Package 'dirichletprocess'

Title: Build Dirichlet Process Objects for Bayesian Modelling
Description: Perform nonparametric Bayesian analysis using Dirichlet processes without the need to program the inference algorithms. Utilise included pre-built models or specify custom models and allow the 'dirichletprocess' package to handle the Markov chain Monte Carlo sampling. Our Dirichlet process objects can act as building blocks for a variety of statistical models including and not limited to: density estimation, clustering and prior distributions in hierarchical models. See Teh, Y. W. (2011) <https://www.stats.ox.ac.uk/~teh/research/npbayes/Teh2010a.pdf>, among many other sources.
Authors: Gordon J. Ross [aut], Dean Markwick [aut, cre], Kees Mulder [ctb] , Giovanni Sighinolfi [ctb], Filippo Fiocchi [ctb]
Maintainer: Dean Markwick <[email protected]>
License: GPL-3
Version: 0.4.2
Built: 2025-02-15 04:40:24 UTC
Source: https://github.com/dm13450/dirichletprocess

Help Index

Create a Beta mixture with zeros at the boundaries.

Description

Create a Beta mixture with zeros at the boundaries.

Usage

BetaMixture2Create(priorParameters = 2, mhStepSize = c(1, 1), maxT = 1)

Arguments

priorParameters

The prior parameters for the base measure.
mhStepSize

The Metropolis Hastings step size. A numeric vector of length 2.
maxT

The upper bound of the Beta distribution. Defaults to 1 for the standard Beta distribution.

Value

A mixing distribution object.

Create a Beta mixing distribution.

Description

See DirichletProcessBeta for the default prior and hyper prior distributions.

Usage

BetaMixtureCreate(
  priorParameters = c(2, 8),
  mhStepSize = c(1, 1),
  maxT = 1,
  hyperPriorParameters = c(1, 0.125)
)

Arguments

priorParameters

The prior parameters for the base measure.
mhStepSize

The Metropolis Hastings step size. A numeric vector of length 2.
maxT

The upper bound of the Beta distribution. Defaults to 1 for the standard Beta distribution.
hyperPriorParameters

The parameters for the hyper prior.

Value

A mixing distribution object.

Add burn-in to a dirichletprocess object

Description

Add burn-in to a dirichletprocess object

Usage

Burn(dpobj, niter)

Arguments

dpobj

A dirichletprocess object.
niter

Number of iterations to burn.

Value

A dirichletprocess object where all chain objects have the first niter iterations are removed.

Examples

dp <- Fit(DirichletProcessGaussian(rnorm(10)), 100)
DiagnosticPlots(dp)
burned_dp <- Burn(dp, 50)
DiagnosticPlots(burned_dp)

Change the observations of fitted Dirichlet Process.

Description

Using a fitted Dirichlet process object include new data. The new data will be assigned to the best fitting cluster for each point.

Usage

ChangeObservations(dpobj, newData)

Arguments

dpobj

The Dirichlet process object.
newData

New data to be included

Value

Changed Dirichlet process object

Examples

y <- rnorm(10)
dp <- DirichletProcessGaussian(y)
dp <- ChangeObservations(dp, rnorm(10))

Update the component of the Dirichlet process

Description

Update the cluster assignment for each data point.

Usage

ClusterComponentUpdate(dpObj)

## S3 method for class 'conjugate'
ClusterComponentUpdate(dpObj)

## S3 method for class 'hierarchical'
ClusterComponentUpdate(dpObj)

Arguments

dpObj

Dirichlet Process object

Value

Dirichlet process object with update components.

Examples

dp <- DirichletProcessGaussian(rnorm(10))
dp <- ClusterComponentUpdate(dp)

Predict the cluster labels of some new data.

Description

Given a fitted Dirichlet process object and some new data use this function to predict what clusters the new data belong to and associated cluster parameters.

Usage

ClusterLabelPredict(dpobj, newData)

Arguments

dpobj

Fitted Dirichlet Process
newData

New data to have cluster labels predicted.

Value

A list of the predicted cluster labels of some new unseen data.

Examples

y <- rnorm(10)
dp <- DirichletProcessGaussian(y)
dp <- Fit(dp, 5)
newY <- rnorm(10, 1)
pred <- ClusterLabelPredict(dp, newY)

Update the cluster parameters of the Dirichlet process.

Description

Update the parameters of each individual cluster using all the data assigned to the particular cluster. A sample is taken from the posterior distribution using a direct sample if the mixing distribution is conjugate or the Metropolis Hastings algorithm for non-conjugate mixtures.

