Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/LaplacesDemon.R
The LaplacesDemon
function is the main function of Laplace's
Demon. Given data, a model specification, and initial values,
LaplacesDemon
maximizes the logarithm of the unnormalized joint
posterior density with MCMC and provides samples of the marginal
posterior distributions, deviance, and other monitored variables.
The LaplacesDemon.hpc
function extends LaplacesDemon
to
parallel chains for multicore or cluster high performance computing.
1 2 3 4 5 6 7 8 9  LaplacesDemon(Model, Data, Initial.Values, Covar=NULL, Iterations=10000,
Status=100, Thinning=10, Algorithm="MWG", Specs=list(B=NULL),
Debug=list(DB.chol=FALSE, DB.eigen=FALSE, DB.MCSE=FALSE,
DB.Model=TRUE), LogFile="", ...)
LaplacesDemon.hpc(Model, Data, Initial.Values, Covar=NULL,
Iterations=10000, Status=100, Thinning=10, Algorithm="MWG",
Specs=list(B=NULL), Debug=list(DB.chol=FALSE, DB.eigen=FALSE,
DB.MCSE=FALSE, DB.Model=TRUE), LogFile="", Chains=2, CPUs=2,
Type="PSOCK", Packages=NULL, Dyn.libs=NULL)

Model 
This required argument receives the model from a
userdefined function that must be named Model. The userdefined
function is where the model is specified. 
Data 
This required argument accepts a list of data. The list of
data must contain 
Initial.Values 
For 
Covar 
This argument defaults to 
Iterations 
This required argument accepts integers larger than
10, and determines the number of iterations that Laplace's Demon
will update the parameters while searching for target
distributions. The required amount of computer memory will increase
with 
Status 
This argument accepts an integer between 1 and the
number of iterations, and indicates how often, in iterations, the
user would like the status printed to the screen or log
file. Usually, the following is reported: the number of iterations,
the proposal type (for example, multivariate or componentwise, or
mixture, or subset), and LP. For example, if a model is updated for
1,000 iterations and 
Thinning 
This argument accepts integers between 1 and the
number of iterations, and indicates that every nth iteration will be
retained, while the other iterations are discarded. If

Algorithm 
This argument accepts the abbreviated name of the MCMC algorithm, which must appear in quotes. A list of MCMC algorithms appears below in the Details section, and the abbreviated name is in parenthesis. 
Specs 
This argument defaults to 
Debug 
This argument accepts a list of logical scalars that
control whether or not errors or warnings are reported due to a

LogFile 
This argument is used to specify a log file name in
quotes in the working directory as a destination, rather than the
console, for the output messages of 
Chains 
This argument is required only for

CPUs 
This argument is required for parallel independent or
interactive chains in 
Type 
This argument defaults to 
Packages 
This optional argument is for use with parallel
independent or interacting chains, and defaults to 
Dyn.libs 
This optional argument is for use with parallel
independent or interacting chain, and defaults to 
... 
Additional arguments are unused. 
