Version: 0.7-6
Date: 2023-04-11
Title: Bayesian Mixture Models with JAGS
Depends: R (≥ 2.10),
Imports: graphics, stats, methods, rjags (≥ 2.1.0), coda (≥ 0.13)
Description: Fits finite mixture models of univariate Gaussian distributions using JAGS within a Bayesian framework.
URL: https://statmath.wu.ac.at/~gruen/BayesMix/
License: GPL-2 | GPL-3
NeedsCompilation: no
Packaged: 2023-04-12 13:21:18 UTC; gruen
Author: Bettina Gruen ORCID iD [aut, cre], Martyn Plummer ORCID iD [ctb]
Maintainer: Bettina Gruen <Bettina.Gruen@R-project.org>
Repository: CRAN
Date/Publication: 2023-04-12 13:50:02 UTC

Plot identifiability diagnostics for JAGSrun object

Description

Two different plots are currently provided: a plot of different variables against each other and a plot of the same variable against its values in the other classes.

Usage

BMMdiag(object, which = 1:2, variables, ask = interactive(), fct1,
        fct2, xlim, ylim, auto.layout = TRUE, caption = NULL,
        main = "", ...)

Arguments

object

a JAGSrun object with model of class BMMmodel.

which

if only one of the plots is required, specify its number.

variables

if variables is missing, the names are taken from the JAGSrun object.

ask

prompt user before each page of plots

fct1

string: name of transformation function for variable on x-axis.

fct2

string: name of transformation function for variable on y-axis.

xlim

if no range for xlim is specified, a sensible range is taken.

ylim

if no range for ylim is specified, a sensible range is taken.

auto.layout

logical: if TRUE puts each of the two different plots on one figure.

caption

captions to appear above the plots.

main

title to each plot (in addition to the above 'caption').

...

further graphical parameters (see 'plot.xy' and 'par') may also be supplied as arguments.

Details

The plots help determining which variable will induce a unique labelling when taken for ordering of the segments and indicate if the model is overfitted by specifying too many segments.

Author(s)

Bettina Gruen

Creates bugs model.

Description

Creates the BUGS-model specification and return the values for the initialization, the prior specification and the observations.

Usage

BMMmodel(y, k, priors, inits = "initsFS", aprioriWeights = 1,
         no.empty.classes = FALSE, restrict = "none", ...)

Arguments

y

a numeric vector.

k

integer indicating the number of segments.

priors

specification of priors by a named list or a BMMpriors object.

inits

specification of initial values by a named list or string indicating the function to be called.

aprioriWeights

specification of prior of the a-priori weights. If aprioriWeights does not have length = k, there is an equal prior for the a-priori weights assumed.

no.empty.classes

logical: should it be prevented that empty classes arise during sampling.

restrict

one of "none", "mu", "tau".

...

further parameters for the function specified in inits.

Details

By default the function initsFS is called for generating initial values. Any other function specified by inits is assumed to have at least x, k and restrict as input parameters.

The parameter restrict indicates if a location-shift model ("tau"), a scale contaminated model ("mu") or a model where both variables vary over components shall be fitted.

If the logical no.empty.classes is TRUE there are observations added to the model that the classes are not empty. This signifies that the likelihood when sampling the class affiliations is changed thus that any data point which is sampled and is the last one in its class stays there.

Value

If y is specified an object of class BMMmodel is returned with components:

inits

named list.

data

named list.

bugs

text for .bug-file with prefix missing.

If y is missing an object of class BMMsetup is returned containing the parameter specifications. When JAGScall is called with this object as model argument, BMMmodel is called with y and the other parameters as input arguments before calling JAGS.

Author(s)

Bettina Gruen

See Also

JAGSrun, initsFS

Examples

data("fish", package = "bayesmix")
model <- BMMmodel(fish, k = 4, priors = list(kind = "independence",
                  parameter = "priorsFish", hierarchical = "tau"),
                  initialValues = list(S0 = 2))
model

Plot aposteriori probabilities of data points

Description

Given a JAGSrun object with model of class BMMmodel the aposteriori probabilities are determined. If plot=TRUE, the resulting object of class BMMposteriori is plotted.

Usage

BMMposteriori(object, class, caption = NULL, plot = TRUE,
              auto.layout = TRUE, ...)

Arguments

object

a JAGSrun object with model of class BMMmodel.

class

a vector of integers indicating for which classes the posterior probabilities shall be plotted. The default is all.

caption

captions to appear above the plots.

plot

logical indicating if a plot shall be made.

auto.layout

logical: if TRUE puts all classes in the posterior probabilities plot on the same figure.

...

further graphical parameters may also be supplied as arguments.

Details

Given a JAGSrun object with model of class BMMmodel the a posteriori probabilities are calculated for the unique data points with respect to the components specified by class.

Value

There is a BMMposteriori object returned which is a list including the following components

data

vector of unique data points.

post

a matrix including the posteriori probability of the data points for each class.

Author(s)

Bettina Gruen

See Also

plot.BMMposteriori

Create a 'BMMpriors' object

Description

This function enables a comfortable creation of BMMpriors objects, which can be used for specifying the priors of a BMMmodel.