Usage

ClusterParameterUpdate(dpObj)

Arguments

dpObj

Dirichlet process object

Value

Dirichlet process object with update cluster parameters

Examples

dp <- DirichletProcessGaussian(rnorm(10))
dp <- ClusterParameterUpdate(dp)

Diagnostic plots for dirichletprocess objects

Description

Plot several diagnostic plots for dirichletprocess objects. Because the dimension of the dirichletprocess mixture is constantly changing, it is not simple to create meaningful plots of the sampled parameters. Therefore, the plots focus on the likelihood, alpha, and the number of clusters.

Usage

DiagnosticPlots(dpobj, gg = FALSE)

AlphaTraceplot(dpobj, gg = TRUE)

AlphaPriorPosteriorPlot(
  dpobj,
  prior_color = "#2c7fb8",
  post_color = "#d95f02",
  gg = TRUE
)

ClusterTraceplot(dpobj, gg = TRUE)

LikelihoodTraceplot(dpobj, gg = TRUE)

Arguments

dpobj

A dirichletprocess object that was fit.
gg

Logical; whether to create a ggplot or base R plot (if gg = FALSE). For DiagnosticPlots, this means that the plots will be given one-by-one, while base plots can be arranged in a grid.
prior_color

For AlphaPriorPosteriorPlot, the color of the prior function.
post_color

For AlphaPriorPosteriorPlot, the color of the posterior histogram.

Value

If gg = TRUE, a ggplot2 object. Otherwise, nothing is returned and a base plot is plotted.

Functions

  • AlphaTraceplot(): Trace plot of alpha.

  • AlphaPriorPosteriorPlot(): Plot of the prior and posterior of alpha.

  • ClusterTraceplot(): Trace plot of the number of clusters.

  • LikelihoodTraceplot(): Trace plot of the likelihood of the data for each iteration.

Examples

dp <- Fit(DirichletProcessGaussian(rnorm(10)), 100)
DiagnosticPlots(dp)

Create a generic Dirichlet process hidden Markov Model

Description

Create a hidden Markov model where the data is believed to be generated from the mixing object distribution.

Usage

DirichletHMMCreate(x, mdobj, alpha, beta)

Arguments

x

Data to be modelled
mdobj

Mixing disitribution object
alpha

Alpha parameter
beta

Beta parameter

A flexible package for fitting Bayesian non-parametric models.

Description

Create, fit and take posterior samples from a Dirichlet process.

Dirichlet process mixture of the Beta distribution.

Description

Create a Dirichlet process object using the mean and scale parameterisation of the Beta distribution bounded on (0,maxY)(0, maxY).

Usage

DirichletProcessBeta(
  y,
  maxY,
  g0Priors = c(2, 8),
  alphaPrior = c(2, 4),
  mhStep = c(1, 1),
  hyperPriorParameters = c(1, 0.125),
  verbose = TRUE,
  mhDraws = 250
)

Arguments

y

Data for which to be modelled.
maxY

End point of the data
g0Priors

Prior parameters of the base measure (α0,β0)(\alpha _0, \beta _0).
alphaPrior

Prior parameters for the concentration parameter. See also UpdateAlpha.
mhStep

Step size for Metropolis Hastings sampling algorithm.
hyperPriorParameters

Hyper-prior parameters for the prior distributions of the base measure parameters (a,b)(a, b).
verbose

Logical, control the level of on screen output.
mhDraws

Number of Metropolis-Hastings samples to perform for each cluster update.

Details

G0(μ,ν∣maxY,α0,β0)=U(μ∣0,maxY)Inv−Gamma(ν∣α0,β0)G_0 (\mu , \nu | maxY, \alpha _0 , \beta _0) = U(\mu | 0, maxY) \mathrm{Inv-Gamma} (\nu | \alpha _0, \beta _0).

The parameter β0\beta _0 also has a prior distribution β0∼Gamma(a,b)\beta _0 \sim \mathrm{Gamma} (a, b) if the user selects Fit(...,updatePrior=TRUE).

Value

Dirichlet process object

Dirichlet process mixture of Beta distributions with a Uniform Pareto base measure.

Description

Create a Dirichlet process object using the mean and scale parameterisation of the Beta distribution bounded on (0,maxY)(0, maxY). The Pareto distribution is used as a prior on the scale parameter to ensure that the likelihood is 0 at the boundaries.

Usage

DirichletProcessBeta2(
  y,
  maxY,
  g0Priors = 2,
  alphaPrior = c(2, 4),
  mhStep = c(1, 1),
  verbose = TRUE,
  mhDraws = 250
)

Arguments

y

Data for which to be modelled.
maxY

End point of the data
g0Priors

Prior parameters of the base measure (γ(\gamma.
alphaPrior

Prior parameters for the concentration parameter. See also UpdateAlpha.
mhStep

Step size for Metropolis Hastings sampling algorithm.
verbose

Logical, control the level of on screen output.
mhDraws

Number of Metropolis-Hastings samples to perform for each cluster update.

