bmixgamma {bmixture} | R Documentation |
This function consists of several sampling algorithms for Bayesian estimation for finite mixture of Gamma distributions.
bmixgamma( data, k = "unknown", iter = 1000, burnin = iter / 2, lambda = 1, mu = NULL, nu = NULL, kesi = NULL, tau = NULL, k.start = NULL, alpha.start = NULL, beta.start = NULL, pi.start = NULL, k_max = 30, trace = TRUE )
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 |
mu |
The parameter of alpha in mixture distribution. |
nu |
The parameter of alpha in mixture distribution. |
kesi |
The parameter of beta in mixture distribution. |
tau |
The parameter of beta in mixture distribution. |
k.start |
For the case |
alpha.start |
Initial value for parameter of mixture distribution. |
beta.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{α}, \underline{β}) = ∑_{i=1}^{k} π_{i} Gamma(x|α_{i}, β_{i}),
where k
is the number of components of mixture distribution (as a defult we assume is unknown
) and
Gamma(x|α_{i}, β_{i})=\frac{(β_{i})^{α_{i}}}{Γ(α_{i})} x^{α_{i}-1} e^{-β_{i}x}.
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).
An object with S3
class "bmixgamma"
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 |
alpha_sample |
A vector which includes the MCMC samples after burn-in from parameter |
beta_sample |
A vector which includes the MCMC samples after burn-in from parameter |
data |
original data. |
Reza Mohammadi a.mohammadi@uva.nl
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
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
Wade, S. and Ghahramani, Z. (2018) Bayesian Cluster Analysis: Point Estimation and Credible Balls (with Discussion). Bayesian Analysis, 13(2):559-626
## Not run: # simulating data from mixture of gamma with two components n = 1000 # number of observations weight = c( 0.6, 0.4 ) alpha = c( 12 , 1 ) beta = c( 3 , 2 ) data <- rmixgamma( n = n, weight = weight, alpha = alpha, beta = beta ) # plot for simulation data hist( data, prob = TRUE, nclass = 50, col = "gray" ) x = seq( 0, 10, 0.05 ) truth = dmixgamma( x, weight, alpha, beta ) lines( x, truth, lwd = 2 ) # Runing bdmcmc algorithm for the above simulation data set bmixgamma.obj <- bmixgamma( data, iter = 1000 ) summary( bmixgamma.obj ) plot( bmixgamma.obj ) ## End(Not run)