# mcmc: Utility functions for MCMC output analysis In dlm: Bayesian and Likelihood Analysis of Dynamic Linear Models

## Description

Returns the mean, the standard deviation of the mean, and a sequence of partial means of the input vector or matrix.

## Usage

 ```1 2 3 4``` ```mcmcMean(x, sd = TRUE) mcmcMeans(x, sd = TRUE) mcmcSD(x) ergMean(x, m = 1) ```

## Arguments

 `x` vector or matrix containing the output of a Markov chain Monte Carlo simulation. `sd` logical: should an estimate of the Monte Carlo standard deviation be reported? `m` ergodic means are computed for `i` in `m:NROW(x)`

## Details

The argument `x` is typically the output from a simulation. If a matrix, rows are considered consecutive simulations of a target vector. In this case means, standard deviations, and ergodic means are returned for each column. The standard deviation of the mean is estimated using Sokal's method (see the reference). `mcmcMeans` is an alias for `mcmcMean`.

## Author(s)

Giovanni Petris [email protected]

## References

P. Green (2001). A Primer on Markov Chain Monte Carlo. In Complex Stochastic Systems, (Barndorff-Nielsen, Cox and Kl\"uppelberg, eds.). Chapman and Hall/CRC.

## Examples

 ```1 2 3 4 5 6``` ```x <- matrix(rexp(1000), nc=4) dimnames(x) <- list(NULL, LETTERS[1:NCOL(x)]) mcmcSD(x) mcmcMean(x) em <- ergMean(x, m = 51) plot(ts(em, start=51), xlab="Iteration", main="Ergodic means") ```

### Example output

```         A          B          C          D
0.05791186 0.06034600 0.05941779 0.06943281
A        B        C        D
0.9366   0.9688   1.0260   1.0400
(0.0579) (0.0603) (0.0594) (0.0694)
```

dlm documentation built on June 14, 2018, 1:03 a.m.