4,606 research outputs found
Dirichlet Posterior Sampling with Truncated Multinomial Likelihoods
We consider the problem of drawing samples from posterior distributions
formed under a Dirichlet prior and a truncated multinomial likelihood, by which
we mean a Multinomial likelihood function where we condition on one or more
counts being zero a priori. Sampling this posterior distribution is of interest
in inference algorithms for hierarchical Bayesian models based on the Dirichlet
distribution or the Dirichlet process, particularly Gibbs sampling algorithms
for the Hierarchical Dirichlet Process Hidden Semi-Markov Model. We provide a
data augmentation sampling algorithm that is easy to implement, fast both to
mix and to execute, and easily scalable to many dimensions. We demonstrate the
algorithm's advantages over a generic Metropolis-Hastings sampling algorithm in
several numerical experiments
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Music Among Friends
Program listing performers and works performe
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code
POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models
The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the "univariate" approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in "multivariate" approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts.
Feedback-enhanced algorithm for aberration correction of holographic atom traps
We show that a phase-only spatial light modulator can be used to generate
non-trivial light distributions suitable for trapping ultracold atoms, when the
hologram calculation is included within a simple and robust feedback loop that
corrects for imperfect device response and optical aberrations. This correction
reduces the discrepancy between target and experimental light distribution to
the level of a few percent (RMS error). We prove the generality of this
algorithm by applying it to a variety of target light distributions of
relevance for cold atomic physics.Comment: 5 pages, 4 figure
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