Description Usage Arguments Details Value Author(s) References See Also Examples

This function consists of several sampling algorithms for Bayesian estimation for finite mixture of Normal distributions.

1 2 3 |

`data ` |
The vector of data with size |

`k ` |
The number of components of mixture distribution. Defult is |

`iter ` |
The number of iteration for the sampling algorithm. |

`burnin ` |
The number of burn-in iteration for the sampling algorithm. |

`lambda ` |
For the case |

`k.start ` |
For the case |

`mu.start ` |
Initial value for parameter of mixture distribution. |

`sig.start` |
Initial value for parameter of mixture distribution. |

`pi.start ` |
Initial value for parameter of mixture distribution. |

`k_max ` |
For the case |

`trace ` |
Logical: if TRUE (default), tracing information is printed. |

Sampling from finite mixture of Gamma distribution, with density:

*Pr(x|k, \underline{π}, \underline{μ}, \underline{σ}) = ∑_{i=1}^{k} π_{i} N(x|μ_{i}, σ_{i}),*

where `k`

is the number of components of mixture distribution (as a defult we assume is `unknown`

).
The prior distributions are defined as below

* P(K=k) \propto \frac{λ^k}{k!}, \ \ \ k=1,...,k_{max},*

* π_{i} | k \sim Dirichlet( 1,..., 1 ),*

* α_{i} | k \sim Gamma(ν, υ),*

* β_i | k \sim G(η, τ),*

for more details see Mohammadi et al. (2013) and Mohammadi and Salehi-Rad (2012).

An object with `S3`

class `"bmixnorm"`

is returned:

`all_k ` |
A vector which includes the waiting times for all iterations. It is needed for monitoring the convergence of the BD-MCMC algorithm. |

`all_weights` |
A vector which includes the waiting times for all iterations. It is needed for monitoring the convergence of the BD-MCMC algorithm. |

`pi_sample ` |
A vector which includes the MCMC samples after burn-in from parameter |

`mu_sample ` |
A vector which includes the MCMC samples after burn-in from parameter |

`sig_sample ` |
A vector which includes the MCMC samples after burn-in from parameter |

`data ` |
The original data. |

Reza Mohammadi [email protected]

Stephens, M. (2000) Bayesian analysis of mixture models with an unknown number of components-an alternative to reversible jump methods. *Annals of statistics*, 28(1):40-74

Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components. *Journal of the Royal Statistical Society: series B*, 59(4):731-792

Green, P. J. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. *Biometrika*, 82(4):711-732

Cappe, O., Christian P. R., and Tobias, R. (2003) Reversible jump, birth and death and more general continuous time Markov chain Monte Carlo samplers. *Journal of the Royal Statistical Society: Series B*, 65(3):679-700

Mohammadi, A., Salehi-Rad, M. R., and Wit, E. C. (2013) Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. *Computational Statistics*, 28(2):683-700

Mohammadi, A. and Salehi-Rad, M. R. (2012) Bayesian inference and prediction in an M/G/1 with optional second service. *Communications in Statistics-Simulation and Computation*, 41(3):419-435

Wade, S. and Ghahramani, Z. (2018) Bayesian Cluster Analysis: Point Estimation and Credible Balls (with Discussion). *Bayesian Analysis*, 13(2):559-626

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ```
## Not run:
data( galaxy )
# Runing bdmcmc algorithm for the galaxy dataset
mcmc_sample = bmixnorm( data = galaxy )
summary( mcmc_sample )
plot( mcmc_sample )
print( mcmc_sample)
# simulating data from mixture of Normal with 3 components
n = 500
weight = c( 0.3, 0.5, 0.2 )
mean = c( 0 , 10 , 3 )
sd = c( 1 , 1 , 1 )
data = rmixnorm( n = n, weight = weight, mean = mean, sd = sd )
# plot for simulation data
hist( data, prob = TRUE, nclass = 30, col = "gray" )
x = seq( -20, 20, 0.05 )
densmixnorm = dmixnorm( x, weight, mean, sd )
lines( x, densmixnorm, lwd = 2 )
# Runing bdmcmc algorithm for the above simulation data set
bmixnorm.obj = bmixnorm( data, k = 3, iter = 1000 )
summary( bmixnorm.obj )
## End(Not run)
``` |

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