Bayesian Procedures for the Estimation of Mutation Rates from Fluctuation Experiments

Bayesian procedures are developed for estimating mutation rates from fluctuation experiments. Three Bayesian point estimators are compared with four traditional ones using the results of 10,000 simulated experiments. The Bayesian estimators were found to be at least as efficient as the best of the previously known estimators. The best Bayesian estimator is one that uses (1/m(2)) as the prior probability density function and a quadratic loss function. The advantage of using these estimators is most pronounced when the number of fluctuation test tubes is small. Bayesian estimation allows the incorporation of prior knowledge about the estimated parameter, in which case the resulting estimators are the most efficient. It enables the straightforward construction of confidence intervals for the estimated parameter. The increase of efficiency with prior information and the narrowing of the confidence intervals with additional experimental results are investigated. The results of the simulations show that any potential inaccuracy of estimation arising from lumping together all cultures with more than n mutants (the jackpots) almost disappears at n = 70 (provided that the number of mutations in a culture is low). These methods are applied to a set of experimental data to illustrate their use.     

Estimation of the noise autocorrelation function in auditory evoked potential applications

This work presents a simple and accurate method to estimate the noise autocorrelation function in auditory evoked potential applications. It basically consists in applying a conventional correlation function estimator over the contaminated evoked potential signal processed by a comb filter. The main feature of the proposed technique is the possibility of obtaining information on large correlation lags without the need of extra time intervals, minimizing the estimation time. A theoretical analysis is provided showing that, under certain but achievable conditions, the correlation function of the processed signal approximates the real noise correlation function. Simulation results and an example with a single-trial evoked potential estimation technique illustrate the expected performance. The proposed method is of special interest to either single or small number of trials evoked potential estimation techniques in anaesthesia monitoring applications.     

Ranked set sampling for replicated sampling designs

In practical ecological sampling studies, a certain design (such as plot sampling or line-intercept sampling) is usually replicated more than once. For each replication, the Horvitz-Thompson estimation of the objective parameter is considered. Finally, an overall estimator is achieved by averaging the single Horvitz-Thompson estimators. Because the design replications are drawn independently and under the same conditions, the overall estimator is simply the sample mean of the Horvitz-Thompson estimators under simple random sampling. This procedure may be wisely improved by using ranked set sampling. Hence, we propose the replicated protocol under ranked set sampling, which gives rise to a more accurate estimation than the replicated protocol under simple random sampling.     

Simultaneous estimation of parameters in different linear models and applications to biometric problems.

Empirical Bayes procedure is employed in simultaneous estimation of vector parameters from a number of Gauss-Markoff linear models. It is shown that with respect to quadratic loss function, empirical Bayes estimators are better than least squares estimators. While estimating the parameter for a particular linear model, a suggestion has been made for distinguishing between the loss due to decision maker and the loss due to individual. A method has been proposed but not fully studied to achieve balance between the two losses. Finally the problem of predicting future observations in a linear model has been considered.     

Optimized estimation of respiratory impedance by signal averaging in the time domain.

The spontaneous breathing of a subject during measurements of respiratory impedance (Zrs) by the forced oscillation technique (FOT) induces errors that result in biased impedance estimates, especially at low frequencies. Although in standard measurements this bias may be avoided by using special impedance estimators, there are two applications of FOT for which such estimators are not useful: when a head generator is used and when measurements are made during intubation. In this paper we describe a data-processing procedure for unbiased impedance estimation for all FOT setups. The proposed estimator (Z) was devised for pseudorandom excitation and is based on time-domain signal averaging before frequency analysis. The performance of estimator Z was first analyzed by computer simulation of a head generator setup and a setup including an endotracheal tube to measure (2-32 Hz) a resistance-inertance-elastance model mimicking Zrs of a healthy subject. Second, Z was assessed during real measurements in 16 healthy subjects. The results obtained in the simulation (e.g., error in elastance was reduced from 15.6% with most conventional estimators to 3.3% with Z in simulation of head generator setup) and in the measurements in subjects (differences of less than 1.6% between Z and a reference) confirmed the theoretical lack of bias of Z and its practical suitability for the different FOT setups. In addition to its applicability in the situations in which no other unbiased estimators are available, estimator Z is also advantageous in most conventional applications of FOT, since it requires much less computing time and thus allows on-line Zrs measurements.     

