# Posterior distribution of the H parameter of the HKp, using a Metropolis algorithm.

### Description

The function inferfmetrop is used to create a sample from the posterior distribution of H. The function uses the eq.10 in Tyralis and Koutsoyiannis (2014) and a Metropolis algorithm to make inference on H.

### Usage

1 2 | ```
inferHmetrop(data, theta.init=0.7, burnin = 500, mcmc = 20000, thin = 1,
tune = 1,verbose = 0,seed = NA)
``` |

### Arguments

`data` |
time series data |

`theta.init` |
Starting values for the sampling. Must be of the appropriate
dimension. It must also be the case that |

`burnin` |
The number of burn-in iterations for the sampler. |

`mcmc` |
The number of MCMC iterations after burnin. |

`thin` |
The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value. |

`tune` |
The tuning parameter for the Metropolis sampling. Can be either a
positive scalar or a |

`verbose` |
A switch which determines whether or not the progress of the
sampler is printed to the screen. If |

`seed` |
The seed for the random number generator. If NA, the Mersenne
Twister generator is used with default seed 12345; if an integer is passed it
is used to seed the Mersenne twister. The user can also pass a list of length
two to use the L'Ecuyer random number generator, which is suitable for parallel
computation. The first element of the list is the L'Ecuyer seed, which is a
vector of length six or NA (if NA a default seed of |

### Value

An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.

### Note

The Metropolis algorithm uses the function MCMCmetrop1R from the package MCMCpack (Martin et al. 2011).

### Author(s)

Hristos Tyralis

### References

Martin A.D., Quinn K.M., Park J.H. (2011) MCMCpack: Markov chain Monte Carlo in
R, *Journal of Statistical Software* **42(9)**, 1–21.
http://www.jstatsoft.org/v42/i09.

Tyralis H., Koutsoyiannis, D. (2014) A Bayesian statistical model for deriving
the predictive distribution of hydroclimatic variables,
*Climate Dynamics* **42(11-12)**, 2867–2883.
http://dx.doi.org/10.1007/s00382-013-1804-y.

### Examples

1 2 3 4 5 6 | ```
# Posterior distribution of the H parameter of the HKp for the Nile time series.
samp.sim <- inferHmetrop(Nile,theta.init = 0.7,burnin = 500,mcmc = 500,thin = 1,
tune = 1,seed = 12345)
hist(samp.sim,breaks = 20,main = "Histogram of H",xlab = "H")
``` |