3,774 research outputs found
Empirical Bayes and Hierarchical Bayes Estimation of Skew Normal Populations
We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications
Scheduling and Codeword Length Optimization in Time Varying Wireless Networks
In this paper, a downlink scenario in which a single-antenna base station
communicates with K single antenna users, over a time-correlated fading
channel, is considered. It is assumed that channel state information is
perfectly known at each receiver, while the statistical characteristics of the
fading process and the fading gain at the beginning of each frame are known to
the transmitter. By evaluating the random coding error exponent of the
time-correlated fading channel, it is shown that there is an optimal codeword
length which maximizes the throughput. The throughput of the conventional
scheduling that transmits to the user with the maximum signal to noise ratio is
examined using both fixed length codewords and variable length codewords.
Although optimizing the codeword length improves the performance, it is shown
that using the conventional scheduling, the gap between the achievable
throughput and the maximum possible throughput of the system tends to infinity
as K goes to infinity. A simple scheduling that considers both the signal to
noise ratio and the channel time variation is proposed. It is shown that by
using this scheduling, the gap between the achievable throughput and the
maximum throughput of the system approaches zero
Scalable quantum computation with fast gates in two-dimensional microtrap arrays of trapped ions
We theoretically investigate the use of fast pulsed two-qubit gates for
trapped ion quantum computing in a two-dimensional microtrap architecture. In
one dimension, such fast gates are optimal when employed between nearest
neighbours, and we examine the generalisation to a two-dimensional geometry. We
demonstrate that fast pulsed gates are capable of implementing high-fidelity
entangling operations between ions in neighbouring traps faster than the
trapping period, with experimentally demonstrated laser repetition rates.
Notably, we find that without increasing the gate duration, high-fidelity gates
are achievable even in large arrays with hundreds of ions. To demonstrate the
usefulness of this proposal, we investigate the application of these gates to
the digital simulation of a 40-mode Fermi-Hubbard model. This also demonstrates
why shorter chains of gates required to connect arbitrary pairs of ions makes
this geometry well suited for large-scale computation
Empirical Bayesian Approach to Testing Multiple Hypotheses with Separate Priors for Left and Right Alternatives
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of data from biological experiments: HIV-transfected cell-line mRNA expression data, and a quantitative trait genome-wide SNP data set. We have developed a user-friendly web-based shiny App for the proposed method which is available through URL https://npseb.shinyapps.io/npseb/. The HIV and SNP data can be directly accessed, and the results presented in this paper can be executed
Empirical Bayesian Approach to Testing Multiple Hypotheses with Separate Priors for Left and Right Alternatives
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of data from biological experiments: HIV-transfected cell-line mRNA expression data, and a quantitative trait genome-wide SNP data set. We have developed a user-friendly web-based shiny App for the proposed method which is available through URL https://npseb.shinyapps.io/npseb/. The HIV and SNP data can be directly accessed, and the results presented in this paper can be executed
The Scalar Curvature Problem on the Four Dimensional Half Sphere
In this paper, we consider the problem of prescribing the scalar curvature
under minimal boundary conditions on the standard four dimensional half sphere.
We provide an Euler-Hopf type criterion for a given function to be a scalar
curvature to a metric conformal to the standard one. Our proof involves the
study of critical points at infinity of the associated variational problem.Comment: 19 page
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