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.     

Single-sweep cortical somatosensory evoked potentials: N20 and evoked bursts in sevoflurane anaesthesia

Cortical evoked responses to median nerve stimulation were recorded from 21 subjects during sevoflurane anaesthesia at the level of burst suppression in EEG. The N20/P22 wave had the typical form of a negative wave postcentrally, and positive precentrally. The amplitude exceeded 4 μV in all patients, making it easily visible without averaging on the low-amplitude suppression. These results show that two kinds of somatosensory evoked potential can be studied without averaging during EEG suppression in deep anaesthesia. One is the localised N20/P22 wave, which is seen regularly during suppression after stimuli with intervals exceeding 1 s. The other is the burst, involving the whole cortex, which is not evoked by every stimulus. We suggest that somatosensory evoked potentials can be monitored during sevoflurane-induced EEG suppression, and often can be evaluated reliably from a couple of single sweeps with stimulation interval exceeding 1 s. The enhancement of early cortical components of SEP, their adaptation to repeated stimuli, and the disappearance of later polysynaptic components during EEG suppression, give new possibilities to study the generators of SEP and the different effects of anaesthetics.     

Applications of a signal averager for neurophysiological investigations in clinical function laboratories using a general signal-processing unit

A general 'coherent signal averager' software package which can be run on a small laboratory computer is presented as an application of a new approach to medical instrumentation. The combination of the minicomputer, preprocessing hardware and the above-mentioned software yields a flexible multipurpose averaging system for electrophysiological signals. The possibilities of the system are discussed with reference to visual evoked potential measurements in a clinical function laboratory.     

Bayesian Reliability Estimation of a Two-parameter Cauchy Distribution

This paper gives an approximate Bayes procedure for the estimation of the reliability function of a two-parameter Cauchy distribution using Jeffreys' non-informative prior with a squared-error loss function, and with a log-odds ratio squared-error loss function. Based on a Monte Carlo simulation study, two such Bayes estimators of the reliability are compared with the maximum likelihood estimator.     

Distributed File System Virtualization Techniques Supporting On-Demand Virtual Machine Environments for Grid Computing

This paper presents a data management solution which allows fast Virtual Machine (VM) instantiation and efficient run-time execution to support VMs as execution environments in Grid computing. It is based on novel distributed file system virtualization techniques and is unique in that: (1) it provides on-demand cross-domain access to VM state for unmodified VM monitors; (2) it enables private file system channels for VM instantiation by secure tunneling and session-key based authentication; (3) it supports user-level and write-back disk caches, per-application caching policies and middleware-driven consistency models; and (4) it leverages application-specific meta-data associated with files to expedite data transfers. The paper reports on its performance in wide-area setups using VMware-based VMs. Results show that the solution delivers performance over 30% better than native NFS and with warm caches it can bring the application-perceived overheads below 10% compared to a local-disk setup. The solution also allows a VM with 1.6 GB virtual disk and 320 MB virtual memory to be cloned within 160 seconds for the first clone and within 25 seconds for subsequent clones. Ming Zhao is a PhD candidate in the department of Electrical and Computer Engineering and a member of the Advance Computing and Information Systems Laboratory, at University of Florida. He received the degrees of BE and ME from Tsinghua University. His research interests are in the areas of computer architecture, operating systems and distributed computing. Jian Zhang is a PhD student in the Department of Electrical and Computer Engineering at University of Florida and a member of the Advance Computing and Information Systems Laboratory (ACIS). Her research interest is in virtual machines and Grid computing. She is a member of the IEEE and the ACM. Renato J. Figueiredo received the B.S. and M.S. degrees in Electrical Engineering from the Universidade de Campinas in 1994 and 1995, respectively, and the Ph.D. degree in Electrical and Computer Engineering from Purdue University in 2001. From 2001 until 2002 he was on the faculty of the School of Electrical and Computer Engineering of Northwestern University at Evanston, Illinois. In 2002 he joined the Department of Electrical and Computer Engineering of the University of Florida as an Assistant Professor. His research interests are in the areas of computer architecture, operating systems, and distributed systems.     