LaplacesDemon
offers numerous MCMC algorithms for numerical
approximation in Bayesian inference. The algorithms are
Adaptive Directional MetropoliswithinGibbs (ADMG)
Adaptive GriddyGibbs (AGG)
Adaptive Hamiltonian Monte Carlo (AHMC)
Adaptive Metropolis (AM)
Adaptive MetropoliswithinGibbs (AMWG)
AdaptiveMixture Metropolis (AMM)
AffineInvariant Ensemble Sampler (AIES)
Componentwise HitAndRun Metropolis (CHARM)
Delayed Rejection Adaptive Metropolis (DRAM)
Delayed Rejection Metropolis (DRM)
Differential Evolution Markov Chain (DEMC)
Elliptical Slice Sampler (ESS)
Gibbs Sampler (Gibbs)
GriddyGibbs (GG)
Hamiltonian Monte Carlo (HMC)
Hamiltonian Monte Carlo with DualAveraging (HMCDA)
HitAndRun Metropolis (HARM)
Independence Metropolis (IM)
Interchain Adaptation (INCA)
MetropolisAdjusted Langevin Algorithm (MALA)
MetropolisCoupled Markov Chain Monte Carlo (MCMCMC)
MetropoliswithinGibbs (MWG)
MultipleTry Metropolis (MTM)
NoUTurn Sampler (NUTS)
Oblique Hyperrectangle Slice Sampler (OHSS)
Preconditioned CrankNicolson (pCN)
Random Dive MetropolisHastings (RDMH)
RandomWalk Metropolis (RWM)
Reflective Slice Sampler (RSS)
Refractive Sampler (Refractive)
ReversibleJump (RJ)
Robust Adaptive Metropolis (RAM)
Sequential Adaptive MetropoliswithinGibbs (SAMWG)
Sequential MetropoliswithinGibbs (SMWG)
Slice Sampler (Slice)
Stochastic Gradient Langevin Dynamics (SGLD)
Tempered Hamiltonian Monte Carlo (THMC)
twalk (twalk)
Univariate Eigenvector Slice Sampler (UESS)
Updating Sequential Adaptive MetropoliswithinGibbs (USAMWG)
Updating Sequential MetropoliswithinGibbs (USMWG)
It is a goal for the documentation in the LaplacesDemon to be
extensive. However, details of MCMC algorithms are best explored
online at https://web.archive.org/web/20150206014000/http://www.bayesianinference.com/mcmc, as well
as in the "LaplacesDemon Tutorial" vignette, and the "Bayesian
Inference" vignette. Algorithm specifications (Specs
) are
listed below:
A
is used in AFSS, HMCDA, MALA, NUTS, OHSS, and UESS. In
MALA, it is the maximum acceptable value of the Euclidean norm of
the adaptive parameters mu and sigma, and the Frobenius norm of the
covariance matrix. In AFSS, HMCDA, NUTS, OHSS, and UESS, it is the
number of initial, adaptive iterations to be discarded as burnin.
Adaptive
is the iteration in which adaptation begins,
and is used in AM, AMM, DRAM, INCA, and Refractive. Most of these
algorithms adapt according to an observed covariance matrix, and
should sample before beginning to adapt.
alpha.star
is the target acceptance rate in MALA and
RAM, and is optional in CHARM and HARM. The recommended value for
multivariate proposals is alpha.star=0.234
, for componentwise
proposals is alpha.star=0.44
, and for MALA is
alpha.star=0.574
.
at
affects the traverse move in twalk. at=6
is
recommended. It helps when some parameters are highly correlated,
and the correlation structure may change through the
statespace. The traverse move is associated with an acceptance rate
that decreases as the number of parameters increases, and is the
reason that n1
is used to select a subset of parameters each
iteration. If adjusted, it is recommended to stay in the interval
[2,10].
aw
affects the walk move in twalk, and aw=1.5
is
recommended. If adjusted, it is recommended to stay in the
interval [0.3,2].
beta
is a scale parameter for AIES, and defaults to 2,
or an autoregressive parameter for pCN.
bin.n
is the scalar size parameter for a binomial prior
distribution of model size for the RJ algorithm.
bin.p
is the scalar probability parameter for a
binomial prior distribution of model size for the RJ algorithm.
B
is a list of blocked parameters. Each component of
the list represents a block of parameters, and contains a vector in
which each element is the position of the associated parameter in
parm.names. This function is optional in the AFSS, AMM, AMWG, ESS,
HARM, MWG, RAM, RWM, Slice, and UESS algorithms. For more
information on blockwise sampling, see the Blocks
function.
Begin
indicates the timeperiod in which to begin
updating (filtering or predicting) in the USAMWG and USMWG
algorithms.
