Nmix {Nmix}

Bayesian Inference on Univariate Normal Mixtures

Description

Wrapper for Nmix Fortran program that uses a Reversible jump Markov chain sampler to simulate from the posterior distribution of a univariate normal mixture model

Usage

Nmix(y,tag="",seed=0,nsweep=10000,nburnin=0,
	kinit=1,qempty=1,qprior=0,qunif=0,qfix=0,qrkpos=0,qrange=1,qkappa=0,qbeta=1,
	alpha=2,beta=0.02,delta=1,eee=0,fff=0,ggg=0.2,
	hhh=10,unhw=1.0,kappa=1.0,lambda=-1,xi=0.0,sp=1,
	out="Dkdep",nspace=nsweep%/%1000,
	nmax=length(y),ncmax=30,ncmax2=10,ncd=7,ngrid=200,k1k2=c(2,8),
	idebug=-1,qdebug=0)

Arguments

y

either (i) a numerical data vector, (ii) a character scalar naming a numerical data vector in the global environment or (iii) a character scalar identifying a file y.dat in the current working directory containing a dataset

tag

name for the dataset, in the case that y is a numerical vector

seed

positive integer to set random number seed for a reproducible run, or 0 to initialise this process; output value can be used to replicate run subsequently

nsweep

number of sweeps

nburnin

length of burn in

kinit

integer, initial number of components

qempty

integer, 1 or 0 according to whether the empty-component birth/death moves should be used

qprior

integer, 1 or 0 according to whether the prior should be simulated instead of the posterior

qunif

integer, 1 or 0 according to whether the uniform proposals should be used for the component means instead of gaussian ones

qfix

integer, 1 or 0 according to whether the number of components should be held fixed (at the value of kinit)

qrkpos

integer, 1 or 0 according to whether the the number of non-empty components should be reported throughout

qrange

integer, 1 or 0 according to whether range-based parameter priors should be used

qkappa

integer, 1 or 0 according to whether kappa should be updated

qbeta

integer, 1 or 0 according to whether beta should be updated

alpha

numeric, set value of parameter alpha

beta

numeric, set value of parameter beta

delta

numeric, set value of parameter delta

eee

numeric, set value of parameter e

fff

numeric, set value of parameter f

ggg

numeric, set value of parameter g

hhh

numeric, set value of parameter h

unhw

numeric, set value of half-width for uniform proposals

kappa

numeric, set value of parameter kappa

lambda

numeric, set value of parameter lambda; the value -1 (the default) means a prior for k uniform on 1,2,...ncmax

xi

numeric, set value of parameter xi

sp

numeric, set value of parameter s

out

character string to specify optional output: string containing letters 'D','C','A','p','k','d','e','a' (any others are ignored); "*" is equivalent to "DCApkeda". See Details.

nspace

spacing between samples recorded in time-series traces (see Details)

nmax

integer, set upper bound for n

ncmax

integer, set upper bound for k; the same as kmax in the references

ncmax2

integer, set upper bound for k in output components pe and avn

ncd

integer, set number of conditional densities computed

ngrid

integer, set number of grid points for density evaluation

k1k2

vector of 2 integers, set minimum and maximum number of components for classification calculation

idebug

integer, number of sweep from which to print debugging information

qdebug

integer 1 or 0 according to whether debugging information is to be printed

Details

Output options: Summaries

letter		output component
D	density	den
C	classification	pcl and scl
A	average component occupancy	avn

Traces

letter		component of traces
p	parameters	pars
k	number of components	k
d	deviance	deviance
e	entropy	entropy
a	allocations	alloc

Value

An object of class nmix. List with numerous components, including

post

posterior distribution of number of components k

pe

list whose k'th component is a k by 3 matrix of estimated posterior means of weights, means and sd's for a mixture with k components

den

matrix of density estimates for k=1,2,...,6 and overall, preceded by row of abcissae at which they are evaluated - only when out includes "D"

avn

order-ncmax2 square matrix with (i,j) entry the posterior expected number of observations allocated to component i when there are j components in the mixture - only when out includes "A"

traces

list of named vectors, traces of selected statistics k, entropy (as defined in Green and Richardson, 2001), etc, sub-sampled to every nspace sweeps

iflag

integer flagging successful completion of simulation (0) or not (1)

Author(s)

Peter J. Green

References

Richardson, S. and Green, P. J. On Bayesian analysis of mixtures with an unknown number of components (with discussion), J. R. Statist. Soc. B, 1997, 59, 731-792; see also the correction in J. R. Statist. Soc. B, 1998, 60, 661.

Green, P. J. and Richardson, S. Modelling heterogeneity with and without the Dirichlet process, Scandinavian Journal of Statistics, 2001, 28, 355-375.

The author is grateful to Peter Soerensen for providing the interface to the C i/o routines used here, borrowed from his package qgg.

Examples

data(galx)
z<-Nmix('galx',nsweep=10000,nburnin=1000,out="Dkd")
print(z)
summary(z)
plot(z)