Details

G0(μ,ν∣maxY,α)=U(μ∣0,maxY)Pareto(ν∣xm,γ)G_0 (\mu , \nu | maxY, \alpha ) = U(\mu | 0, maxY) \mathrm{Pareto} (\nu | x_m, \gamma).

Value

Dirichlet process object

Create a Dirichlet Process object

Description

Using a previously created Mixing Distribution Object (mdObject) create a Dirichlet process object. 'alphaPriorParameters sets the parameters for alpha using the shape-rate specification of the gamma distribution.

Usage

DirichletProcessCreate(
  x,
  mdObject,
  alphaPriorParameters = c(1, 1),
  mhDraws = 250
)

Arguments

x

Data
mdObject

Mixing Distribution Object
alphaPriorParameters

Prior parameters for the concentration parameter of the Dirichlet Process
mhDraws

Number of posterior samples to take in the nonconjugate case

Create a Dirichlet Mixture of Exponentials

Description

This is the constructor function to produce a dirichletprocess object with a Exponential mixture kernel with unknown rate. The base measure is a Gamma distribution that is conjugate to the posterior distribution.

Usage

DirichletProcessExponential(y, g0Priors = c(0.01, 0.01), alphaPriors = c(2, 4))

Arguments

y

Data
g0Priors

Base Distribution Priors α0,β0)\alpha _0 , \beta _0)
alphaPriors

Alpha prior parameters. See UpdateAlpha.

Details

G0(θ∣α0,β0)=Gamma(θ∣α0,β0)G_0(\theta | \alpha _0, \beta_0) = \mathrm{Gamma} \left(\theta | \alpha_0, \beta_0 \right)

Value

Dirichlet process object

Create a Dirichlet Mixture of Gaussians

Description

This is the constructor function to produce a dirichletprocess object with a Gaussian mixture kernel with unknown mean and variance. The base measure is a Normal Inverse Gamma distribution that is conjugate to the posterior distribution.

Usage

DirichletProcessGaussian(y, g0Priors = c(0, 1, 1, 1), alphaPriors = c(2, 4))

Arguments

y

Data
g0Priors

Base Distribution Priors γ=(μ0,k0,α0,β0)\gamma = (\mu _0, k_0 , \alpha _0 , \beta _0)
alphaPriors

Alpha prior parameters. See UpdateAlpha.

Details

G0(θ∣γ)=N(μ∣μ0,σ2k0)Inv−Gamma(σ2∣α0,β0)G_0(\theta | \gamma) = N \left(\mu | \mu_0, \frac{\sigma^2}{k_0} \right) \mathrm{Inv-Gamma} \left(\sigma^2 | \alpha_0, \beta_0 \right)

We recommend scaling your data to zero mean and unit variance for quicker convergence.

Value

Dirichlet process object

Create a Dirichlet Mixture of the Gaussian Distribution with fixed variance.

Description

Create a Dirichlet Mixture of the Gaussian Distribution with fixed variance.

Usage

DirichletProcessGaussianFixedVariance(
  y,
  sigma,
  g0Priors = c(0, 1),
  alphaPriors = c(2, 4)
)

Arguments

y

Data.
sigma

The fixed variance
g0Priors

Base Distribution Priors.
alphaPriors

Prior parameter distributions for the alpha concentration parameter.

Value

Dirichlet process object

Create a Hierarchical Dirichlet Mixture of Beta Distributions

Description

Create a Hierarchical Dirichlet Mixture of Beta Distributions

Usage

DirichletProcessHierarchicalBeta(
  dataList,
  maxY,
  priorParameters = c(2, 8),
  hyperPriorParameters = c(1, 0.125),
  gammaPriors = c(2, 4),
  alphaPriors = c(2, 4),
  mhStepSize = c(0.1, 0.1),
  numSticks = 50,
  mhDraws = 250
)

Arguments

dataList

List of data for each separate Dirichlet mixture object
maxY

Maximum value for the Beta distribution.
priorParameters

Prior Parameters for the top level base distribution.
hyperPriorParameters

Hyper prior parameters for the top level base distribution.
gammaPriors

Prior parameters for the top level concentration parameter.
alphaPriors

Prior parameters for the individual parameters.
mhStepSize

Metropolis Hastings jump size.
numSticks

Truncation level for the Stick Breaking formulation.
mhDraws

Number of Metropolis-Hastings samples to perform for each cluster update.

Value

dpobjlist A Hierarchical Dirichlet Process object that can be fitted, plotted etc.

