Neo-Normal Distributions Family for MCMC Models in JAGS

The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

Generate data

Create model for JAGS

mod <- "
model {
  # Likelihood
  for (i in 1:100) {
    x[i] ~ djskew.ep(2,1,0.8,1)
  }
}
"

Compile the model

modelv <- jags.model(textConnection(mod), n.chains=1, inits = list(".RNG.name" = "base::Wichmann-Hill",".RNG.seed" = 314159))
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 0
#>    Unobserved stochastic nodes: 100
#>    Total graph size: 103
#> 
#> Initializing model

Generate samples

samplesv <- coda.samples(modelv, variable.names = c("x"), n.iter = 1)
gen_datav <- (as.data.frame(as.matrix(samplesv)))
x <- as.numeric(gen_datav[1,])

Parameter Estimation

Create model for JAGS

model_string <- "
model {
  # Likelihood
  for (i in 1:100) {
    x[i] ~ djskew.ep(mu, tau,nu1, nu2)
  }
  
  # Prior distributions
  mu ~ dnorm(2,10000)
  tau ~ dgamma(10,10)
  nu1 ~ dgamma(10,10)
  nu2 ~ dgamma(10,10)
}
"

Compile the model

model <- jags.model(textConnection(model_string), data = list(x=c(x)),n.chains=2)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 100
#>    Unobserved stochastic nodes: 4
#>    Total graph size: 107
#> 
#> Initializing model

Generate samples from the posterior distribution

samples<- coda.samples(model, variable.names = c("mu", "tau", "nu1", "nu2"), n.iter = 2000)

Summary Samples

summary(samples)
#> 
#> Iterations = 1001:3000
#> Thinning interval = 1 
#> Number of chains = 2 
#> Sample size per chain = 2000 
#> 
#> 1. Empirical mean and standard deviation for each variable,
#>    plus standard error of the mean:
#> 
#>       Mean      SD  Naive SE Time-series SE
#> mu  1.9982 0.01001 0.0001583      0.0001971
#> nu1 0.7418 0.06269 0.0009913      0.0021317
#> nu2 1.1564 0.15378 0.0024315      0.0047601
#> tau 0.9625 0.25215 0.0039868      0.0093037
#> 
#> 2. Quantiles for each variable:
#> 
#>       2.5%    25%    50%    75%  97.5%
#> mu  1.9784 1.9914 1.9980 2.0049 2.0175
#> nu1 0.6323 0.6977 0.7371 0.7812 0.8789
#> nu2 0.8929 1.0504 1.1404 1.2488 1.4964
#> tau 0.5475 0.7865 0.9370 1.1077 1.5220

Traceplot

traceplot(samples)

Probability Density Function (PDF), Cumulative Density Function (CDF), and Invers CDF (Quantile)

model_string1 <- "
model {
    d <- djskew.ep(0.5,2,2,2,2)
        p <- pjskew.ep(0.5,2,2,2,2)
        q <- qjskew.ep(0.5,2,2,2,2)
}
"

Compile the model

model1 <- jags.model(textConnection(model_string1),  n.chains=2)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 0
#>    Unobserved stochastic nodes: 0
#>    Total graph size: 5
#> 
#> Initializing model

Generate samples from the posterior distribution

samples1<- coda.samples(model1, variable.names = c("d","p","q"), n.iter = 2)

Summary samples

summary(samples1)
#> 
#> Iterations = 1:2
#> Thinning interval = 1 
#> Number of chains = 2 
#> Sample size per chain = 2 
#> 
#> 1. Empirical mean and standard deviation for each variable,
#>    plus standard error of the mean:
#> 
#>       Mean SD Naive SE Time-series SE
#> d 0.008864  0        0              0
#> p 0.001350  0        0              0
#> q 2.000000  0        0              0
#> 
#> 2. Quantiles for each variable:
#> 
#>       2.5%      25%      50%      75%    97.5%
#> d 0.008864 0.008864 0.008864 0.008864 0.008864
#> p 0.001350 0.001350 0.001350 0.001350 0.001350
#> q 2.000000 2.000000 2.000000 2.000000 2.000000

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.