Wiener filtration versus averaging of evoked responses

The extraction of the evoked potential by the Wiener filtration technique is performed to compare it with classical averaging. It is well known that the Wiener filter supplies the least square error estimate. On the other hand, it is apparent that this error substantially depends on the choice of the lengths of interstimulation intervals. Artificially simulated examples are processed by both techniques, averaging and Wiener filtration, to show that the proper choice of the interstimulating intervals is much more relevant for decreasing the estimate error than in helping us make the decision which of these methods should be used.     

Generalized centroid estimators in bioinformatics

In a number of estimation problems in bioinformatics, accuracy measures of the target problem are usually given, and it is important to design estimators that are suitable to those accuracy measures. However, there is often a discrepancy between an employed estimator and a given accuracy measure of the problem. In this study, we introduce a general class of efficient estimators for estimation problems on high-dimensional binary spaces, which represent many fundamental problems in bioinformatics. Theoretical analysis reveals that the proposed estimators generally fit with commonly-used accuracy measures (e.g. sensitivity, PPV, MCC and F-score) as well as it can be computed efficiently in many cases, and cover a wide range of problems in bioinformatics from the viewpoint of the principle of maximum expected accuracy (MEA). It is also shown that some important algorithms in bioinformatics can be interpreted in a unified manner. Not only the concept presented in this paper gives a useful framework to design MEA-based estimators but also it is highly extendable and sheds new light on many problems in bioinformatics.     

Evaluation of brain-stem auditory evoked potentials using dynamic time warping

Dynamic time warping is a procedure whereby portions of a temporal sequence of values are stretched or shrunk to make it similar to another sequence. This procedure can be used to align the brain-stem auditory evoked potentials recorded from different subjects prior to averaging. The resultant warp-average more closely resembles the wave form of a typical subject than the conventional average. Dynamic time warping can also be used to compare one brain-stem auditory evoked potential to another. This comparison can show the differences that result from changes in a stimulus parameter such as intensity or repetition rate. When a patient's wave form is compared to a normal template, warping can identify the peaks in the patient's wave form that correspond most closely to the peaks in the normal template. Compared to an experienced human interpreter, warping is very accurate in identifying the waves of normal brain-stem auditory evoked potentials (error rate between 0 and 4%) and reasonably accurate in identifying the peaks in abnormal wave forms (error rate between 3 and 18%).     

Optimal Transmission Radius for Flooding in Large Scale Sensor Networks

One of the principal characteristics of large scale wireless sensor networks is their distributed, multi-hop nature. Due to this characteristic, applications such as query propagation rely regularly on network-wide flooding for information dissemination. If the transmission radius is not set optimally, the flooded packet may be holding the transmission medium for longer periods than are necessary, reducing overall network throughput. We analyze the impact of the transmission radius on the average settling time—the time at which all nodes in the network finish transmitting the flooded packet. Our analytical model takes into account the behavior of the underlying contention-based MAC protocol, as well as edge effects and the size of the network. We show that for large wireless networks there exists an intermediate transmission radius which minimizes the settling time, corresponding to an optimal tradeoff between reception and contention times. We also explain how physical propagation models affect small wireless networks and why there is no intermediate optimal transmission radius observed in these cases. The mathematical analysis is supported and validated through extensive simulations.Marco Zuniga is currently a PhD student in the Department of Electrical Engineering at the University of Southern California. He received his Bachelors degree in Electrical Engineering from the Pontificia Universidad Catolica del Peru in 1998, and his Masters degree in Electrical Engineering from the University of Southern California in 2002. His interests are in the area of Wireless Sensor Networks in general, and more specifically in studying the interaction amongst different layers to improve the performance of these networks. He is a member of IEEE and the Phi Kappa Phi Honor society.Bhaskar Krishnamachari is an Assistant Professor in the Department of Electrical Engineering at the University of Southern California (USC), where he also holds a joint appointment in the Department of Computer Science. He received his Bachelors degree in Electrical Engineering with a four-year full-tuition scholarship from The Cooper Union for the Advancement of Science and Art in 1998. He received his Masters degree and his Ph.D. in Electrical Engineering from Cornell University in 1999 and 2002, under a four-year university graduate fellowship. Dr. Krishnamacharis previous research has included work on critical density thresholds in wireless networks, data centric routing in sensor networks, mobility management in cellular telephone systems, multicast flow control, heuristic global optimization, and constraint satisfaction. His current research is focused on the discovery of fundamental principles and the analysis and design of protocols for next generation wireless sensor networks. He is a member of IEEE, ACM and the Tau Beta Pi and Eta Kappa Nu Engineering Honor Societies     

Neural networks for self-adjusting mutation rate estimation when the recombination rate is unknown

Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics.Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean squared error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and/or are unknown.     

