UCI's Department of Statistics was created in 2002 with an emphasis on research in statistical theory and interdisciplinary collaborations and is actively recruiting additional members.
The Department also intends to capitalize on existing statistical expertise in other Bren School departments as well as other schools at UCI.
In this paper, we propose an approach to estimating traffic matrices that incorporates lightweight Origin- Destination (OD) flow measurements coupled with a computationally lightweight algorithm for producing the OD estimates. There are two key ingredients in our method, called PamTram, for PArtial Measurement of TRAffic Matrices. The first is to actively select a small number of informative OD flows to measure in each estimation time interval. To avoid the heavy computation of an optimal selection, we use a heuristic based on intuition from game theory. Randomized selection rules are developed based on the goals of reducing errors and adapting to traffic changes. We provide an algorithm for selecting a good flow to measure that is fast because it avoids the computations, such as integrating over past intervals, that are needed for optimal selection. The second key aspect of our method is an explanation and proof that an Iterative Proportional Fitting (IPF) algorithm can be used to approximate the traffic matrix estimate when the goal is a minimum mean squared error and the optimization starts from a maximum entropy initial estimate.
In addition, we provide a one-step average error bound for PamTram when the randomized selection rule is uniform and no link counts are used. This bounds the average error for the worst case selection rule. Finally, we validate our method using data from Sprint’s European Tier-1 IP backbone network. Results show that our method generates average errors below the 10% carrier target error rate. Interestingly, we show that it suffices to measure a single OD flow in each estimation interval,which renders our partial measurement method very lightweight in terms of measurement overhead.
Advances in wearables and digital technology now make it possible to deliver behavioral mobile health interventions to individuals in their everyday life. The micro-randomized trial (MRT) is increasingly used to provide data to inform the construction of these interventions. In an MRT, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times, over the course of the trial. This work is motivated by multiple MRTs that have been conducted, or are currently in the field, in which the primary outcome is a longitudinal binary outcome. The primary aim of such MRTs is to examine whether a particular time-varying intervention has an effect on the longitudinal binary outcome, often marginally over all but a small subset of the individual's data. We propose the definition of causal excursion effect that can be used in such primary aim analysis for MRTs with binary outcomes. Under rather restrictive assumptions one can, based on existing literature, derive a semiparametric, locally efficient estimator of the causal effect. We, starting from this estimator, develop an estimator that can be used as the basis of a primary aim analysis under more plausible assumptions. Simulation studies are conducted to compare the estimators. We illustrate the developed methods using data from the MRT, BariFit. In BariFit, the goal is to support weight maintenance for individuals who received bariatric surgery.
Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices-an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods.
The target article on robust modeling (Lee et al. in review) generated a lot of commentary. In this reply, we discuss some of the common themes in the commentaries; some are simple points of agreement while others are extensions of a practical or abstract nature. We also address a small number of disagreements or confusions.