SliceSampler: A simple out stepping Slice sampler class
In dennisthemenace2/Slice: Slice Bayesian Inference Engine

Description Usage Arguments Details Value See Also Examples

This is a simple slice sampler that uses stepping out for interval estimation.

1	sampler = new("SliceSampler",model)

model

Constructor takes the model object create by the lexer

This sampler inherits from MCMCsampler, so that it can benefit from the there implement functionality. It overwrites the sample function that gets called with the likelihood and prior. It samples than a random value regarding the heights and uses the stepping out procedure to estimate the with that height.

Returns a valid sampler object.

Package Overview: Slice-Package

Base sampler class: Sampler

Slice sampler class: MCMCsampler

Maximum likelihood based sampler class: LaplaceApproximation

require('Slice')

#### ordered logit model

#Generate data:
set.seed(1234)
n<-200
x<-cbind(rnorm(n), rnorm(n) ) 
true.beta<-c(0.2,1.1)
true.alpha = c(0.5,1.8)
  

mu = x
y = c()

for( i in 1:n){
  probs=c()
  p = 0
  q = 0
  for(k in 1:(length(true.alpha)) ){
    tmp = 1/(1+exp(-(true.alpha[k]-mu[i]) ) )
    p = tmp -q
    q = tmp;
    probs = c(probs,p)
  }
  p = 1-q
  probs = c(probs,p)
  
  y=c(y,sample(c(1:3),probs,size = 1,replace=FALSE))

}

y = matrix(y,ncol=1)
## data is generated 

data_list = list(y=matrix(y),x1=matrix(x[,1]),x2=matrix(x[,2]) )

###define the model

sigmoid = function(x){ matrix(1/(1+exp(-x) )) }

model_str = '
model{
    mu = x1*beta[1] + x2*beta[2]

  alpha = sort(alpha0) 

    Q[1] =  sigmoid( alpha[1]-mu)
    p[1] = Q[1]

    for(j in 2:2){
      Q[j] = sigmoid(alpha[j]-mu)
      p[j] = Q[j] - Q[j-1]
    }
    p[3] =  1 - Q[2] 
    
    y ~ dcat(p[1],p[2],p[3])

 
  ## priors over thresholds
  for(r in 1:2){
    alpha0[r] ~ dnorm(0,1)
  }

  for(j in 1:2){
    beta[j] ~ dnorm(0,1)
  }
}
'

##create model
lex = new('Lexer')
lex$setModelString(model_str)
lex$setModelData(data_list)

lex$lexModel()

root_plate = lex$parseModel()

sliceSampler = new('SliceSampler',root_plate)

##### ok lets use it to set initial values and sample

samplesFromProblem = sliceSampler$takeSample(100,initialValues =list('alpha0[1]'=matrix(0),'alpha0[2]'=matrix(1) ))

colMeans(samplesFromProblem)