Bounds
is used in the Slice algorithm. It is a vector
of length two with the lower and upper boundary of the slice. For
continuous parameters, it is often set to negative and positive
infinity, while for discrete parameters it is set to the minimum
and maximum discrete values to be sampled. When blocks are used,
this must be supplied as a list with the same number of list
components as the number of blocks.
delta
is used in HMCDA, MALA, and NUTS. In HMCDA and
NUTS, it is the target acceptance rate, and the recommended value is
0.65 in HMCDA and 0.6 in NUTS. In MALA, it is a constant in the
bounded drift function, may be in the interval [1e10,1000], and 1
is the default.
Dist
is the proposal distribution in RAM, and may
either be Dist="t"
for tdistributed or Dist="N"
for
normallydistributed.
dparm
accepts a vector of integers that indicate
discrete parameters. This argument is for use with the AGG or GG
algorithm.
Dyn
is a T x K matrix of dynamic
parameters, where T is the number of timeperiods and K
is the number of dynamic parameters. Dyn
is used by SAMWG,
SMWG, USAMWG, and USMWG. Nondynamic parameters are updated first in
each sampler iteration, then dynamic parameters are updated in a
random order in each timeperiod, and sequentially by timeperiod.
epsilon
is used in AHMC, HMC, HMCDA, MALA, NUTS, SGLD,
and THMC. It is the stepsize in all algorithms except MALA. It is
a vector equal in length to the number of parameters in AHMC, HMC,
and THMC. It is a scalar in HMCDA and NUTS. It is either a scalar
or a vector equal in length to the number of iterations in SGLD.
When epsilon=NULL
in HMCDA or NUTS (only), a reasonable
initial value is found. In MALA, it is a vector of length two. The
first element is the acceptable minimum of adaptive scale sigma, and
the second element is added to the diagonal of the covariance matrix
for regularization.
FC
is used in Gibbs and accepts a function that
receives two arguments: the vector of all parameters and the list of
data (similar to the Model specification function). FC must return
the updated vector of all parameters. The user specifies FC to
calculate the full conditional distribution of one or more
parameters.
file
is the quoted name of a numeric matrix of data,
without headers, for SGLD. The big data set must be a .csv
file. This matrix has Nr
rows and Nc
columns. Each
iteration, SGLD will randomly select a block of rows, where the
number of rows is specified by the size
argument.
Fit
is an object of class demonoid
in the USAMWG
and USMWG algorithms. Posterior samples before the timeperiod
specified in the Begin
argument are not updated, and are used
instead from Fit
.
gamma
controls the step size in DEMC or the decay of
adaptation in MALA and RAM. In DEMC, it is positive and defaults to
2.38/sqrt(2J) when NULL
, where
J is the length of initial values. For RAM, it is in the
interval (0.5,1], and 0.66 is recommended. For MALA, it is in the
interval (1,Iterations
), and defaults to 1.
Grid
accepts either a vector or a list of vectors of
evenlyspaced points on a grid for the AGG or GG algorithm. When the
argument is a vector, the same grid is applied to all
parameters. When the argument is a list, each component in the list
has a grid that is applied to the corresponding parameter. The
algorithm will evaluate each continuous parameter at the latest
value plus each point in the grid, or each discrete parameter (see
dparm
) at each grid point (which should be each discrete
value).
K
is a scalar number of proposals in MTM.
L
is a scalar number of leapfrog steps in AHMC, HMC, and
THMC. When L=1
, the algorithm reduces to Langevin Monte Carlo
(LMC).
lambda
is used in HMCDA and MCMCMC. In HMCDA, it is a
scalar trajectory length. In MCMCMC, it is either a scalar that
controls temperature spacing, or a vector of temperature spacings.
Lmax
is a scalar maximum for L
(see above) in
HMCDA and NUTS.
m
is used in the AFSS, AHMC, HMC, Refractive, RSS, Slice,
THMC, and UESS algorithms. In AHMC, HMC, and THMC, it is a
J x J mass matrix for J initial values. In
AFSS and UESS, it is a scalar, and is the maximum number of steps
for creating the slice interval. In Refractive and RSS, it is a
scalar, and is the number of steps to take per iteration. In Slice,
it is either a scalar or a list with as many list components as
blocks. It must be an integer in [1,Inf], and indicates the maximum
number of steps for creating the slice interval.
mu
is a vector that is equal in length to the initial
values. This vector will be used as the mean of the proposal
distribution, and is usually the posterior mode of a
previouslyupdated LaplaceApproximation
.
