LaplacesDemon {LaplacesDemon}  R Documentation 
Laplace's Demon
Description
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.
Usage
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)
Arguments
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. 
Details
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 isalpha.star=0.234
, for componentwise proposals isalpha.star=0.44
, and for MALA isalpha.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 thatn1
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, andaw=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 theBlocks
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 beDist="t"
for tdistributed orDist="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 aT \times K
matrix of dynamic parameters, whereT
is the number of timeperiods andK
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. Whenepsilon=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 hasNr
rows andNc
columns. Each iteration, SGLD will randomly select a block of rows, where the number of rows is specified by thesize
argument. 
Fit
is an object of classdemonoid
in the USAMWG and USMWG algorithms. Posterior samples before the timeperiod specified in theBegin
argument are not updated, and are used instead fromFit
. 
gamma
controls the step size in DEMC or the decay of adaptation in MALA and RAM. In DEMC, it is positive and defaults to2.38 / \sqrt{2J}
whenNULL
, whereJ
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 (seedparm
) 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. WhenL=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 forL
(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 aJ \times J
mass matrix forJ
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 previouslyupdatedLaplaceApproximation
. 
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, andn1=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. IfPeriodicity=10
, then the algorithm adapts every 10th iteration. A higherPeriodicity
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 asInitial.Values
, and each element of these two vectors must be unique from each other, both before and after being passed to theModel
function.SIV
defaults toNULL
, in which case values are generated withGIV
. 
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 usew=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 weightw
. In the AMM algorithm, a higher value ofw
is associated with more static/symmetric univariate proposals, and a lowerw
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 isw=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 aT \times J
matrix orT \times J \times Nc
array of thinned samples forT
thinned iterations,J
parameters, andNc
chains for DEMC.Z
defaults toNULL
. The matrix of thinned posterior samples from a previous run may be used, in which case the samples are copied across the chains.
Value
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 
CovarDHis 
This 
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 
Author(s)
Statisticat, LLC., Silvere VialetChabrand silvere@vialetchabrand.com
References
Atchade, Y.F. (2006). "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift". Methodology and Computing in Applied Probability, 8, p. 235–254.
Bai, Y. (2009). "An Adaptive Directional MetropoliswithinGibbs Algorithm". Technical Report in Department of Statistics at the University of Toronto.
Beskos, A., Roberts, G.O., Stuart, A.M., and Voss, J. (2008). "MCMC Methods for Diffusion Bridges". Stoch. Dyn., 8, p. 319–350.
Boyles, L.B. and Welling, M. (2012). "Refractive Sampling".
Craiu, R.V., Rosenthal, J., and Yang, C. (2009). "Learn From Thy Neighbor: ParallelChain and Regional Adaptive MCMC". Journal of the American Statistical Assocation, 104(488), p. 1454–1466.
Christen, J.A. and Fox, C. (2010). "A General Purpose Sampling Algorithm for Continuous Distributions (the twalk)". Bayesian Analysis, 5(2), p. 263–282.
Dutta, S. (2012). "Multiplicative Random Walk MetropolisHastings on the Real Line". Sankhya B, 74(2), p. 315–342.
Duane, S., Kennedy, A.D., Pendleton, B.J., and Roweth, D. (1987). "Hybrid Monte Carlo". Physics Letters, B, 195, p. 216–222.
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Geman, S. and Geman, D. (1984). "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images". IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), p. 721–741.
Geyer, C.J. (1991). "Markov Chain Monte Carlo Maximum Likelihood". In Keramidas, E.M. Computing Science and Statistics: Proceedings of the 23rd Symposium of the Interface. Fairfax Station VA: Interface Foundation. p. 156–163.
Goodman J, and Weare, J. (2010). "Ensemble Samplers with Affine Invariance". Communications in Applied Mathematics and Computational Science, 5(1), p. 65–80.
Green, P.J. (1995). "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination". Biometrika, 82, p. 711–732.
Haario, H., Laine, M., Mira, A., and Saksman, E. (2006). "DRAM: Efficient Adaptive MCMC". Statistical Computing, 16, p. 339–354.
Haario, H., Saksman, E., and Tamminen, J. (2001). "An Adaptive Metropolis Algorithm". Bernoulli, 7, p. 223–242.
Hoffman, M.D. and Gelman. A. (2012). "The NoUTurn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo". Journal of Machine Learning Research, p. 1–30.
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Lewis, S.M. and Raftery, A.E. (1997). "Estimating Bayes Factors via Posterior Simulation with the LaplaceMetropolis Estimator". Journal of the American Statistical Association, 92, p. 648–655.
Liu, J., Liang, F., and Wong, W. (2000). "The MultipleTry Method and Local Optimization in Metropolis Sampling". Journal of the American Statistical Association, 95, p. 121–134.
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Mira, A. (2001). "On MetropolisHastings Algorithms with Delayed Rejection". Metron, Vol. LIX, n. 34, p. 231–241.
Murray, I., Adams, R.P., and MacKay, D.J. (2010). "Elliptical Slice Sampling". Journal of Machine Learning Research, 9, p. 541–548.
Neal, R.M. (2003). "Slice Sampling" (with discussion). Annals of Statistics, 31(3), p. 705–767.
Ritter, C. and Tanner, M. (1992), "Facilitating the Gibbs Sampler: the Gibbs Stopper and the GriddyGibbs Sampler", Journal of the American Statistical Association, 87, p. 861–868.
Roberts, G.O. and Rosenthal, J.S. (2009). "Examples of Adaptive MCMC". Computational Statistics and Data Analysis, 18, p. 349–367.
Roberts, G.O. and Tweedie, R.L. (1996). "Exponential Convergence of Langevin Distributions and Their Discrete Approximations". Bernoulli, 2(4), p. 341–363.
Rosenthal, J.S. (2007). "AMCMC: An R interface for adaptive MCMC". Computational Statistics and Data Analysis, 51, p. 5467–5470.
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Thompson, M.D. (2011). "Slice Sampling with Multivariate Steps". http://hdl.handle.net/1807/31955
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See Also
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
.
Examples
# The accompanying Examples vignette is a compendium of examples.
#################### 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