is, the \varepsilon
parameter in the
original paper.
The update of the covariance matrix is done using cov_recursive()
function,
which makes the updates faster. The freq
parameter, besides of indicating the
frequency with which the updates are done, it specifies what are the samples
included in each update, in other words, like a thinning parameter, only every
freq
samples will be used to compute the covariance matrix. Since this
implementation uses the recursive formula for updating the covariance, there is
no practical need to set freq != 1
.
kernel_am
is just an alias for kernel_adapt
.
An object of class fmcmc_kernel. fmcmc_kernel
objects are intended
to be used with the MCMC()
function.
Haario, H., Saksman, E., & Tamminen, J. (2001). An adaptive Metropolis algorithm. Bernoulli, 7(2), 223–242. https://projecteuclid.org/euclid.bj/1080222083
Other kernels:
kernel_mirror
,
kernel_new()
,
kernel_normal()
,
kernel_ram()
,
kernel_unif()
# Update every-step and wait 1,000 steps before starting to adapt
kern <- kernel_adapt(freq = 1, warmup = 1000)
# Two parameters model, the second parameter with a restricted range, i.e.
# a lower bound of 1
kern <- kernel_adapt(lb = c(-.Machine$double.xmax, 0))
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