Estimating intraclass correlation for binary data

This paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study. Some of the estimators are very specific, while others result from general methods such as pseudo-likelihood and extended quasi-likelihood estimation. The simulation study identifies several useful estimators, one of which does not seem to have been considered previously for binary data. Estimators based on extended quasi-likelihood are found to have a substantial bias in some circumstances.     

Presynaptic contributions to response shape in an auditory neuron of the grasshopper

Neuron 714 is morphologically one of the most prominent neurons in the central auditory pathway of the grasshopper with arborizations extending from the abdominal neuromeres of the metathoracic ganglion to the brain. The aim of this study is to explore auditory information flow involving neuron 714 at the level of the ventral nerve cord. Paired intracellular recordings were made from neuron 714 in the mesothorax on the one hand, and from candidate presynaptic auditory neurons of the metathorax on the other. Electrical stimulation of the tympanal nerves provides an estimate of the synaptic distance between these interneurons and auditory afferents. Four, including neuron 714, are monosynaptically connected to afferents, the remainder disynaptically. Current-injection and spike-triggered averaging reveal that of nine neurons examined, seven make either monosynaptic, disynaptic or polysynaptic connections onto neuron 714. All connections are excitatory. Paired recordings show that response duration and response amplitude in synaptically linked cells vary according to the frequency of the stimulus. Measurements of the latency of the first excitatory post-synaptic potential evoked in neuron 714 by afferents and by metathoracic interneurons show how the synaptic drive from these sources shapes the auditory response of neuron 714. Accepted: 14 October 1998     

Visual acuity of the midland banded water snake estimated from evoked telencephalic potentials

The visual acuity of seven midland banded water snakes was measured by recording evoked responses from telencephalon to temporally modulated square wave grating patterns. Using conventional electrophysiological techniques and signal averaging, high contrast square wave gratings of different spatial frequencies were presented. Acuity was estimated by extrapolating relative response amplitude/log₁₀ spatial frequency functions which yielded an average acuity of 4.25 cycles/degree. Refractive state was also estimated by recording evoked potentials to intermediate spatial frequencies with different lenses in front of the eye. Polynomial fits indicated that under the experimental conditions the snakes were around 6.4 diopters hyperopic suggesting a corrected acuity of 4.89 cycles/degree. Reduction of grating luminance resulted in a reduction in evoked potential acuity measurements. These results indicate that the spatial resolution of midland banded water snakes is the equal of cat; about 20/120 in human clinical terms.     

Estimation of the Parameters of two Parallel Regression Lines Under Uncertain Prior Information

The problem of parallelism for bi‐linear regression lines arises in many real life investigations. For two linear regression models with normal errors, the estimation of the slope as well as the intercept parameters is considered when it is apriori suspected that the two lines are parallel. Three different estimators are defined by using both the sample data and the non‐sample uncertain prior information. The relative performances of the unrestricted, restricted and preliminary test estimators are investigated based on the analysis of the bias, and risk functions under quadratic loss. An example based on a medical study is used to illustrate the method.     

The estimation of genetic relationships using molecular markers and their efficiency in estimating heritability in natural populations

Molecular marker data collected from natural populations allows information on genetic relationships to be established without referencing an exact pedigree. Numerous methods have been developed to exploit the marker data. These fall into two main categories: method of moment estimators and likelihood estimators. Method of moment estimators are essentially unbiased, but utilise weighting schemes that are only optimal if the analysed pair is unrelated. Thus, they differ in their efficiency at estimating parameters for different relationship categories. Likelihood estimators show smaller mean squared errors but are much more biased. Both types of estimator have been used in variance component analysis to estimate heritability. All marker-based heritability estimators require that adequate levels of the true relationship be present in the population of interest and that adequate amounts of informative marker data are available. I review the different approaches to relationship estimation, with particular attention to optimizing the use of this relationship information in subsequent variance component estimation.