6,275 research outputs found
EMMIXcskew: an R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions
This paper presents an R package EMMIXcskew for the fitting of the canonical
fundamental skew t-distribution (CFUST) and finite mixtures of this
distribution (FM-CFUST) via maximum likelihood (ML). The CFUST distribution
provides a flexible family of models to handle non-normal data, with parameters
for capturing skewness and heavy-tails in the data. It formally encompasses the
normal, t, and skew-normal distributions as special and/or limiting cases. A
few other versions of the skew t-distributions are also nested within the CFUST
distribution. In this paper, an Expectation-Maximization (EM) algorithm is
described for computing the ML estimates of the parameters of the FM-CFUST
model, and different strategies for initializing the algorithm are discussed
and illustrated. The methodology is implemented in the EMMIXcskew package, and
examples are presented using two real datasets. The EMMIXcskew package contains
functions to fit the FM-CFUST model, including procedures for generating
different initial values. Additional features include random sample generation
and contour visualization in 2D and 3D
EMMIX-uskew: An R Package for Fitting Mixtures of Multivariate Skew t-distributions via the EM Algorithm
This paper describes an algorithm for fitting finite mixtures of unrestricted
Multivariate Skew t (FM-uMST) distributions. The package EMMIX-uskew implements
a closed-form expectation-maximization (EM) algorithm for computing the maximum
likelihood (ML) estimates of the parameters for the (unrestricted) FM-MST model
in R. EMMIX-uskew also supports visualization of fitted contours in two and
three dimensions, and random sample generation from a specified FM-uMST
distribution.
Finite mixtures of skew t-distributions have proven to be useful in modelling
heterogeneous data with asymmetric and heavy tail behaviour, for example,
datasets from flow cytometry. In recent years, various versions of mixtures
with multivariate skew t (MST) distributions have been proposed. However, these
models adopted some restricted characterizations of the component MST
distributions so that the E-step of the EM algorithm can be evaluated in closed
form. This paper focuses on mixtures with unrestricted MST components, and
describes an iterative algorithm for the computation of the ML estimates of its
model parameters.
The usefulness of the proposed algorithm is demonstrated in three
applications to real data sets. The first example illustrates the use of the
main function fmmst in the package by fitting a MST distribution to a bivariate
unimodal flow cytometric sample. The second example fits a mixture of MST
distributions to the Australian Institute of Sport (AIS) data, and demonstrate
that EMMIX-uskew can provide better clustering results than mixtures with
restricted MST components. In the third example, EMMIX-uskew is applied to
classify cells in a trivariate flow cytometric dataset. Comparisons with other
available methods suggests that the EMMIX-uskew result achieved a lower
misclassification rate with respect to the labels given by benchmark gating
analysis
Robust Inference for State-Space Models with Skewed Measurement Noise
Filtering and smoothing algorithms for linear discrete-time state-space
models with skewed and heavy-tailed measurement noise are presented. The
algorithms use a variational Bayes approximation of the posterior distribution
of models that have normal prior and skew-t-distributed measurement noise. The
proposed filter and smoother are compared with conventional low-complexity
alternatives in a simulated pseudorange positioning scenario. In the
simulations the proposed methods achieve better accuracy than the alternative
methods, the computational complexity of the filter being roughly 5 to 10 times
that of the Kalman filter.Comment: 5 pages, 7 figures. Accepted for publication in IEEE Signal
Processing Letter
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