MWG
is used in Gibbs to specify a vector of parameters
that are to receive MetropoliswithinGibbs updates. Each element is
an integer that indicates the parameter.
Nc
is either the number of (unparallelized) parallel
chains in DEMC (and must be at least 3) or the number of columns of
big data in SGLD.
Nr
is the number of rows of big data in SGLD.
n
is the number of previous iterations in ADMG, AFSS,
AMM, AMWG, OHSS, RAM, and UESS.
n1
affects the size of the subset of each set of points
to adjust, and is used in twalk. It relates to the number of
parameters, and n1=4
is recommended. If adjusted, it is
recommended to stay in the interval [2,20].
parm.p
is a vector of probabilities for parameter
selection in the RJ algorithm, and must be equal in length to
the number of initial values.
r
is a scalar used in the Refractive algorithm to
indicate the ratio between r1 and r2.
Periodicity
specifies how often in iterations the
adaptive algorithm should adapt, and is used by AHMC, AM, AMM, AMWG,
DRAM, INCA, SAMWG, and USAMWG. If Periodicity=10
, then the
algorithm adapts every 10th iteration. A higher Periodicity
is associated with an algorithm that runs faster, because it does
not have to calculate adaptation as often, though the algorithm
adapts less often to the target distributions, so it is a
tradeoff. It is recommended to use the lowest value that runs
fast enough to suit the user, or provide sufficient adaptation.
selectable
is a vector of indicators of whether or not
a parameter is selectable for variable selection in the RJ
algorithm. Nonselectable parameters are assigned a zero, and are
always in the model. Selectable parameters are assigned a one. This
vector must be equal in length to the number of initial values.
selected
is a vector of indicators of whether or not
each parameter is selected when the RJ algorithm begins, and
must be equal in length to the number of initial values.
SIV
stands for secondary initial values and is used by
twalk. SIV
must be the same length as Initial.Values
,
and each element of these two vectors must be unique from each
other, both before and after being passed to the Model
function. SIV
defaults to NULL
, in which case values
are generated with GIV
.
size
is the number of rows of big data to be read into
SGLD each iteration.
smax
is the maximum allowable tuning parameter sigma,
the standard deviation of the conditional distribution, in the AGG
algorithm.
Temperature
is used in the THMC algorithm to heat up
the momentum in the first half of the leapfrog steps, and then cool
down the momentum in the last half. Temperature
must be
positive. When greater than 1, THMC should explore more diffuse
distributions, and may be helpful with multimodal distributions.
Type
is used in the Slice algorithm. It is either a
scalar or a list with the same number of list components as blocks.
This accepts "Continuous"
for continuous parameters,
"Nominal"
for discrete parameters that are unordered, and
"Ordinal"
for discrete parameters that are ordered.
w
is used in AFSS, AMM, DEMC, Refractive, RSS, and
Slice. It is a mixture weight for both the AMM and DEMC algorithms,
and in these algorithms it is in the interval (0,1]. For AMM, it is
recommended to use w=0.05
, as per Roberts and Rosenthal
(2009). The two mixture components in AMM are adaptive multivariate
and static/symmetric univariate proposals. The mixture is determined
at each iteration with mixture weight w
. In the AMM
algorithm, a higher value of w
is associated with more
static/symmetric univariate proposals, and a lower w
is
associated with more adaptive multivariate proposals. AMM will be
unable to include the multivariate mixture component until it has
accumulated some history, and models with more parameters will take
longer to be able to use adaptive multivariate proposals. In DEMC,
it indicates the probability that each iteration uses a snooker
update, rather than a projection update, and the recommended default
is w=0.1
. In the Refractive algorithm, w
is a scalar
step size parameter. In AFSS, RSS, and the Slice algorithms, this is
a step size interval for creating the slice interval. In AFSS and
RSS, a scalar or vector equal in length the number of initial values
is accepted. In Slice, a scalar or a list with a number of list
components equal to the number of blocks is accepted.