Usage

BMMpriors(specification, y, eps = 10^-16)

Arguments

specification

named list including kind, parameter, hierarchical and mod.

y

a numeric vector.

eps

a numeric value indicating the smallest value for flat priors.

Details

In specification kind can be used for specifying if an "independent" or a "conditionallyconjugate" prior shall be used. parameter can be a named list of values for the prior variables or a function name (e.g., "priorsUncertain", "priorsFish", "priorsRaftery"). hierarchical can be NULL or "tau" if a hierarchical prior shall be taken for \tau. mod is a named list which provides the possibility to override the values from parameter.

Value

There is an object BMMpriors returned with components

name

vector indicating which kind of prior is specified and if it is an hierarchical prior and if appropriate with respect to which variable.

var

list of variables in the prior and their specified values.

Author(s)

Bettina Gruen

Examples

  data("fish", package = "bayesmix")
  priors <- BMMpriors(y = fish)

Call jags

Description

Using functionality from package rjags the JAGS model is created and posterior draws are sampled.

Usage

JAGScall(model, y, prefix, control, ...)

Arguments

model

JAGSmodel object or output from BMMmodel.

y

a numeric vector.

prefix

character: prefix for .bug-file.

control

named list or JAGScontrol object.

...

additional parameters handed over to BMMmodel.

Value

Returns a "JAGSrun" object.

Author(s)

Bettina Gruen

See Also

JAGSrun

Control parameters for the sampling.

Description

The information on the number of burn-in draws and monitored draws is specified. Furthermore, it includes the information which variables shall be monitored and possibly a seed and a random number generator (RNG).

Usage

JAGScontrol(variables, n.iter = 1000, thin = 1, burn.in = 0, seed,
            rng = c("base::Wichmann-Hill",
                    "base::Marsaglia-Multicarry",
                    "base::Super-Duper",
                    "base::Mersenne-Twister"))

Arguments

variables

names of variables which shall be monitored.

n.iter

number of monitored draws.

thin

thinning interval.

burn.in

number of discarded burn-in draws.

seed

integer setting the seed for the RNG.

rng

specification of RNG.

Value

An object of class JAGScontrol is returned which is a list containing the specified information.

Author(s)

Bettina Gruen

See Also

JAGSrun

Examples

control <- JAGScontrol(variables = "mu")
control

MCMC sampling of Bayesian models

Description

Calls jags for MCMC sampling.

Usage

JAGSrun(y, prefix = yname, model = BMMmodel(k = 2),
        control = JAGScontrol(variables = c("mu", "tau", "eta")),
        tmp = TRUE, cleanup = TRUE, ...)

Arguments

y

a numeric vector.

prefix

character: prefix for .bug-file.

model

object of class JAGSmodel or output from BMMmodel.

control

specification of control by a JAGScontrol object.

tmp

logical: shall the files be written in a temporary directory.

cleanup

logical: shall the created files be removed.

yname

a character string with the actual y argument name.

...

further parameters handed over to BMMmodel where it is used for the function specifying the initial values, e.g., initsFS.

Details

This function is a wrapper calling JAGScall.

Value

Returns a JAGSrun object with components

call

the matched call.

results

MCMC results obtained by calling functionality from package rjags.

model

a JAGSmodel object.

variables

vector containing the names of the monitored variables.

data

a numeric vector.

Author(s)

Bettina Gruen

See Also

JAGScall, BMMmodel, initsFS

Examples

data("fish", package = "bayesmix")
prefix <- "fish"
variables <- c("mu","tau","eta")
k <- 3
modelFish <- BMMmodel(k = k, priors = list(kind = "independence",
                      parameter = "priorsFish", hierarchical = "tau"))
controlFish <- JAGScontrol(variables = c(variables, "S"), n.iter = 100)
z1 <- JAGSrun(fish, prefix, model = modelFish, initialValues = list(S0 = 2),
              control = controlFish, cleanup = TRUE, tmp = FALSE)
zSort <- Sort(z1, "mu")
BMMposteriori(zSort)

data("darwin", package = "bayesmix")
prefix <- "darwin"
k <- 2
modelDarwin <- BMMmodel(k = k, priors = list(kind = "independence",
                        parameter = "priorsUncertain"),
                        aprioriWeights = c(1, 15),
                        no.empty.classes = TRUE, restrict = "tau")
z2 <- JAGSrun(darwin, prefix, model = modelDarwin, control =
              JAGScontrol(variables = variables, n.iter = 3000,
              burn.in = 1000), cleanup = TRUE, tmp = FALSE)
plot(z2, variables = "mu")

Sort MCMC chains according to certain variables

Description

Ascending sorting of results of JAGSrun object with model of class BMMmodel with respect to a given variable.

Usage

Sort(x, by = NULL)

Arguments

x

a JAGSrun object with model of class BMMmodel.

by

variable name according to which the segments shall be ordered.

Details

If by is not specified, the first variable in the corresponding vector of the JAGSrun object is taken.

Value

The input object with results sorted in ascending order according to the variable given in by is returned.

