# Directional Metropolis Hastings Implements Markov Chain Monte Carlo for continuous random vectors using Directional Metropolis Hasting Algorithm ```r metropdir(obj, dobj, initial, lchain, sd.prop = 1, steplen = 0, s = 0.95, ...) ``` ## Arguments - `obj`: an R function that evaluates the log unnormalized probability density of the desired equilibrium distribution of the Markov chain. First argument is the state vector of the Markov chain. Other arguments arbitrary and taken from the `...` arguments of this function. Should return `- Inf` for points of the state space having probability zero under the desired equilibrium distribution. - `dobj`: an R function that evaluates the derivative of the log unnormalized probability density at the current state of the markov chain. - `initial`: Initial state of the markov chain. `obj(state)` must not return #' `-Inf` - `lchain`: length of the chain - `sd.prop`: scale to use for the proposal - `steplen`: tuning parameter in mean of proposal - `s`: tuning parameter in the covariance of proposal - `...`: any arguments to be passed to obj and dobj. ## Returns Returns the following objects in a list: * accept. acceptance rate. * batch. resulting chain. ## Details Runs a Directional Metropolis Hastings algorithm, with multivariate normal proposal producing a Markov chain with equilibrium distribution having a specified unnormalized density. Distribution must be continuous. Support of the distribution is the support of the density specified by argument `obj`. ## Examples ```r ## Not run: Sigma <- matrix(c(1,0.2,0.2,1),2,2) mu <- c(1,1) Sig.Inv <- solve(Sigma) Sig.det.sqrt <- sqrt(det(Sigma)) logf <- function(x,mu,Sig.Inv){ x.center <- as.numeric((x-mu)) out <- crossprod(x.center,Sig.Inv) out <- sum(out*x.center) -out/2 } gr.logf <- function(x,mu,Sig.Inv){ x.center <- as.numeric((x-mu)) out <- crossprod(x.center,Sig.Inv) -as.numeric(out) } set.seed(1234) system.time(out <- metropdir(obj = logf, dobj = gr.logf, initial = c(1,1), lchain = 1e4,sd.prop=1,steplen=0,s=1, mu = mu, Sig.Inv = Sig.Inv)) #acceptance rate out$accept #density plot plot(density(out$batch[,1])) ## End(Not run) ``` ## Author(s) Abhirup Mallik, malli066@umn.edu ## See Also `metropdir.adapt` for adapting DMH, `iact` for integrated auto correlation times, `mcmcdiag`, `msjd` for mean squared jump distance. for summary of diagnostic measures of a chain, `multiESS` for Multivariate effective sample size.

metropdir function