1,675 research outputs found
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
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
Bayesian emulation for optimization in multi-step portfolio decisions
We discuss the Bayesian emulation approach to computational solution of
multi-step portfolio studies in financial time series. "Bayesian emulation for
decisions" involves mapping the technical structure of a decision analysis
problem to that of Bayesian inference in a purely synthetic "emulating"
statistical model. This provides access to standard posterior analytic,
simulation and optimization methods that yield indirect solutions of the
decision problem. We develop this in time series portfolio analysis using
classes of economically and psychologically relevant multi-step ahead portfolio
utility functions. Studies with multivariate currency, commodity and stock
index time series illustrate the approach and show some of the practical
utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table
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