RWHM_chain {EntropyMCMC} | R Documentation |
These functions are used to define the elements $chain
of the MCMC algorithms
that are (and must be) implemented as lists in EntropyMCMC.
These functions are usually only called by higher-level functions, see details below.
RWHM_chain(theta0, it = 100, target, f_param, q_param, q_pdf = gaussian_pdf,
q_proposal = gaussian_proposal)
HMIS_norm_chain(theta0, it = 100, target, f_param, q_param, q_pdf = q_pdf_ISnorm,
q_proposal = q_proposal_ISnorm)
AMHaario_chain(theta0, it = 100, target, f_param, q_param, q_pdf = gaussian_pdf,
q_proposal = gaussian_proposal)
IID_chain(theta0 = NULL, it = 100, target, f_param, q_param = NULL, q_pdf = NULL,
q_proposal = NULL)
it |
the number of iterations to simulate |
theta0 |
the initial position of the chain, a |
target |
the user-defined target density |
f_param |
the parameters (hyperparameters, data) of the user-defined target density |
q_param |
the parameters of the proposal density, which structure depends on the algorithm and the proposal density chosen by the user. Defaults are
for |
q_pdf |
the proposal density |
q_proposal |
the function simulating the proposal for the next move |
Each MCMC algorithm is defined as a list with five elements, see
the object RWHM
for an example. The element $chain
must provide
the name of the function performing simulation of a single chain and returning that chain,
with arguments that must follow the definition above.
Each user can define its own MCMC
starting with the algorithms provided (see also section below).
These functions are thus usually called by higher-level functions like
MCMCcopies
, EntropyParallel
, or their multicore versions,
for simulating copies of MCMC chains in an automatic manner.
RWHM_chain
is used in RWHM
, a standard Randow-Walk Hastings-Metropolis algorithm.
HMIS_norm_chain
is used in HMIS_norm
,
an Independence Sampler HM with gaussian proposal
AMHaario_chain
is used in AMHaario
, the
Haario Adaptive Hastings-Metropolis algorithm (Haario 2001), and is provided as an example
of a benchmark AMCMC.
IID_chain
is used in IID_norm
, a “fake” MCMC that is just a gaussian IID sampler.
A list with elements:
theta |
the simulated chain in an array of |
paccept |
the empirical acceptance rate |
finalcov |
the last covariance matrix |
algo |
the name of the algorithm (for plot methods) |
Didier Chauveau.
H. Haario, E. Saksman, and J. Tamminen (2001), An adaptive Metropolis algorithm. Bernoulli 7, 223–242.
The algorithm already implemented, listed in EntropyMCMC-package
.
The higher level functions that use these functions for simulation:
MCMCcopies
, EntropyParallel
and their multicore versions.