1,628 research outputs found
Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property
The AMP Markov property is a recently proposed alternative Markov property
for chain graphs. In the case of continuous variables with a joint multivariate
Gaussian distribution, it is the AMP rather than the earlier introduced LWF
Markov property that is coherent with data-generation by natural
block-recursive regressions. In this paper, we show that maximum likelihood
estimates in Gaussian AMP chain graph models can be obtained by combining
generalized least squares and iterative proportional fitting to an iterative
algorithm. In an appendix, we give useful convergence results for iterative
partial maximization algorithms that apply in particular to the described
algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic
Analysis of forensic DNA mixtures with artefacts
DNA is now routinely used in criminal investigations and court cases, although DNA samples taken at crime scenes are of varying quality and therefore present challenging problems for their interpretation. We present a statistical model for the quantitative peak information obtained from an electropherogram of a forensic DNA sample and illustrate its potential use for the analysis of criminal cases. In contrast with most previously used methods, we directly model the peak height information and incorporate important artefacts that are associated with the production of the electropherogram. Our model has a number of unknown parameters, and we show that these can be estimated by the method of maximum likelihood in the presence of multiple unknown individuals contributing to the sample, and their approximate standard errors calculated; the computations exploit a Bayesian network representation of the model. A case example from a UK trial, as reported in the literature, is used to illustrate the efficacy and use of the model, both in finding likelihood ratios to quantify the strength of evidence, and in the deconvolution of mixtures for finding likely profiles of the individuals contributing to the sample. Our model is readily extended to simultaneous analysis of more than one mixture as illustrated in a case example. We show that the combination of evidence from several samples may give an evidential strength which is close to that of a single-source trace and thus modelling of peak height information provides a potentially very efficient mixture analysis
New term in effective field theory at fixed topology
A random matrix model for lattice QCD which takes into account the positive
definite nature of the Wilson term is introduced. The corresponding effective
theory for fixed index of the Wilson Dirac operator is derived to next to
leading order. It reveals a new term proportional to the topological index of
the Wilson Dirac operator and the lattice spacing. The new term appears
naturally in a fixed index spurion analysis. The spurion approach reveals that
the term is the first in a new family of such terms and that equivalent terms
are relevant for the effective theory of continuum QCD.Comment: 22 pages, 2 figures, version to appear in PR
Bayesian Networks for Max-linear Models
We study Bayesian networks based on max-linear structural equations as
introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their
independence properties. In particular we emphasize that distributions for such
networks are generally not faithful to the independence model determined by
their associated directed acyclic graph. In addition, we consider some of the
basic issues of estimation and discuss generalized maximum likelihood
estimation of the coefficients, using the concept of a generalized likelihood
ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21].
Finally we argue that the structure of a minimal network asymptotically can be
identified completely from observational data.Comment: 18 page
Poisson and Porter-Thomas Fluctuations in off-Yrast Rotational Transitions
Fluctuations associated with stretched E2 transitions from high spin levels
in nuclei around Yb are investigated by a cranked shell model extended
to include residual two-body interactions. It is found that the gamma-ray
energies behave like random variables and the energy spectra show the Poisson
fluctuation, in the cranked mean field model without the residual interaction.
With two-body residual interaction included, discrete transition pattern with
unmixed rotational bands is still valid up to around 600 keV above yrast, in
good agreement with experiments. At higher excitation energy, a gradual onset
of rotational damping emerges. At 1.8 MeV above yrast, complete damping is
observed with GOE type fluctuations for both energy levels and transition
strengths(Porter-Thomas fluctuations).Comment: 21 pages, phyzzx, YITP/K-99
Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data
Subsequence clustering of multivariate time series is a useful tool for
discovering repeated patterns in temporal data. Once these patterns have been
discovered, seemingly complicated datasets can be interpreted as a temporal
sequence of only a small number of states, or clusters. For example, raw sensor
data from a fitness-tracking application can be expressed as a timeline of a
select few actions (i.e., walking, sitting, running). However, discovering
these patterns is challenging because it requires simultaneous segmentation and
clustering of the time series. Furthermore, interpreting the resulting clusters
is difficult, especially when the data is high-dimensional. Here we propose a
new method of model-based clustering, which we call Toeplitz Inverse
Covariance-based Clustering (TICC). Each cluster in the TICC method is defined
by a correlation network, or Markov random field (MRF), characterizing the
interdependencies between different observations in a typical subsequence of
that cluster. Based on this graphical representation, TICC simultaneously
segments and clusters the time series data. We solve the TICC problem through
alternating minimization, using a variation of the expectation maximization
(EM) algorithm. We derive closed-form solutions to efficiently solve the two
resulting subproblems in a scalable way, through dynamic programming and the
alternating direction method of multipliers (ADMM), respectively. We validate
our approach by comparing TICC to several state-of-the-art baselines in a
series of synthetic experiments, and we then demonstrate on an automobile
sensor dataset how TICC can be used to learn interpretable clusters in
real-world scenarios.Comment: This revised version fixes two small typos in the published versio
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Survey and alignment at the ALS
This paper describes survey and alignment at the Lawrence Berkeley National Laboratory`s Advanced Light Source (ALS) accelerators from 1993 to 1995. The ALS is a 1.0 - 1.9 GeV electron accelerator producing extremely bright synchrotron light in the UV and soft-X-ray wavelengths. At the ALS, electrons are accelerated in a LINAC to 50 MeV, injected into a booster ring for further acceleration and finally injected into the storage ring. This is shown schematically in Figure 1. The storage ring, some 200 m in circumference, has been run with electron currents above 400 mA with lifetimes as high as 24 hours. The ALS is a third generation light source and requires for efficient storage ring operation, magnets aligned to within 150 mm of their ideal position. To accomplish this a network of monuments was established and their positions measured with respect to one another. The data was reduced using GEONET`` and STAR*NET`` software. Using the monuments as reference points, magnet positions were measured and alignment confirmed using the Kem Electronic Coordinate Determination System (ECDS``). A number of other papers dealing with survey and alignment (S&A) at the ALS have been written that may further elucidate some details of the methods and systems described in this paper
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