CopulaDTA: An R Package for Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework

The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression and the bivariate random-effects meta-analysis model (BRMA). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large. This tutorial on advanced statistical methods for meta-analysis of diagnostic accuracy studies discusses and demonstrates Bayesian modeling using CopulaDTA package in R to fit different models to obtain the meta-analytic parameter estimates. The focus is on the joint modelling of sensitivity and specificity using copula based bivariate beta distribution. Essentially, we extend the work of Nikoloulopoulos by: i) presenting the Bayesian approach which offers flexibility and ability to perform complex statistical modelling even with small data sets and ii) including covariate information, and iii) providing an easy to use code. The statistical methods are illustrated by re-analysing data of two published meta-analyses. Modelling sensitivity and specificity using the bivariate beta distribution provides marginal as well as study-specific parameter estimates as opposed to using bivariate normal distribution (e.g., in BRMA) which only yields study-specific parameter estimates. Moreover, copula based models offer greater flexibility in modelling different correlation structures in contrast to the normal distribution which allows for only one correlation structure.Comment: 26 pages, 5 figure

On the seismic modelling of rotating B-type pulsators in the traditional approximation

The CoRoT and Kepler data revolutionised our view on stellar pulsation. For massive stars, the space data revealed the simultaneous presence of low-amplitude low-order modes and dominant high-order gravity modes in several B-type pulsators. The interpretation of such a rich set of detected oscillations requires new tools. We present computations of oscillations for B-type pulsators taking into account the effects of the Coriolis force in the so-called traditional approximation. We discuss the limitations of classical frequency matching to tune these stars seismically and show that the predictive power is limited in the case of high-order gravity mode pulsators, except if numerous modes of consecutive radial order can be identified.Comment: 8 pages, 4 figures. Paper submitted for publication in the Proceedings of the 61st Fujihara Seminar: Progress in solar/stellar physics with helio- and asteroseismology to appear in ASP Conference Serie

Lower bounds on the estimation performance in low complexity quantize-and-forward cooperative systems

Cooperative communication can effectively mitigate the effects of multipath propagation fading by using relay channels to provide spatial diversity. A relaying scheme suitable for half-duplex devices is the quantize-and-forward (QF) protocol, in which the information received from the source is quantized at the relay before being forwarded to the destination. In this contribution, the Cramer-Rao bound (CRB) is obtained for the case where all channel parameters in a QF system are estimated at the destination. The CRB is a lower bound (LB) on the mean square estimation error (MSEE) of an unbiased estimate and can thus be used to benchmark practical estimation algorithms. Additionally, the modified Cramer-Rao bound (MCRB) is also presented, which is a looser but computationally less complex bound. An importance sampling technique is developed to speed up the computation of the MCRBs, and the MSEE performance of a practical estimation algorithm is compared with the (M)CRBs. We point out that the parameters of the source-destination and relay-destination channels can be accurately estimated but that inevitably the source-relay channel estimate is poor when the instantaneous SNR on the relay-destination channel is low; however, in this case, the decoder performance is not affected by the inaccurate source-relay channel estimate

The Cramer-Rao Bound for channel estimation in block fading amplify-and-forward relaying networks

In this paper, we express the Cramer-Rao Bound (CRB) for channel coefficient and noise variance estimation at the destination of an Amplify-and- Forward (AF) based cooperative system, in terms of the a posteriori expectation of the codewords. An algorithm based on factor graphs can be applied in order to calculate this expectation. As the computation of the CRB is rather intensive, the modified CRB (MCRB), which is a looser bound, is derived in closed form. It can be shown that the MCRB coincides with the CRB in the high signal-to-noise ratio (SNR) limit and to that end the CRB/MCRB ratio is simulated in case of uncoded and convolutional encoded transmission

A novel quantize-and-forward cooperative system : channel parameter estimation techniques

