Exact computational analyses for adaptive designs

Abstract We show how to compute optimal designs and exact analyses of allocation rules for various sequential allocation problems. The problems we have solved include parameter estimation in an industrial scenario, and testing in a clinical trial. Our computational approach incorporates backward induction, dynamic programming, and a new technique of forward induction. By utilizing e cient algorithms and careful implementation, we are able to determine exact solutions to practical problems previously approached only through simulation or approximation

Optimal allocation for estimating the mean of a bivariate polynomial", Seq

Suppose we wish to estimate the mean of some polynomial function of random variables from two independent Bernoulli populations, the parameters of which, themselves, are modeled as independent beta random variables. It is assumed that the total sample size for the experiment is fixed, but that the number of experimental units observed from each population may be random. This problem arises, for example, when estimating the fault tolerance of a system by testing its components individually. Using a decision theoretic approach, we seek to minimize the Bayes risk that arises from using a squared error loss function. The Bayes estimator can be determined in a straightforward manner, so the problem of optimal estimation reduces, therefore, to a problem of optimal allocation of the samples between the two populations. This can be solved via dynamic programming. Similar programming techniques are utilized to evaluate properties of a number of ad hoc allocation strategies that might also be considered for use in this problem. Two sample polynomials are analyzed along with a number of examples indicating the effects of different prior parameter settings. The effects of differences between prior parameters used in the design and analysis stages of the experiment are also examined. For the polynomials considered, the adaptive strategies are found to be especially robust. We discuss computational techniques that facilitate such analyses by permitting rapid re-evaluation of strategies. Capabilities of this sort encourage people to explore designs more fully and to consider them from a number of different viewpoints. 1

Sequential Allocation with Minimal Switching

This paper describes algorithms for the design of sequential experiments where extensive switching is undesirable. Given an objective function to minimize by sampling between Bernoulli populations, two different models are considered. The constraint model optimizes the tradeoff of the maximum number of switches vs. the objective function, while the cost model optimizes the tradeoff for the expected number of switches. For each model, an algorithm is developed which produces the optimal sequential experiment. The algorithms are quite general, and give users flexibility in incorporating practical considerations in the design of experiments. To show the usability of these algorithms, they are applied to a bandit problem and an estimation problem. It is observed that the expected number of switches grows approximately as the square root of the sample size, for sample sizes up to a few hundred. It is also observed that one can dramatically reduce the number of switches without substantially..

Statistical Analysis of Communication Time on the IBM SP2

For parallel computers, the execution time of communication routines is an important determinate of users ’ performance. For one parallel computer, the IBM SP2, all of the higher-level communications routines show a drop in performance as the number of processors involved in the communication increases. Such a drop is unexpected and does not occur on most other parallel machines. While a few others have also recently studied the SP2’s communication performance, they have reported only average performance, and failed to comment on the drop in performance or its causes [1, 9]. We generated a distribution of times for these routines and developed a simulator in an attempt to recreate the observed distribution. By studying distributions of communication times and by refining the simulator, we were able to discern that the performance decrease is due to the variation in the communication times of the lower-level primitives upon which the higher-level communication routines are built. This variation is in turn caused by the deleterious effects of interrupts generated by an operating system untuned to highperformance parallel computing

Statistical Analysis of Communication Time on the IBM SP2

For parallel computers, the execution time of communication routines is an important determinate of users' performance. For one parallel computer, the IBM SP2, all of the higher-level communications routines show a drop in performance as the number of processors involved in the communication increases. Such a drop is unexpected and does not occur on most other parallel machines. While a few others have also recently studied the SP2's communication performance, they have reported only average performance, and failed to comment on the drop in performance or its causes [1, 9]. We generated a distribution of times for these routines and developed a simulator in an attempt to recreate the observed distribution. By studying distributions of communication times and by re ning the simulator, we were able to discern that the performance decrease is due to the variation in the communication times of the lowerlevel primitives upon which the higher-level communication routines are built. This variation is in turn caused by the deleterious e ects of interrupts generated by an operating system untuned to high-performance parallel computing

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

International audienceSpinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far