Z
accepts a T x J matrix or T x J x Nc array of thinned samples for T
thinned iterations, J parameters, and Nc chains for
DEMC. Z
defaults to NULL
. The matrix of thinned
posterior samples from a previous run may be used, in which case the
samples are copied across the chains.
LaplacesDemon
returns an object of class demonoid
, and
LaplacesDemon.hpc
returns an object of class
demonoid.hpc
that is a list of objects of class
demonoid
, where the number of components in the list
is the number of parallel chains. Each object of class demonoid
is a list with the following components:
Acceptance.Rate 
This is the acceptance rate of the MCMC
algorithm, indicating the percentage of iterations in which the
proposals were accepted. For more information on acceptance rates,
see the 
Algorithm 
This reports the specific algorithm used. 
Call 
This is the matched call of 
Covar 
This stores the K x K proposal
covariance matrix (where K is the dimension or number of
parameters), variance vector, or list of covariance matrices.
If variance or covariance is used for adaptation, then this
covariance is returned. Otherwise, the variance of the samples of
each parameter is returned. If the model is updated in the future,
then this vector, matrix, or list can be used to start the next
update where the last update left off. Only the diagonal of this
matrix is reported in the associated 
CovarDHis 
This N x K matrix stores the diagonal of the proposal covariance matrix of each adaptation in each of N rows for K dimensions, where the dimension is the number of parameters or length of the initial values vector. The proposal covariance matrix should change less over time. An exception is that the AHMC algorithm stores an algorithm specification here, which is not the diagonal of the proposal covariance matrix. 
Deviance 
This is a vector of the deviance of the model, with a length equal to the number of thinned samples that were retained. Deviance is useful for considering model fit, and is equal to the sum of the loglikelihood for all rows in the data set, which is then multiplied by negative two. 
DIC1 
This is a vector of three values: Dbar, pD, and DIC. Dbar
is the mean deviance, pD is a measure of model complexity indicating
the effective number of parameters, and DIC is the Deviance
Information Criterion, which is a model fit statistic that is the
sum of Dbar and pD. 
DIC2 
This is identical to 
Initial.Values 
This is the vector of 
Iterations 
This reports the number of 
LML 
This is an approximation of the logarithm of the marginal
likelihood of the data (see the 
Minutes 
This indicates the number of minutes that

Model 
This contains the model specification 
Monitor 
This is a vector or matrix of one or more monitored
variables, which are variables that were specified in the

Parameters 
This reports the number of parameters. 
Posterior1 
This is a matrix of marginal posterior distributions composed of thinned samples, with a number of rows equal to the number of thinned samples and a number of columns equal to the number of parameters. This matrix includes all thinned samples. 
Posterior2 
This is a matrix equal to 
Rec.BurnIn.Thinned 
This is the recommended burnin for the
thinned samples, where the value indicates the first row that was
stationary across all parameters, and previous rows are discarded
as burnin. Samples considered as burnin are discarded because they
do not represent the target distribution and have not adequately
forgotten the initial value of the chain (or Markov chain, if

Rec.BurnIn.UnThinned 
This is the recommended burnin for all samples, in case thinning will not be necessary. 
Rec.Thinning 
This is the recommended value for the

Specs 
This is an optional list of algorithm specifications. 
Status 
This is the value in the 
Summary1 
This is a matrix that summarizes the marginal
posterior distributions of the parameters, deviance, and monitored
variables over all samples in 
Summary2 
This matrix is identical to the matrix in

Thinned.Samples 
This is the number of thinned samples that were retained. 