Create a Hierarchical Dirichlet Mixture of semi-conjugate Multivariate Normal Distributions

Description

Create a Hierarchical Dirichlet Mixture of semi-conjugate Multivariate Normal Distributions

Usage

DirichletProcessHierarchicalMvnormal2(
  dataList,
  g0Priors,
  gammaPriors = c(2, 4),
  alphaPriors = c(2, 4),
  numSticks = 50,
  numInitialClusters = 1,
  mhDraws = 250
)

Arguments

dataList

List of data for each separate Dirichlet mixture object
g0Priors

Prior Parameters for the top level base distribution.
gammaPriors

Prior parameters for the top level concentration parameter.
alphaPriors

Prior parameters for the individual parameters.
numSticks

Truncation level for the Stick Breaking formulation.
numInitialClusters

Number of clusters to initialise with.
mhDraws

Number of Metropolis-Hastings samples to perform for each cluster update.

Value

dpobjlist A Hierarchical Dirichlet Process object that can be fitted, plotted etc.

Create a Dirichlet mixture of multivariate normal distributions.

Description

G0(μ,Λ∣μ0,κ0,ν0,T0)=N(μ∣μ0,(κ0Λ)−1)Wiν0(Λ∣T0)G_0 (\boldsymbol{\mu} , \Lambda | \boldsymbol{\mu _0} , \kappa _0, \nu _0, T_0) = N ( \boldsymbol{\mu} | \boldsymbol{\mu _0} , (\kappa _0 \Lambda )^{-1} ) \mathrm{Wi} _{\nu _0} (\Lambda | T_0)

Usage

DirichletProcessMvnormal(
  y,
  g0Priors,
  alphaPriors = c(2, 4),
  numInitialClusters = 1
)

Arguments

y

Data
g0Priors

Prior parameters for the base distribution.
alphaPriors

Alpha prior parameters. See UpdateAlpha.
numInitialClusters

Number of clusters to initialise with.

Create a Dirichlet mixture of multivariate normal distributions with semi-conjugate prior.

Description

Create a Dirichlet mixture of multivariate normal distributions with semi-conjugate prior.

Usage

DirichletProcessMvnormal2(y, g0Priors, alphaPriors = c(2, 4))

Arguments

y

Data
g0Priors

Prior parameters for the base distribution.
alphaPriors

Alpha prior parameters. See UpdateAlpha.

Create a Dirichlet Mixture of the Weibull distribution

Description

The likelihood is parameterised as Weibull(y∣a,b)=abya−1exp⁡(−xab)\mathrm{Weibull} (y | a, b) = \frac{a}{b} y ^{a-1} \exp \left( - \frac{x^a}{b} \right). The base measure is a Uniform Inverse Gamma Distribution. G0(a,b∣ϕ,α0,β0)=U(a∣0,ϕ)Inv−Gamma(b∣α0,β0)G_0 (a, b | \phi, \alpha _0 , \beta _0) = U(a | 0, \phi ) \mathrm{Inv-Gamma} ( b | \alpha _0, \beta _0) ϕ∼Pareto(xm,k)\phi \sim \mathrm{Pareto}(x_m , k) β∼Gamma(α0,β0)\beta \sim \mathrm{Gamma} (\alpha _0 , \beta _0) This is a semi-conjugate distribution. The cluster parameter a is updated using the Metropolis Hastings algorithm an analytical posterior exists for b.

Usage

DirichletProcessWeibull(
  y,
  g0Priors,
  alphaPriors = c(2, 4),
  mhStepSize = c(1, 1),
  hyperPriorParameters = c(6, 2, 1, 0.5),
  verbose = FALSE,
  mhDraws = 250
)

Arguments

y

Data.
g0Priors

Base Distribution Priors.
alphaPriors

Prior for the concentration parameter.
mhStepSize

Step size for the new parameter in the Metropolis Hastings algorithm.
hyperPriorParameters

Hyper prior parameters.
verbose

Set the level of screen output.
mhDraws

Number of Metropolis-Hastings samples to perform for each cluster update.

Value

Dirichlet process object

References

Kottas, A. (2006). Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. Journal of Statistical Planning and Inference, 136(3), 578-596.

Create a Exponential mixing distribution

Description

See DirichletProcessExponential for details on the base measure.

Usage

ExponentialMixtureCreate(priorParameters = c(0.01, 0.01))

Arguments

priorParameters

Prior parameters for the base measure.

Value

Mixing distribution object

Fit the Dirichlet process object

Description

Using Neal's algorithm 4 or 8 depending on conjugacy the sampling procedure for a Dirichlet process is carried out. Lists of both cluster parameters, weights and the sampled concentration values are included in the fitted dpObj. When update_prior is set to TRUE the parameters of the base measure are also updated.

Usage

Fit(dpObj, its, updatePrior = FALSE, progressBar = TRUE)

Arguments

dpObj

Initialised Dirichlet Process object
its

Number of iterations to use
updatePrior

Logical flag, defaults to FAlSE. Set whether the parameters of the base measure are updated.
progressBar

Logical flag indicating whether to display a progress bar.

