anm.mc.bvn {asbio} R Documentation

## Animation of Markov Chain Monte Carlo walks in bivariate normal space

### Description

The algorithm can use three different variants on MCMC random walks: Gibbs sampling, the Metropolis algorithm, and the Metropolis-Hastings algorithms to move through univariate `anm.mc.norm` and bivariate normal probability space. The jumping distribution is also bivariate normal with a mean vector at the current bivariate coordinates. The jumping kernel modifies the jumping distribution through multiplying the variance covariance of this distribution by the specified constant.

### Usage

```anm.mc.bvn(start = c(-4, -4), mu = c(0, 0), sigma = matrix(2, 2, data = c(1, 0,
0, 1)), length = 1000, sim = "M", jump.kernel = 0.2, xlim = c(-4, 4),
ylim = c(-4, 4), interval = 0.01, show.leg = TRUE, cex.leg = 1, ...)

anm.mc.norm(start = -4, mu = 0, sigma = 1, length = 2000, sim = "M",
jump.kernel = 0.2, xlim = c(-4, 4), ylim = c(0, 0.4), interval = 0.01,
show.leg = TRUE,...)

anm.mc.bvn.tck()
```

### Arguments

 `start` A two element vector specifying the bivariate starting coordinates. `mu` A two element vector specifying the mean vector for the proposal distribution. `sigma` A 2 x 2 matrix specifying the variance covariance matrix for the proposal distribution. `length` The length of the MCMC chain. `sim` Simulation method used. Must be one of `"G"` indicating Gibbs sampling, `"M"` indicating the Metropolis algorithm, or `"MH"` indicating the Metropolis-Hastings algorithm (Gibbs sampling is not implemented for `anm.mc.norm`). `jump.kernel` A number > 0 that will serve as a (squared) multiplier for the proposal variance covariance. The result of this multiplication will be used as the variance covariance matrix for the jumping distribution. `xlim` A two element vector describing the upper and lower limits of the x-axis. `ylim` A two element vector describing the upper and lower limits of the y-axis. `interval` Animation interval `show.leg` Logical. Indicating whether or not the chain length should be shown. `cex.leg` Character expansion for legend. `...` Additional arguments from `plot`.

### Value

The function returns two plots. These are: 1) the proposal bivariate normal distribution in which darker shading indicates higher density, and 2) an animated plot showing the MCMC algorithm walking through the probability space.

Ken Aho

### References

Gelman, A., Carlin, J. B., Stern, H. S., and D. B. Rubin (2003) Bayesian Data Analysis, 2nd edition. Chapman and Hall/CRC.

[Package asbio version 1.7 Index]