8,624 research outputs found
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
Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression
We propose a general algorithm for approximating nonstandard Bayesian
posterior distributions. The algorithm minimizes the Kullback-Leibler
divergence of an approximating distribution to the intractable posterior
distribution. Our method can be used to approximate any posterior distribution,
provided that it is given in closed form up to the proportionality constant.
The approximation can be any distribution in the exponential family or any
mixture of such distributions, which means that it can be made arbitrarily
precise. Several examples illustrate the speed and accuracy of our
approximation method in practice
Regime switching volatility calibration by the Baum-Welch method
Regime switching volatility models provide a tractable method of modelling stochastic
volatility. Currently the most popular method of regime switching calibration is the
Hamilton filter. We propose using the Baum-Welch algorithm, an established technique
from Engineering, to calibrate regime switching models instead. We demonstrate the
Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample
Computing semiparametric bounds on the expected payments of insurance instruments via column generation
It has been recently shown that numerical semiparametric bounds on the
expected payoff of fi- nancial or actuarial instruments can be computed using
semidefinite programming. However, this approach has practical limitations.
Here we use column generation, a classical optimization technique, to address
these limitations. From column generation, it follows that practical univari-
ate semiparametric bounds can be found by solving a series of linear programs.
In addition to moment information, the column generation approach allows the
inclusion of extra information about the random variable; for instance,
unimodality and continuity, as well as the construction of corresponding
worst/best-case distributions in a simple way
Assessing the Number of Components in Mixture Models: a Review.
Despite the widespread application of finite mixture models, the decision of how many classes are required to adequately represent the data is, according to many authors, an important, but unsolved issue. This work aims to review, describe and organize the available approaches designed to help the selection of the adequate number of mixture components (including Monte Carlo test procedures, information criteria and classification-based criteria); we also provide some published simulation results about their relative performance, with the purpose of identifying the scenarios where each criterion is more effective (adequate).Finite mixture; number of mixture components; information criteria; simulation studies.
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