mh: Fit a generic model using Metropolis-Hastings (MH)
In hmclearn: Fit Statistical Models Using Hamiltonian Monte Carlo

Description Usage Arguments Value Elements for hmclearn objects Available logPOSTERIOR functions Author(s) Examples

This function runs the MH algorithm on a generic model provided the logPOSTERIOR function. All parameters specified within the list param are passed to these the posterior function.

mh(
  N,
  theta.init,
  qPROP,
  qFUN,
  logPOSTERIOR,
  nu = 0.001,
  varnames = NULL,
  param = list(),
  chains = 1,
  parallel = FALSE,
  ...
)

`N`	Number of MCMC samples
`theta.init`	Vector of initial values for the parameters
`qPROP`	Function to generate proposal
`qFUN`	Probability for proposal function. First argument is where to evaluate, and second argument is the conditional parameter
`logPOSTERIOR`	Function to calculate and return the log posterior given a vector of values of `theta`
`nu`	Single value or vector parameter passed to `qPROP` or `qFUN` for the proposal density
`varnames`	Optional vector of theta parameter names
`param`	List of additional parameters for `logPOSTERIOR` and `glogPOSTERIOR`
`chains`	Number of MCMC chains to run
`parallel`	Logical to set whether multiple MCMC chains should be run in parallel
`...`	Additional parameters for `logPOSTERIOR`

Object of class hmclearn

Elements for `hmclearn` objects

N: Number of MCMC samples
theta: Nested list of length N of the sampled values of theta for each chain
thetaCombined: List of dataframes containing sampled values, one for each chain
r: NULL for Metropolis-Hastings
theta.all: Nested list of all parameter values of theta sampled prior to accept/reject step for each
r.all: NULL for Metropolis-Hastings
accept: Number of accepted proposals. The ratio accept / N is the acceptance rate
accept_v: Vector of length N indicating which samples were accepted
M: NULL for Metropolis-Hastings
algorithm: MH for Metropolis-Hastings
varnames: Optional vector of parameter names
chains: Number of MCMC chains

Available `logPOSTERIOR` functions

linear_posterior: Linear regression: log posterior
logistic_posterior: Logistic regression: log posterior
poisson_posterior: Poisson (count) regression: log posterior
lmm_posterior: Linear mixed effects model: log posterior
glmm_bin_posterior: Logistic mixed effects model: log posterior
glmm_poisson_posterior: Poisson mixed effects model: log posterior

Samuel Thomas samthoma@iu.edu, Wanzhu Tu wtu@iu.edu

# Linear regression example
set.seed(521)
X <- cbind(1, matrix(rnorm(300), ncol=3))
betavals <- c(0.5, -1, 2, -3)
y <- X%*%betavals + rnorm(100, sd=.2)

f1_mh <- mh(N = 3e3,
         theta.init = c(rep(0, 4), 1),
         nu <- c(rep(0.001, 4), 0.1),
         qPROP = qprop,
         qFUN = qfun,
         logPOSTERIOR = linear_posterior,
         varnames = c(paste0("beta", 0:3), "log_sigma_sq"),
         param=list(y=y, X=X), parallel=FALSE, chains=1)

summary(f1_mh, burnin=1000)