Thinning 
This is the value of the 
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AcceptanceRate
,
as.initial.values
,
as.parm.names
,
BayesFactor
,
Blocks
,
BMK.Diagnostic
,
Combine
,
Consort
,
dcrmrf
,
ESS
,
GIV
,
is.data
,
is.model
,
IterativeQuadrature
,
LaplaceApproximation
,
LaplacesDemon.RAM
,
LML
, and
MCSE
.
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#################### Load the LaplacesDemon Library #####################
library(LaplacesDemon)
############################## Demon Data ###############################
data(demonsnacks)
y < log(demonsnacks$Calories)
X < cbind(1, as.matrix(log(demonsnacks[,c(1,4,10)]+1)))
J < ncol(X)
for (j in 2:J) X[,j] < CenterScale(X[,j])
######################### Data List Preparation #########################
mon.names < "LP"
parm.names < as.parm.names(list(beta=rep(0,J), sigma=0))
pos.beta < grep("beta", parm.names)
pos.sigma < grep("sigma", parm.names)
PGF < function(Data) {
beta < rnorm(Data$J)
sigma < runif(1)
return(c(beta, sigma))
}
MyData < list(J=J, PGF=PGF, X=X, mon.names=mon.names,
parm.names=parm.names, pos.beta=pos.beta, pos.sigma=pos.sigma, y=y)
########################## Model Specification ##########################
Model < function(parm, Data)
{
### Parameters
beta < parm[Data$pos.beta]
sigma < interval(parm[Data$pos.sigma], 1e100, Inf)
parm[Data$pos.sigma] < sigma
### LogPrior
beta.prior < sum(dnormv(beta, 0, 1000, log=TRUE))
sigma.prior < dhalfcauchy(sigma, 25, log=TRUE)
### LogLikelihood
mu < tcrossprod(Data$X, t(beta))
LL < sum(dnorm(Data$y, mu, sigma, log=TRUE))
### LogPosterior
LP < LL + beta.prior + sigma.prior
Modelout < list(LP=LP, Dev=2*LL, Monitor=LP,
yhat=rnorm(length(mu), mu, sigma), parm=parm)
return(Modelout)
}
#library(compiler)
#Model < cmpfun(Model) #Consider bytecompiling for more speed
set.seed(666)
############################ Initial Values #############################
Initial.Values < GIV(Model, MyData, PGF=TRUE)
###########################################################################
# Examples of MCMC Algorithms #
###########################################################################
#################### Automated Factor Slice Sampler #####################
Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
Covar=NULL, Iterations=1000, Status=100, Thinning=1,
Algorithm="AFSS", Specs=list(A=Inf, B=NULL, m=100, n=0, w=1))
Fit
print(Fit)
#Consort(Fit)
#plot(BMK.Diagnostic(Fit))
#PosteriorChecks(Fit)
#caterpillar.plot(Fit, Parms="beta")
#BurnIn < Fit$Rec.BurnIn.Thinned
#plot(Fit, BurnIn, MyData, PDF=FALSE)
#Pred < predict(Fit, Model, MyData, CPUs=1)
#summary(Pred, Discrep="ChiSquare")
#plot(Pred, Style="Covariates", Data=MyData)
#plot(Pred, Style="Density", Rows=1:9)
#plot(Pred, Style="ECDF")
#plot(Pred, Style="Fitted")
#plot(Pred, Style="JarqueBera")
#plot(Pred, Style="Predictive Quantiles")
#plot(Pred, Style="Residual Density")
#plot(Pred, Style="Residuals")
#Levene.Test(Pred)
#Importance(Fit, Model, MyData, Discrep="ChiSquare")
############# Adaptive Directional MetropoliswithinGibbs ##############
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="ADMG", Specs=list(n=0, Periodicity=50))
######################## Adaptive GriddyGibbs ##########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AGG", Specs=list(Grid=GaussHermiteQuadRule(3)$nodes,
# dparm=NULL, smax=Inf, CPUs=1, Packages=NULL, Dyn.libs=NULL))
################## Adaptive Hamiltonian Monte Carlo #####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AHMC", Specs=list(epsilon=0.02, L=2, m=NULL,