Value

A Dirichlet Process object with the fitted cluster parameters and labels.

References

Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of computational and graphical statistics, 9(2), 249-265.

Fit a Hidden Markov Dirichlet Process Model

Description

Fit a Hidden Markov Dirichlet Process Model

Usage

## S3 method for class 'markov'
Fit(dpObj, its, updatePrior = F, progressBar = F)

Arguments

dpObj

Initialised Dirichlet Process object
its

Number of iterations to use
updatePrior

Logical flag, defaults to FAlSE. Set whether the parameters of the base measure are updated.
progressBar

Logical flag indicating whether to display a progress bar.

Value

A Dirichlet Process object with the fitted cluster parameters and states.

Create a Gaussian Mixing Distribution with fixed variance.

Description

Create a Gaussian Mixing Distribution with fixed variance.

Usage

GaussianFixedVarianceMixtureCreate(priorParameters = c(0, 1), sigma)

Arguments

priorParameters

The prior parameters for the base measure.
sigma

The fixed variance of the model.

Value

A mixing distribution object.

Create a Normal mixing distribution

Description

See DirichletProcessGaussian for details on the base measure.

Usage

GaussianMixtureCreate(priorParameters = c(0, 1, 1, 1))

Arguments

priorParameters

Prior parameters for the base measure.

Value

Mixing distribution object

Update the parameters of the hierarchical Dirichlet process object.

Description

Update the parameters of the hierarchical Dirichlet process object.

Usage

GlobalParameterUpdate(dpobjlist)

Arguments

dpobjlist

List of Dirichlet Process objects.

Create a Mixing Object for a hierarchical Beta Dirichlet process object.

Description

Create a Mixing Object for a hierarchical Beta Dirichlet process object.

Usage

HierarchicalBetaCreate(
  n,
  priorParameters,
  hyperPriorParameters,
  alphaPrior,
  maxT,
  gammaPrior,
  mhStepSize,
  num_sticks
)

Arguments

n

Number of data sets
priorParameters

The prior parameters for the top level base distribution.
hyperPriorParameters

Hyper prior parameters for the top level base distribution.
alphaPrior

Individual level concentration parameter priors.
maxT

Bounding value of the data.
gammaPrior

Concentration parameter for the top level priors.
mhStepSize

Metropolis Hastings step size for the posterior drawing.
num_sticks

Number of stick breaking values to use.

Value

A mixing distribution object.

Create a Mixing Object for a hierarchical semi-conjugate Multivariate Normal Dirichlet process object.

Description

Create a Mixing Object for a hierarchical semi-conjugate Multivariate Normal Dirichlet process object.

Usage

HierarchicalMvnormal2Create(
  n,
  priorParameters,
  alphaPrior,
  gammaPrior,
  num_sticks
)

Arguments

n

Number of data sets
priorParameters

The prior parameters for the top level base distribution.
alphaPrior

Individual level concentration parameter priors.
gammaPrior

Concentration parameter for the top level priors.
num_sticks

Number of stick breaking values to use.

Value

A mixing distribution object.

Initialise a Dirichlet process object

Description

Initialise a Dirichlet process object by assigning all the data points to a single cluster with a posterior or prior draw for parameters.

Usage

Initialise(
  dpObj,
  posterior = TRUE,
  m = 3,
  verbose = TRUE,
  numInitialClusters = 1
)

Arguments

dpObj

A Dirichlet process object.
posterior

TRUE/FALSE value for whether the cluster parameters should be from the posterior. If false then the values are from the prior.
m

Number of auxiliary variables to use for a non-conjugate mixing distribution. Defaults to m=3. See ClusterComponentUpdate for more details on m.
verbose

Logical flag indicating whether to output the acceptance ratio for non-conjugate mixtures.
numInitialClusters

Number of clusters to initialise with.

Value

A Dirichlet process object that has initial cluster allocations.

Mixing Distribution Likelihood

Description

Evaluate the Likelihood of some data xx for some parameter θ\theta.

Usage

## S3 method for class 'beta'
Likelihood(mdObj, x, theta)

## S3 method for class 'beta2'
Likelihood(mdObj, x, theta)

## S3 method for class 'exponential'
Likelihood(mdObj, x, theta)

Likelihood(mdObj, x, theta)

## S3 method for class 'mvnormal'
Likelihood(mdObj, x, theta)

## S3 method for class 'mvnormal2'
Likelihood(mdObj, x, theta)

## S3 method for class 'normalFixedVariance'
Likelihood(mdObj, x, theta)

## S3 method for class 'normal'
Likelihood(mdObj, x, theta)

Arguments

mdObj

Mixing Distribution
x

Data
theta

Parameters of distribution

Value

Likelihood of the data

The likelihood of the Dirichlet process object

Description

Calculate the likelihood of each data point with its parameter.

