Description Usage Arguments Value Examples
Let p=(p1,...,pn) be a probability distribution defined on ysamp, the set of observed values, in a sample of size n from some population. p is assumed to belong to a polytope which is a lower dimensional subset of the n-dimensional simplex. The polytope is defined by a collection of linear equality and inequality constraints. A dependent sequence of values for p are generated by a Markov chain using the Metropolis-Hastings algorithm whose stationary distribution is the uniform distribution over the polytope. For each generated value of p the corresponding mean, sum(p*y) is found.
1 | constrppmn(A1,A2,A3,b1,b2,b3,initsol,reps,ysamp,burnin)
|
A1 |
The matrix for the equality constraints.This must always
contain the constraint |
A2 |
The matrix for the |
A3 |
The matrix for the |
b1 |
The rhs vector for |
b2 |
The rhs vector for |
b3 |
The rhs vector for |
initsol |
A vector which lies in the interior of the polytope. |
reps |
The total length of the chain that is generated. |
ysamp |
The observed sample from the population of interest. |
burnin |
The point in the chain at which the set of computed means begins. |
The returned value is a list whose first component is the chain
of the means of length reps - burnin -1
, whose second component
is the mean of the first component (i.e. the Polya estimate of the
population mean) and whose third component is the 2.5th and 97.5th
quantiles of the first component (i.e. an approximate 95 percent
confidence interval of the population mean).
1 2 3 4 5 6 7 8 9 10 11 12 | A1<-rbind(rep(1,6),1:6)
A2<-rbind(c(2,5,7,1,10,8),diag(-1,6))
b1<-c(1,3.5)
b2<-c(6,rep(0,6))
initsol<-rep(1/6,6)
rep<-1006
burnin<-1000
ysamp<-c(1,2.5,3.5,7,4.5,6)
out<-constrppmn(A1,A2,NULL,b1,b2,NULL,initsol,rep,ysamp,burnin)
out[[1]] # the Markov chain of the means.
out[[2]] # the average of out[[1]]
out[[3]] # the 2.5th and 97.5th quantiles of out[[1]]
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