```
# NOT RUN {
# 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], 1e-100, Inf)
parm[Data$pos.sigma] <- sigma
### Log-Prior
beta.prior <- sum(dnormv(beta, 0, 1000, log=TRUE))
sigma.prior <- dhalfcauchy(sigma, 25, log=TRUE)
### Log-Likelihood
mu <- tcrossprod(Data$X, t(beta))
LL <- sum(dnorm(Data$y, mu, sigma, log=TRUE))
### Log-Posterior
LP <- LL + beta.prior + sigma.prior
Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP,
yhat=rnorm(length(mu), mu, sigma), parm=parm)
return(Modelout)
}
#library(compiler)
#Model <- cmpfun(Model) #Consider byte-compiling for more speed
set.seed(666)
############################ Initial Values #############################
Initial.Values <- GIV(Model, MyData, PGF=TRUE)
###########################################################################
# Examples of MCMC Algorithms #
###########################################################################
#################### Automated Factor Slice Sampler #####################
Fit <- LaplacesDemon(Model, Data=MyData, Initial.Values,
Covar=NULL, Iterations=1000, Status=100, Thinning=1,
Algorithm="AFSS", Specs=list(A=Inf, B=NULL, m=100, n=0, w=1))
Fit
print(Fit)
#Consort(Fit)
#plot(BMK.Diagnostic(Fit))
#PosteriorChecks(Fit)
#caterpillar.plot(Fit, Parms="beta")
#BurnIn <- Fit$Rec.BurnIn.Thinned
#plot(Fit, BurnIn, MyData, PDF=FALSE)
#Pred <- predict(Fit, Model, MyData, CPUs=1)
#summary(Pred, Discrep="Chi-Square")
#plot(Pred, Style="Covariates", Data=MyData)
#plot(Pred, Style="Density", Rows=1:9)
#plot(Pred, Style="ECDF")
#plot(Pred, Style="Fitted")
#plot(Pred, Style="Jarque-Bera")
#plot(Pred, Style="Predictive Quantiles")
#plot(Pred, Style="Residual Density")
#plot(Pred, Style="Residuals")
#Levene.Test(Pred)
#Importance(Fit, Model, MyData, Discrep="Chi-Square")
############# Adaptive Directional Metropolis-within-Gibbs ##############
#Fit <- LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="ADMG", Specs=list(n=0, Periodicity=50))
######################## Adaptive Griddy-Gibbs ##########################
#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 Metropolis-within-Gibbs ####################
#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))
###################### Adaptive-Mixture 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))
################### Affine-Invariant 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 Hit-And-Run Metropolis ##################
#Fit <- LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="CHARM", Specs=NULL)
########### Componentwise Hit-And-Run (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$pos.sigma], 1e-100, Inf)
# sigma2 <- sigma*sigma
# ### Hyperparameters
# betamu <- rep(0,length(beta))
# betaprec <- diag(length(beta))/1000
# ### Update beta
# XX <- crossprod(Data$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 byte-compiling 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))
############################# Griddy-Gibbs ##############################
#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 Dual-Averaging ###############
#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))
####################### Hit-And-Run Metropolis ##########################
#Fit <- LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="HARM", Specs=NULL)
################## Hit-And-Run (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)
################ Metropolis-Adjusted 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(1e-6,1e-7)))
############# Metropolis-Coupled 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))
####################### Metropolis-within-Gibbs #########################
#Fit <- LaplacesDemon(Model, Data=MyData, Initial.Values,
# Covar=NULL, Iterations=1000, Status=100, Thinning=1,
# Algorithm="MWG", Specs=list(B=NULL))
######################## Multiple-Try 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))
########################## No-U-Turn 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 Crank-Nicolson #####################
#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 Metropolis-Hastings ####################
#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))
########################### Reversible-Jump #############################
#bin.n <- J-1
#bin.p <- 0.2
#parm.p <- c(1, rep(1/(J-1),(J-1)), 1)
#selectable <- c(0, rep(1,J-1), 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,J-1),0)))
######################## Random-Walk 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=1e-5))
############## Sequential Adaptive Metropolis-within-Gibbs ##############
#NOTE: The SAMWG algorithm is only for state-space 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 Metropolis-within-Gibbs ###################
#NOTE: The SMWG algorithm is only for state-space 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=1e-4, 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))
############################### t-walk #################################
#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 Metropolis-within-Gibbs #########
#NOTE: The USAMWG algorithm is only for state-space 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 Metropolis-within-Gibbs ##############
#NOTE: The USMWG algorithm is only for state-space 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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