Usage

LikelihoodDP(dpobj)

Arguments

dpobj

The dirichletprocess object on which to calculate the likelihood.

The Likelihood function of a Dirichlet process object.

Description

Collecting the fitted cluster parameters and number of datapoints associated with each parameter a likelihood can be calculated. Each cluster is weighted by the number of datapoints assigned.

Usage

LikelihoodFunction(dpobj, ind)

Arguments

dpobj

Dirichlet process object.
ind

The iteration number. Defaults to the last iteration.

Value

A function f(x) that represents the Likelihood of the dpobj.

Examples

y <- rnorm(10)
dp <- DirichletProcessGaussian(y)
dp <- Fit(dp, 5)
f <- LikelihoodFunction(dp)
plot(f(-2:2))

Create a mixing distribution object

Description

The constructor function for a mixing distribution object. Use this function to prepare an object for use with the appropriate distribution functions.

Usage

MixingDistribution(
  distribution,
  priorParameters,
  conjugate,
  mhStepSize = NULL,
  hyperPriorParameters = NULL
)

Arguments

distribution

The name of the distribution mixture
priorParameters

The prior parameters
conjugate

Whether the prior is conjugate to the Likelihood.
mhStepSize

The scale of the proposal parameter for the Metropolis Hastings algorithm. Not needed for conjugate mixtures.
hyperPriorParameters

Vector of hyperPriorParameters for the distribution.

Create a multivariate normal mixing distribution with semi conjugate prior

Description

Create a multivariate normal mixing distribution with semi conjugate prior

Usage

Mvnormal2Create(priorParameters)

Arguments

priorParameters

The prior parameters for the Multivariate Normal.

Create a multivariate normal mixing distribution

Description

Create a multivariate normal mixing distribution

Usage

MvnormalCreate(priorParameters)

Arguments

priorParameters

The prior parameters for the Multivariate Normal.

Calculate the parameters that maximise the penalised likelihood.

Description

Used to find suitable starting parameters for nonconjugate mixtures. For some mixing distributions this hasn't been implemented yet.

Usage

## S3 method for class 'beta'
PenalisedLikelihood(mdObj, x)

PenalisedLikelihood(mdObj, x)

## Default S3 method:
PenalisedLikelihood(mdObj, x)

Arguments

mdObj

Mixing distribution object
x

Data

Plot the Dirichlet process object

Description

For a univariate Dirichlet process plot the density of the data with the posterior distribution and credible intervals overlayed. For multivariate data the first two columns of the data are plotted with the data points coloured by their cluster labels. The additional arguments are not used for multivariate data.

Usage

## S3 method for class 'dirichletprocess'
plot(x, ...)

plot_dirichletprocess_univariate(
  x,
  likelihood = FALSE,
  single = TRUE,
  data_fill = "black",
  data_method = "density",
  data_bw = NULL,
  ci_size = 0.05,
  xgrid_pts = 100,
  quant_pts = 100,
  xlim = NA
)

plot_dirichletprocess_multivariate(x)

Arguments

x

Dirichlet Process Object to plot
...

Further arguments, currently ignored.
likelihood

Logical, indicating whether to plot the likelihood from the dpobj.
single

Logical, indicating whether to draw the posterior from the last iteration or use the full cluster sequence.
data_fill

Passed to 'fill' in the data geom, for example a color. Defaults to "black".
data_method

A string containing either "density" (default), "hist"/"histogram", or "none". Data is plotted according to this method.
data_bw

Bandwith to be passed either as the binwidth of geom_histogram, or as the bw of geom_density.
ci_size

Numeric, the interval size to use. Defaults to .05.
xgrid_pts

Integer, the number of points on the x-axis to evaluate.
quant_pts

Integer, the number of posterior functions to use to obtain the posterior and its interval.
xlim

Default NA. If a vector of length two, the limits on the x-axis of the plot. If NA (default), the limits will be automatically chosen.

Value

A ggplot object.

Examples

dp <- DirichletProcessGaussian(c(rnorm(50, 2, .2), rnorm(60)))
dp <- Fit(dp, 100)
plot(dp)

plot(dp, likelihood = TRUE, data_method = "hist",
     data_fill = rgb(.5, .5, .8, .6), data_bw = .3)

Generate the posterior clusters of a Dirichlet Process

Description

Using the stick breaking representation the user can draw the posterior clusters and weights for a fitted Dirichlet Process. See also PosteriorFunction.

Usage

PosteriorClusters(dpobj, ind)

Arguments

dpobj

Fitted Dirichlet process
ind

Index for which the posterior will be drawn from. Defaults to the last iteration of the fit.

Value

A list with the weights and cluster parameters that form the posterior of the Dirichlet process.