The Quantize and Forward cooperative communication protocol improves the reliability of data transmission by allowing a relay to forward to the destination a quantized version of the signal received from the source. In prior studies of the Quantize and Forward protocol, all channel parameters are assumed to be perfectly known at the destination, while in reality these need to be estimated. This paper proposes a novel Quantize and Forward protocol in which the relay compensates for the rotation on the source-relay channel using a crude channel estimate, before quantizing the phase of the received M-PSK data symbols. Therefore, as far as the source-relay channel is concerned, only an SNR estimate is needed at the destination. Further, the destination applies the EM algorithm to improve the estimates of the source-destination and relay-destination channel coefficients. The resulting performance is shown to be close to that of a system with known channel parameters

Low-complexity a posteriori probability approximation in EM-based channel estimation for trellis-coded systems

When estimating channel parameters in linearly modulated communication systems, the iterative expectation-maximization (EM) algorithm can be used to exploit the signal energy associated with the unknown data symbols. It turns out that the channel estimation requires at each EM iteration the a posteriori probabilities (APPs) of these data symbols, resulting in a high computational complexity when channel coding is present. In this paper, we present a new approximation of the APPs of trellis-coded symbols, which is less complex and requires less memory than alternatives from literature. By means of computer simulations, we show that the Viterbi decoder that uses the EM channel estimate resulting from this APP approximation experiences a negligible degradation in frame error rate (FER) performance, as compared to using the exact APPs in the channel estimation process

EM based channel estimation in an amplify-and-forward relaying network

Cooperative communication offers a way to obtain spatial diversity in a wireless network without increasing hardware demands. The different cooperation protocols proposed in the literature [1] are often studied under the assumption that all channel state information is available at the destination. In a practical scenario, channel estimates need to be derived from the broadcasted signals. In this paper, we study the Amplify-and-Forward protocol and use the expectation-maximization (EM) algorithm to obtain the channel estimates in an iterative way. Our results show that the performance of the system that knows the channels can be approached at the cost of an increased computational complexity. In case a small constellation is used, a low complexity approximation is proposed with a similar performance

EM based channel estimation in an amplify-and-forward relaying network

Cooperative communication offers a way to obtain spatial diversity in a wireless network without increasing hardware demands. The different cooperation protocols proposed in the literature [1] are often studied under the assumption that all channel state information is available at the destination. In a practical scenario, channel estimates need to be derived from the broadcasted signals. In this paper, we study the Amplify-and-Forward protocol and use the expectation-maximization (EM) algorithm to obtain the channel estimates in an iterative way. Our results show that the performance of the system that knows the channels can be approached at the cost of an increased computational complexity. In case a small constellation is used, a low complexity approximation is proposed with a similar performance

Impact of helium diffusion and helium-flash-induced carbon production on gravity-mode pulsations in subdwarf B stars

Realistic stellar models are essential to the forward modelling approach in asteroseismology. For practicality however, certain model assumptions are also required. For example, in the case of subdwarf B stars, one usually starts with zero-age horizontal branch structures without following the progenitor evolution. We analyse the effects of common assumptions in subdwarf B models on the g-mode pulsational properties. We investigate if and how the pulsation periods are affected by the H-profile in the core-envelope transition zone. Furthermore, the effects of C-production and convective mixing during the core helium flash are evaluated. Finally, we reanalyse the effects of stellar opacities on the mode excitation in subdwarf B stars. We find that helium settling causes a shift in the theoretical blue edge of the g-mode instability domain to higher effective temperatures. This results in a closer match to the observed instability strip of long-period sdB pulsators, particularly for l<=3 modes. We show further that the g-mode spectrum is extremely sensitive to the H-profile in the core-envelope transition zone. If atomic diffusion is efficient, details of the initial shape of the profile become less important in the course of evolution. Diffusion broadens the chemical gradients, and results in less effective mode trapping and different pulsation periods. Furthermore, we report on the possible consequences of the He-flash for the g-modes. The outer edge of a flash-induced convective region introduces an additional chemical transition in the stellar models, and the corresponding spike in the Brunt-Vaisala frequency produces a complicated mode trapping signature in the period spacings.Comment: 9 pages, 6 figures, 1 table, accepted for publication in A&