Parameter Expansion and Efficient Inference

This EM review article focuses on parameter expansion, a simple technique introduced in the PX-EM algorithm to make EM converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between parameter expansion and efficient inference. It reviews the statistical interpretation of the PX-EM algorithm, in terms of efficient inference via bias reduction, and further unfolds the PX-EM mystery by looking at PX-EM from different perspectives. In addition, it briefly discusses potential applications of parameter expansion to statistical inference and the broader impact of statistical thinking on understanding and developing other iterative optimization algorithms.Comment: Published in at http://dx.doi.org/10.1214/10-STS348 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Monitoring Networked Applications With Incremental Quantile Estimation

Networked applications have software components that reside on different computers. Email, for example, has database, processing, and user interface components that can be distributed across a network and shared by users in different locations or work groups. End-to-end performance and reliability metrics describe the software quality experienced by these groups of users, taking into account all the software components in the pipeline. Each user produces only some of the data needed to understand the quality of the application for the group, so group performance metrics are obtained by combining summary statistics that each end computer periodically (and automatically) sends to a central server. The group quality metrics usually focus on medians and tail quantiles rather than on averages. Distributed quantile estimation is challenging, though, especially when passing large amounts of data around the network solely to compute quality metrics is undesirable. This paper describes an Incremental Quantile (IQ) estimation method that is designed for performance monitoring at arbitrary levels of network aggregation and time resolution when only a limited amount of data can be transferred. Applications to both real and simulated data are provided.Comment: This paper commented in: [arXiv:0708.0317], [arXiv:0708.0336], [arXiv:0708.0338]. Rejoinder in [arXiv:0708.0339]. Published at http://dx.doi.org/10.1214/088342306000000583 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rejoinder: Monitoring Networked Applications With Incremental Quantile Estimation

Rejoinder: Monitoring Networked Applications With Incremental Quantile Estimation [arXiv:0708.0302]Comment: Published at http://dx.doi.org/10.1214/088342306000000592 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A master\u27s recital in conducting

Logan Scott Vander Wiel conducted on three recitals which took place on the evenings of Thursday, November 9, 2017; Wednesday, February 21, 2018; and Wednesday, April 18, 2018, in the Great Hall at the Gallagher Bluedorn Performing Arts Center. The recitals were presented in partial fulfillment of a Master of Music in conducting. The full program consisted of five contrasting pieces from the standard repertoire: Alfred Reed’s Russian Christmas Music for wind band, Gordon Jacob’s An Original Suite for wind band and his Old Wine in New Bottles for thirteen winds, Michael Daugherty’s Alligator Alley for wind band, and Guy Woolfenden’s Gallimaufry for wind band. The performing ensembles were the University of Northern Iowa Symphonic Band, the University of Northern Iowa Concert Band, and a chamber group comprised of undergraduate and graduate students from the University of Northern Iowa School of Music

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour

The Non-homogeneous Poisson Process for Fast Radio Burst Rates

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model changes in the rate as a function of both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 586.88 events per sky per day above a flux of 1 Jy (95\% CI: 271.86, 923.72) and a flux power-law index of 0.91 (95\% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al. 2016.Comment: 19 pages, 2 figure

Comparison of RFI Mitigation Strategies for Dispersed Pulse Detection

Impulsive radio-frequency signals from astronomical sources are dispersed by the frequency dependent index of refraction of the interstellar media and so appear as chirped signals when they reach earth. Searches for dispersed impulses have been limited by false detections due to radio frequency interference (RFI) and, in some cases, artifacts of the instrumentation. Many authors have discussed techniques to excise or mitigate RFI in searches for fast transients, but comparisons between different approaches are lacking. This work develops RFI mitigation techniques for use in searches for dispersed pulses, employing data recorded in a "Fly's Eye" mode of the Allen Telescope Array as a test case. We gauge the performance of several RFI mitigation techniques by adding dispersed signals to data containing RFI and comparing false alarm rates at the observed signal-to-noise ratios of the added signals. We find that Huber filtering is most effective at removing broadband interferers, while frequency centering is most effective at removing narrow frequency interferers. Neither of these methods is effective over a broad range of interferers. A method that combines Huber filtering and adaptive interference cancellation provides the lowest number of false positives over the interferers considered here. The methods developed here have application to other searches for dispersed pulses in incoherent spectra, especially those involving multiple beam systems.Comment: Accepted for publication in Ap

Some aspects of monitoring and control of univariate dynamic systems

Four aspects of statistical monitoring and control of manufacturing processes are studied. First a machining process is modeled using a random walk observed with error and adjusted in discrete steps. An optimal adjustment policy is derived to minimize the expectation of variable off target costs plus fixed adjustment costs. Under some regularity conditions the optimal policy is shown to make nonzero adjustments only when the process is perceived to be substantially off target;A more common control objective is to minimize process variance. Monitoring techniques are studied for detecting abrupt changes in autoregressive moving average transfer function (ARMAX) systems under minimum variance feedback control. An example shows that a simple cumulative sum (CUSUM) monitoring scheme performs very favorably in comparison to several other schemes for detecting an underlying step shift in the process level;Properties of a likelihood ratio based monitoring scheme for ARMAX systems can be investigated using a Markov chain to approximate the scheme's stochastic behavior. A general approach is described for approximating signaling time distributions for such monitoring schemes possessing a certain recursive calculation structure;Finally, concepts and an application of algorithmic statistical process control (ASPC) are presented. ASPC refers to the use of feedforward and feedback techniques to reduce predictable quality variations in conjunction with statistical process monitoring to detect and remove root causes of unpredictable quality changes. The application describes the development of a minimum variance control algorithm and a CUSUM monitor for a polymerization process at the General Electric Company. The application resulted in a 35% reduction in off specification material as well as several fundamental process improvements attributable to signals from the CUSUM monitor.</p

Time-Varying Network Tomography: Router Link Data

The origin-destination (OD) traffic matrix of a computer network is useful for solving problems in design, routing, con guration debugging, monitoring, and pricing. Directly measuring this matrix is not usually feasible but less informative link measurements are easy to obtain. This work studies the inference of OD byte counts from link byte counts measured at router interfaces under a fixed routing scheme. A basic model of the OD counts assumes that they are independent normal over OD pairs and iid over successive measurement periods. The normal means and variances are functionally related through a power law. We deal with the time-varying nature of the counts by fitting the basic iid model locally using a moving data window. Identifiability of the model is proved for router link data and maximum likelihood is used for parameter estimation. The OD counts are estimated by their conditional expectations given the link counts and estimated parameters. OD estimates are forced to be ..