Examples

y <- rnorm(10)
dp <- DirichletProcessGaussian(y)
dp <- Fit(dp, 5)
postClusters <- PosteriorClusters(dp)

Draw from the posterior distribution

Description

Draw from the posterior distribution

Usage

## S3 method for class 'exponential'
PosteriorDraw(mdObj, x, n = 1, ...)

PosteriorDraw(mdObj, x, n = 1, ...)

## S3 method for class 'mvnormal'
PosteriorDraw(mdObj, x, n = 1, ...)

## S3 method for class 'mvnormal2'
PosteriorDraw(mdObj, x, n = 1, ...)

## S3 method for class 'normalFixedVariance'
PosteriorDraw(mdObj, x, n = 1, ...)

## S3 method for class 'normal'
PosteriorDraw(mdObj, x, n = 1, ...)

## S3 method for class 'weibull'
PosteriorDraw(mdObj, x, n = 100, ...)

Arguments

mdObj

Mixing Distribution
x

Data
n

Number of draws
...

For a non-conjugate distribution the starting parameters. Defaults to a draw from the prior distribution.

Value

A sample from the posterior distribution

Calculate the posterior mean and quantiles from a Dirichlet process object.

Description

Calculate the posterior mean and quantiles from a Dirichlet process object.

Usage

PosteriorFrame(dpobj, xgrid, ndraws = 1000, ci_size = 0.1)

Arguments

dpobj

The Dirichlet process object to be drawn from.
xgrid

The x values the posterior is to be evaluated at.
ndraws

The number of posterior draws to take.
ci_size

The size of the credible interval draw in terms of percentage.

Value

A dataframe consisting of the posterior mean and credible intervals.

Generate the posterior function of the Dirichlet function

Description

Generate the posterior function of the Dirichlet function

Usage

PosteriorFunction(dpobj, ind)

Arguments

dpobj

Fitted Dirichlet Process object
ind

What iteration to draw the posterior function from. Defaults to the last iteration.

Value

A posterior function f(x).

Examples

y <- rnorm(10)
dp <- DirichletProcessGaussian(y)
dp <- Fit(dp, 5)
postFuncDraw <- PosteriorFunction(dp)
plot(-3:3, postFuncDraw(-3:3))

Calculate the posterior parameters for a conjugate prior.

Description

Calculate the posterior parameters for a conjugate prior.

Usage

PosteriorParameters(mdObj, x)

## S3 method for class 'mvnormal'
PosteriorParameters(mdObj, x)

## S3 method for class 'normalFixedVariance'
PosteriorParameters(mdObj, x)

## S3 method for class 'normal'
PosteriorParameters(mdObj, x)

Arguments

mdObj

Mixing distribution object
x

Data

Value

Parameters of the posterior distribution

Calculate how well the prior predicts the data.

Description

Calculate how well the prior predicts the data.

Usage

## S3 method for class 'exponential'
Predictive(mdObj, x)

Predictive(mdObj, x)

## S3 method for class 'mvnormal'
Predictive(mdObj, x)

## S3 method for class 'normalFixedVariance'
Predictive(mdObj, x)

## S3 method for class 'normal'
Predictive(mdObj, x)

Arguments

mdObj

The distribution
x

The data

Value

The probability of the data being from the prior.

Print the Dirichlet process object

Description

Print a Dirichlet process object. This will print some basic information about the dirichletprocess object.

Usage

## S3 method for class 'dirichletprocess'
print(x, param_summary = FALSE, digits = 2, ...)

Arguments

x

Dirichlet Process Object to print.
param_summary

If TRUE, print the overall averages of each parameter of the model. Note that this averages over all clusters and over all iterations, so it will only give a loose sense of the resulting DPM model.
digits

Integer; Number of digits to display.
...

Further arguments passed to or from other methods.

Examples

dp <- Fit(DirichletProcessGaussian(rnorm(10)), 100)
dp

Draw prior clusters and weights from the Dirichlet process

Description

Draw prior clusters and weights from the Dirichlet process

Usage

PriorClusters(dpobj)

Arguments

dpobj

A Dirichlet process object

Value

A list of weights and parameters of the prior distribution of the Dirichcet process

Calculate the prior density of a mixing distribution

Description

Calculate the prior density of a mixing distribution

Usage

## S3 method for class 'beta'
PriorDensity(mdObj, theta)

## S3 method for class 'beta2'
PriorDensity(mdObj, theta)

PriorDensity(mdObj, theta)

## S3 method for class 'weibull'
PriorDensity(mdObj, theta)

Arguments

mdObj

Mixing distribution
theta

Prior parameters

Draw from the prior distribution

Description

Draw from the prior distribution

Usage

## S3 method for class 'beta'
PriorDraw(mdObj, n = 1)

## S3 method for class 'beta2'
PriorDraw(mdObj, n = 1)

## S3 method for class 'exponential'
PriorDraw(mdObj, n)

PriorDraw(mdObj, n)

## S3 method for class 'mvnormal'
PriorDraw(mdObj, n = 1)

## S3 method for class 'mvnormal2'
PriorDraw(mdObj, n = 1)

## S3 method for class 'normalFixedVariance'
PriorDraw(mdObj, n = 1)

## S3 method for class 'normal'
PriorDraw(mdObj, n = 1)

## S3 method for class 'weibull'
PriorDraw(mdObj, n = 1)

Arguments

mdObj

Mixing Distribution
n

Number of draws.