# Periodicity=10))
########################## Adaptive Metropolis ##########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AM", Specs=list(Adaptive=500, Periodicity=10))
################### Adaptive MetropoliswithinGibbs ####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AMWG", Specs=list(B=NULL, n=0, Periodicity=50))
###################### AdaptiveMixture Metropolis ######################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AMM", Specs=list(Adaptive=500, B=NULL, n=0,
# Periodicity=10, w=0.05))
################### AffineInvariant Ensemble Sampler ###################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="AIES", Specs=list(Nc=2*length(Initial.Values), Z=NULL,
# beta=2, CPUs=1, Packages=NULL, Dyn.libs=NULL))
################# Componentwise HitAndRun Metropolis ##################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="CHARM", Specs=NULL)
########### Componentwise HitAndRun (Adaptive) Metropolis #############
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="CHARM", Specs=list(alpha.star=0.44))
################# Delayed Rejection Adaptive Metropolis #################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="DRAM", Specs=list(Adaptive=500, Periodicity=10))
##################### Delayed Rejection Metropolis ######################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="DRM", Specs=NULL)
################## Differential Evolution Markov Chain ##################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="DEMC", Specs=list(Nc=3, Z=NULL, gamma=NULL, w=0.1))
####################### Elliptical Slice Sampler ########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="ESS", Specs=list(B=NULL))
############################# Gibbs Sampler #############################
### NOTE: Unlike the other samplers, Gibbs requires specifying a
### function (FC) that draws from full conditionals.
#FC < function(parm, Data)
# {
# ### Parameters
# beta < parm[Data$pos.beta]
# sigma < interval(parm[Data$pos.sigma], 1e100, Inf)
# sigma2 < sigma*sigma
# ### Hyperparameters
# betamu < rep(0,length(beta))
# betaprec < diag(length(beta))/1000
# ### Update beta
# XX < crossprod(Data$X)
# Xy < crossprod(Data$X, Data$y)
# IR < backsolve(chol(XX/sigma2 + betaprec), diag(length(beta)))
# btilde < crossprod(t(IR)) %*% (Xy/sigma2 + betaprec %*% betamu)
# beta < btilde + IR %*% rnorm(length(beta))
# return(c(beta,sigma))
# }
##library(compiler)
##FC < cmpfun(FC) #Consider bytecompiling for more speed
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="Gibbs", Specs=list(FC=FC, MWG=pos.sigma))
############################# GriddyGibbs ##############################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="GG", Specs=list(Grid=seq(from=0.1, to=0.1, len=5),
# dparm=NULL, CPUs=1, Packages=NULL, Dyn.libs=NULL))
####################### Hamiltonian Monte Carlo #########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="HMC", Specs=list(epsilon=0.001, L=2, m=NULL))
############# Hamiltonian Monte Carlo with DualAveraging ###############
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=1, Thinning=1,
# Algorithm="HMCDA", Specs=list(A=500, delta=0.65, epsilon=NULL,
# Lmax=1000, lambda=0.1))
####################### HitAndRun Metropolis ##########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="HARM", Specs=NULL)
################## HitAndRun (Adaptive) Metropolis ####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="HARM", Specs=list(alpha.star=0.234, B=NULL))