Warning

If there arise problems, the original object is returned with a warning.

Author(s)

Bettina Gruen

Differences in heights between plants

Description

A numeric vector containing 15 observations of differences in heights between pairs of self-fertilized and cross-fertilized plants grown in the same condition.

Usage

data(darwin)

Format

A numeric vector of length 15.

Details

Darwin's data set contains two extremely small values. Therefore, this data set can be used for outlier modelling.

Source

Abraham, B. and G. Box (1978) Linear models and spurious observations. Applied Statistics, 27, 131–8.

Examples

data("darwin", package = "bayesmix")
## Estimated sample density
plot(density(darwin[[1]]), ylim = c(0, 0.02), main = "Outlier modelling")
ss <- seq(-100, 100, by = 1)
## Normal density with estimated mean and sd of whole sample
lines(ss, dnorm(ss, mean = mean(darwin[[1]]), sd = sd(darwin[[1]])), col = "red")
## Normal density with estimated mean and sd of sample, where the 2
## extremely small values are removed
lines(ss, dnorm(ss, mean = mean(darwin[-c(1:2),1]),
      sd = sd(darwin[-c(1:2),1])), col = "green")

Fish length data

Description

A numeric vector containing 256 observations of fish lengths.

Usage

data(fish)

Format

A numeric vector of length 256.

Details

This data set can be used for modeling unobserved heterogeneity, as it can be assumed that underlying categories present in the data are the age groups to which the fish belong.

Source

D. M. Titterington, A. F. M. Smith and U.E. Makov (1985) Statistical Analysis of Finite Mixture Distributions. Wiley.

Examples

data("fish", package = "bayesmix")
ss <- seq(-3, 13, by = 0.01)
hist(fish[[1]], 20, freq = FALSE, main = "Fish data")
lines(ss, dnorm(ss, mean(fish[[1]]), sd(fish[[1]])), col = "red")

Create initial values

Description

Initial values for nodes are created after the suggestion in Sylvia Fruehwirth-Schnatter's book.

Usage

initsFS(x, k, restrict, initialValues = list())

Arguments

x

a numeric vector.

k

number of segments.

initialValues

additional initial values specifications.

restrict

one of "none", "mu", "tau".

Details

The initial values for \mu are determined by the quantiles of the data, those for \eta give equal weight on each segment and those for \tau are equal for all segments and estimated by the inverse of the IQR of the data divided by 1.34 and squared.

Value

A list with initial values for the parameter indicated by the name of the respective list element is returned.

Author(s)

Bettina Gruen

Plot a posteriori probabilities of data points

Description

Plot method for object of class BMMposteriori, typically called by BMMposteriori.

Usage

## S3 method for class 'BMMposteriori'
plot(x, caption, main = "", ...)

Arguments

x

a BMMposteriori object.

caption

captions to appear above the plots.

main

title to each plot-in addition to the above caption.

...

further graphical parameters may also be supplied as arguments.

Details

This function is called by BMMposteriori if plot = TRUE.

Author(s)

Bettina Gruen

See Also

BMMposteriori

Plot JAGSrun object

Description

Plots mcmc chains of a JAGSrun object.

Usage

## S3 method for class 'JAGSrun'
plot(x, variables = NULL, trace = TRUE, density = TRUE,
     smooth = TRUE, bwf, num, xlim, auto.layout = TRUE,
     ask = interactive(), ...)

Arguments

x

a JAGSrun object.

variables

names of variables which shall be plotted. Default are all names of results except those with a column dimension larger than the number of classes k.

trace

plot trace of each variable.

density

plot density estimate of each variable.

smooth

draw a smooth line through trace plots.

bwf

bandwidth function for density plots.

num

if not all classes of a variable shall be plotted, a subset can be specified.

xlim

if not specified, the range of each variable over all classes is taken as default.

auto.layout

automatically generate output format.

ask

prompt user before each page of plots.

...

further arguments for densityplot.

Details

Adapted from plot.mcmc.

Currently only implemented for JAGSrun objects with model of class BMMmodel. Otherwise the default plot method for the results of the JAGSrun object is called (plot.mcmc).

Author(s)

Bettina Gruen

See Also

plot.mcmc, BMMdiag, BMMposteriori

Create list of prior specifications

Description

Given the data values for the priors are determined.

Usage

priorsFish(y, eps = 10^-16)
priorsRaftery(y)
priorsUncertain(y, eps = 10^-16)

Arguments

y

a numeric vector.

eps

a numeric value indicating the smallest value for flat priors.

Details

Values for the prior parameter b0, B0, nu0 and S0 are determined.

Value

There is a list returned with named components of the prior parameters.

Author(s)

Bettina Gruen

Randomly permute segments for MCMC draws

Description

Random permutation of segment labels for each draw in order to get a better estimate of the unrestricted likelihood.

Usage

randomPermutation(x)

Arguments

x

a JAGSrun object with model of class BMMmodel.

Details

The draws are permuted with respect to the different classes k.

Value

The input object with permuted results for each draw is returned.

Warning

Any variables where there are neither k different chains nor only one chain observed are dropped.

Author(s)

Bettina Gruen