Value

A sample from the prior distribution

Generate the prior function of the Dirichlet process

Description

Generate the prior function of the Dirichlet process

Usage

PriorFunction(dpobj)

Arguments

dpobj

A Dirichlet process object

Value

A function f(x) that represents a draw from the prior distrubtion of the Dirichlet process.

@export

Update the prior parameters of a mixing distribution

Description

Update the prior parameters of a mixing distribution

Usage

## S3 method for class 'beta'
PriorParametersUpdate(mdObj, clusterParameters, n = 1)

PriorParametersUpdate(mdObj, clusterParameters, n = 1)

## S3 method for class 'weibull'
PriorParametersUpdate(mdObj, clusterParameters, n = 1)

Arguments

mdObj

Mixing Distribution Object
clusterParameters

Current cluster parameters
n

Number of samples

Value

mdobj New Mixing Distribution object with updated cluster parameters

Tumour incidences in rats

Description

Rat tumour data from Tarone (1982). Data from Table 5.1 of Bayesian Data Analysis

Usage

rats

Format

y

number of rats with a tumour

N

total number of rats in the experiment

Source

http://www.stat.columbia.edu/~gelman/book/data/rats.asc

The Stick Breaking representation of the Dirichlet process.

Description

A Dirichlet process can be represented using a stick breaking construction

G=∑i=1npiiδθiG = \sum _{i=1} ^n pi _i \delta _{\theta _i}

, where πk=βk∏k=1n−1(1−βk)\pi _k = \beta _k \prod _{k=1} ^{n-1} (1- \beta _k ) are the stick breaking weights. The atoms δθi\delta _{\theta _i} are drawn from G0G_0 the base measure of the Dirichlet Process. The βk∼Beta(1,α)\beta _k \sim \mathrm{Beta} (1, \alpha). In theory nn should be infinite, but we chose some value of NN to truncate the series. For more details see reference.

Usage

StickBreaking(alpha, N)

piDirichlet(betas)

Arguments

alpha

Concentration parameter of the Dirichlet Process.
N

Truncation value.
betas

Draws from the Beta distribution.

Value

Vector of stick breaking probabilities.

Functions

  • piDirichlet(): Function for calculating stick lengths.

References

Ishwaran, H., & James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453), 161-173.

Identifies the correct clusters labels, in any dimension, when cluster parameters and global parameters are matched.

Description

Identifies the correct clusters labels, in any dimension, when cluster parameters and global parameters are matched.

Usage

true_cluster_labels(array, dpObj)

Arguments

array

The array containing matching indexes.
dpObj

A hierarchical dirichletprocess object.

Value

The array containing the correct matching indexes

Update the Dirichlet process concentration parameter.

Description

Using the procedure outlined in West (1992) we sample the concentration parameter of the Dirichlet process. See reference for further details.

Usage

UpdateAlpha(dpobj)

## Default S3 method:
UpdateAlpha(dpobj)

## S3 method for class 'hierarchical'
UpdateAlpha(dpobj)

Arguments

dpobj

Dirichlet process object.

Value

A Dirichlet process object with updated concentration parameter.

References

West, M. (1992). Hyperparameter estimation in Dirichlet process mixture models. ISDS Discussion Paper# 92-A03: Duke University.

Update the α\alpha and β\beta parameter of a hidden Markov Dirichlet process model.

Description

Update the α\alpha and β\beta parameter of a hidden Markov Dirichlet process model.

Usage

UpdateAlphaBeta(dp)

Arguments

dp

Dirichlet process object

Create a Weibull mixing distribution.

Description

See DirichletProcessWeibull for the default prior and hyper prior distributions.

Usage

WeibullMixtureCreate(
  priorParameters,
  mhStepSize,
  hyperPriorParameters = c(6, 2, 1, 0.5)
)

Arguments

priorParameters

Prior parameters for the Weibull parameters
mhStepSize

Metropolis Hastings Step Size
hyperPriorParameters

Parameters for the hyper-priors

Value

A mixing distribution object.

Generate a weighted function.

Description

Generate a weighted function.

Usage

weighted_function_generator(func, weights, params)

Arguments

func

Function that is used of the form func(x, params).
weights

Weighting of each cluster.
params

Cluster parameter list

Value

weighted function