######################## Independence Metropolis ########################
### Note: the mu and Covar arguments are populated from a previous Laplace
### Approximation.
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=Fit$Covar, Iterations=1000, Status=100, Thinning=1,
# Algorithm="IM",
# Specs=list(mu=Fit$Summary1[1:length(Initial.Values),1]))
######################### Interchain Adaptation #########################
#Initial.Values < rbind(Initial.Values, GIV(Model, MyData, PGF=TRUE))
#Fit < LaplacesDemon.hpc(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="INCA", Specs=list(Adaptive=500, Periodicity=10),
# LogFile="MyLog", Chains=2, CPUs=2, Type="PSOCK", Packages=NULL,
# Dyn.libs=NULL)
################ MetropolisAdjusted Langevin Algorithm #################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="MALA", Specs=list(A=1e7, alpha.star=0.574, gamma=1,
# delta=1, epsilon=c(1e6,1e7)))
############# MetropolisCoupled Markov Chain Monte Carlo ###############
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="MCMCMC", Specs=list(lambda=1, CPUs=2, Packages=NULL,
# Dyn.libs=NULL))
####################### MetropoliswithinGibbs #########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="MWG", Specs=list(B=NULL))
######################## MultipleTry Metropolis ########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="MTM", Specs=list(K=4, CPUs=1, Packages=NULL, Dyn.libs=NULL))
########################## NoUTurn Sampler ############################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=1, Thinning=1,
# Algorithm="NUTS", Specs=list(A=500, delta=0.6, epsilon=NULL,
# Lmax=Inf))
################# Oblique Hyperrectangle Slice Sampler ##################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="OHSS", Specs=list(A=Inf, n=0))
##################### Preconditioned CrankNicolson #####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="pCN", Specs=list(beta=0.1))
###################### Robust Adaptive Metropolis #######################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="RAM", Specs=list(alpha.star=0.234, B=NULL, Dist="N",
# gamma=0.66, n=0))
################### Random Dive MetropolisHastings ####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="RDMH", Specs=NULL)
########################## Refractive Sampler ###########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="Refractive", Specs=list(Adaptive=1, m=2, w=0.1, r=1.3))
########################### ReversibleJump #############################
#bin.n < J1
#bin.p < 0.2
#parm.p < c(1, rep(1/(J1),(J1)), 1)
#selectable < c(0, rep(1,J1), 0)
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="RJ", Specs=list(bin.n=bin.n, bin.p=bin.p,
# parm.p=parm.p, selectable=selectable,
# selected=c(0,rep(1,J1),0)))
######################## RandomWalk Metropolis #########################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="RWM", Specs=NULL)
######################## Reflective Slice Sampler #######################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="RSS", Specs=list(m=5, w=1e5))
############## Sequential Adaptive MetropoliswithinGibbs ##############
#NOTE: The SAMWG algorithm is only for statespace models (SSMs)
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="SAMWG", Specs=list(Dyn=Dyn, Periodicity=50))
################## Sequential MetropoliswithinGibbs ###################
#NOTE: The SMWG algorithm is only for statespace models (SSMs)
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="SMWG", Specs=list(Dyn=Dyn))
############################# Slice Sampler #############################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=1, Thinning=1,
# Algorithm="Slice", Specs=list(B=NULL, Bounds=c(Inf,Inf), m=100,
# Type="Continuous", w=1))
################# Stochastic Gradient Langevin Dynamics #################
#NOTE: The Data and Model functions must be coded differently for SGLD.
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=10, Thinning=10,
# Algorithm="SGLD", Specs=list(epsilon=1e4, file="X.csv", Nr=1e4,
# Nc=6, size=10))
################### Tempered Hamiltonian Monte Carlo ####################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="THMC", Specs=list(epsilon=0.001, L=2, m=NULL,
# Temperature=2))
############################### twalk #################################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="twalk", Specs=list(SIV=NULL, n1=4, at=6, aw=1.5))
################# Univariate Eigenvector Slice Sampler #################
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="UESS", Specs=list(A=Inf, B=NULL, m=100, n=0))
########## Updating Sequential Adaptive MetropoliswithinGibbs #########
#NOTE: The USAMWG algorithm is only for statespace model updating
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=100000, Status=100, Thinning=100,
# Algorithm="USAMWG", Specs=list(Dyn=Dyn, Periodicity=50, Fit=Fit,
# Begin=T.m))
############## Updating Sequential MetropoliswithinGibbs ##############
#NOTE: The USMWG algorithm is only for statespace model updating
#Fit < LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=100000, Status=100, Thinning=100,
# Algorithm="USMWG", Specs=list(Dyn=Dyn, Fit=Fit, Begin=T.m))
#End

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