90 research outputs found
Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models
Bayesian inference for stochastic volatility models using MCMC methods highly depends
on actual parameter values in terms of sampling efficiency. While draws from the posterior
utilizing the standard centered parameterization break down when the volatility of volatility parameter
in the latent state equation is small, non-centered versions of the model show deficiencies
for highly persistent latent variable series. The novel approach of ancillarity-sufficiency
interweaving has recently been shown to aid in overcoming these issues for a broad class of
multilevel models. In this paper, we demonstrate how such an interweaving strategy can be
applied to stochastic volatility models in order to greatly improve sampling efficiency for all
parameters and throughout the entire parameter range. Moreover, this method of "combining
best of different worlds" allows for inference for parameter constellations that have previously
been infeasible to estimate without the need to select a particular parameterization beforehand.Series: Research Report Series / Department of Statistics and Mathematic
Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models
Finite mixture models and their extensions to Markov mixture andmixture of experts models are very popular in analysing data of various kind.A challenge for these models is choosing the number of components basedon marginal likelihoods. The present paper suggests two innovative, genericbridge sampling estimators of the marginal likelihood that are based on con-structing balanced importance densities from the conditional densities arisingduring Gibbs sampling. The full permutation bridge sampling estimator is de-rived from considering all possible permutations of the mixture labels for asubset of these densities. For the double random permutation bridge samplingestimator, two levels of random permutations are applied, first to permute thelabels of the MCMC draws and second to randomly permute the labels ofthe conditional densities arising during Gibbs sampling. Various applicationsshow very good performance of these estimators in comparison to importanceand to reciprocal importance sampling estimators derived from the same im-portance densities
Applied State Space Modelling of Non-Gaussian Time Series using Integration-based Kalman-filtering
The main topic of the paper is on-line filtering for non-Gaussian dynamic (state space) models by approximate computation of the first two posterior moments using efficient numerical integration. Based on approximating the prior of the state vector by a normal density, we prove that the posterior moments of the state vector are related to the posterior moments of the linear predictor in a simple way. For the linear predictor Gauss-Hermite integration is carried out with automatic reparametrization based on an approximate posterior mode filter. We illustrate how further topics in applied state space modelling such as estimating hyperparameters, computing model likelihoods and predictive residuals, are managed by integration-based Kalman-filtering. The methodology derived in the paper is applied to on-line monitoring of ecological time series and filtering for small count data. (author's abstract)Series: Forschungsberichte / Institut für Statisti
Bayesian Inference in the Multinomial Logit Model
The multinomial logit model (MNL) possesses a latent variable
representation in terms of random variables following a multivariate logistic distribution. Based on multivariate finite mixture approximations of the multivariate
logistic distribution, various data-augmented Metropolis-Hastings algorithms are developed for a Bayesian inference of the MNL model
From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering
In model-based-clustering mixture models are used to group data points into
clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli
et al (2016) are sparse finite mixtures, where the prior distribution on the
weight distribution of a mixture with components is chosen in such a way
that a priori the number of clusters in the data is random and is allowed to be
smaller than with high probability. The number of cluster is then inferred
a posteriori from the data.
The present paper makes the following contributions in the context of sparse
finite mixture modelling. First, it is illustrated that the concept of sparse
finite mixture is very generic and easily extended to cluster various types of
non-Gaussian data, in particular discrete data and continuous multivariate data
arising from non-Gaussian clusters. Second, sparse finite mixtures are compared
to Dirichlet process mixtures with respect to their ability to identify the
number of clusters. For both model classes, a random hyper prior is considered
for the parameters determining the weight distribution. By suitable matching of
these priors, it is shown that the choice of this hyper prior is far more
influential on the cluster solution than whether a sparse finite mixture or a
Dirichlet process mixture is taken into consideration.Comment: Accepted versio
Vertex finding by sparse model-based clustering
The application of sparse model-based clustering to the problem of primary vertex finding is discussed. The observed z-positions of the charged primary tracks in a bunch crossing are modeled by a Gaussian mixture. The mixture parameters are estimated via Markov Chain Monte Carlo (MCMC). Sparsity is achieved by an appropriate prior on the mixture weights. The results are shown and compared to clustering by the expectation-maximization (EM) algorithm
Bayesian Clustering of Categorical Time Series Using Finite Mixtures of Markov Chain Models
Two approaches for model-based clustering of categorical time series based on time- homogeneous first-order Markov chains are discussed. For Markov chain clustering the in- dividual transition probabilities are fixed to a group-specific transition matrix. In a new approach called Dirichlet multinomial clustering the rows of the individual transition matri- ces deviate from the group mean and follow a Dirichlet distribution with unknown group- specific hyperparameters. Estimation is carried out through Markov chain Monte Carlo. Various well-known clustering criteria are applied to select the number of groups. An appli- cation to a panel of Austrian wage mobility data leads to an interesting segmentation of the Austrian labor market
Dynamic Mixture of Finite Mixtures of Factor Analysers with Automatic Inference on the Number of Clusters and Factors
Mixtures of factor analysers (MFA) models represent a popular tool for
finding structure in data, particularly high-dimensional data. While in most
applications the number of clusters, and especially the number of latent
factors within clusters, is mostly fixed in advance, in the recent literature
models with automatic inference on both the number of clusters and latent
factors have been introduced. The automatic inference is usually done by
assigning a nonparametric prior and allowing the number of clusters and factors
to potentially go to infinity. The MCMC estimation is performed via an adaptive
algorithm, in which the parameters associated with the redundant factors are
discarded as the chain moves. While this approach has clear advantages, it also
bears some significant drawbacks. Running a separate factor-analytical model
for each cluster involves matrices of changing dimensions, which can make the
model and programming somewhat cumbersome. In addition, discarding the
parameters associated with the redundant factors could lead to a bias in
estimating cluster covariance matrices. At last, identification remains
problematic for infinite factor models. The current work contributes to the MFA
literature by providing for the automatic inference on the number of clusters
and the number of cluster-specific factors while keeping both cluster and
factor dimensions finite. This allows us to avoid many of the aforementioned
drawbacks of the infinite models. For the automatic inference on the cluster
structure, we employ the dynamic mixture of finite mixtures (MFM) model.
Automatic inference on cluster-specific factors is performed by assigning an
exchangeable shrinkage process (ESP) prior to the columns of the factor loading
matrices. The performance of the model is demonstrated on several benchmark
data sets as well as real data applications
Identifying Mixtures of Mixtures Using Bayesian Estimation
The use of a finite mixture of normal distributions in model-based clustering
allows to capture non-Gaussian data clusters. However, identifying the clusters
from the normal components is challenging and in general either achieved by
imposing constraints on the model or by using post-processing procedures.
Within the Bayesian framework we propose a different approach based on sparse
finite mixtures to achieve identifiability. We specify a hierarchical prior
where the hyperparameters are carefully selected such that they are reflective
of the cluster structure aimed at. In addition this prior allows to estimate
the model using standard MCMC sampling methods. In combination with a
post-processing approach which resolves the label switching issue and results
in an identified model, our approach allows to simultaneously (1) determine the
number of clusters, (2) flexibly approximate the cluster distributions in a
semi-parametric way using finite mixtures of normals and (3) identify
cluster-specific parameters and classify observations. The proposed approach is
illustrated in two simulation studies and on benchmark data sets.Comment: 49 page
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