Time Series Analysis of fMRI Data: Spatial Modelling and Bayesian Computation

Time series analysis of fMRI data is an important area of medical statistics for neuroimaging data. The neuroimaging community has embraced mean-field variational Bayes (VB) approximations, which are implemented in Statistical Parametric Mapping (SPM) software. While computationally efficient, the quality of VB approximations remains unclear even though they are commonly used in the analysis of neuroimaging data. For reliable statistical inference, it is important that these approximations be accurate and that users understand the scenarios under which they may not be accurate. We consider this issue for a particular model that includes spatially-varying coefficients. To examine the accuracy of the VB approximation we derive Hamiltonian Monte Carlo (HMC) for this model and conduct simulation studies to compare its performance with VB. As expected we find that the computation time required for VB is considerably less than that for HMC. In settings involving a high or moderate signal-to-noise ratio (SNR) we find that the two approaches produce very similar results suggesting that the VB approximation is useful in this setting. On the other hand, when one considers a low SNR, substantial differences are found, suggesting that the approximation may not be accurate in such cases and we demonstrate that VB produces Bayes estimators with larger mean squared error (MSE). A real application related to face perception is also carried out. Overall, our work clarifies the usefulness of VB for the spatiotemporal analysis of fMRI data, while also pointing out the limitation of VB when the SNR is low and the utility of HMC in this case

Performance Evaluation of Finite-Source Cognitive Radio Networks with Impatient Customers

The current paper takes into consideration a cognitive radio network with impatient customers, by the help of finite-source retrial queueing system. We consider two different types of customers (Primary and Secondary) assigned to two interconnected frequency bands. A first frequency band with a priority queue and a second one with an orbit, both are respectively dedicated for the Primary Users (PUs) and Secondary Users (SUs). In case the servers are busy, both customers (Licensed and Unlicensed) join either the queue or the orbit. Before joining the orbit, secondary customers receive a random retrial time according to exponential distribution, which is the holding time before the next retry. Unlicensed users (impatient) are obliged to leave the system once their total waiting time exceeds a given maximum waiting time. The novelty of this work is the investigation of the abandonment and its impact on several performance measures of the system such as the mean response time and waiting time of users, probability of abandonment of SU, etc. Several figures illustrate the problem in question by the help of simulation

Conceptual Logic Production Line Modelling System

Many industrial sectors on the world are structured as a series as the production stages. Row material come from the beginning of the first step and enter into the process which various kind of processes like bath and continue where limited in the time as the constrain of the flow of the process to transfer to be products in to the next step, in the process they usually use conceptual logic or separately equipment to separate the eligible product and send second product to transfer to another equipment to be additional process where it should be make the added value for the second product. This modelling do the conceptual logic in production line system and analyse the factor of time between arrival raw material in the warehouse then directly process to the process unit then send it again to to the next process as well. The result of this study are decreased sharply in the beginning of the initial times for variables like number of waiting or queue, total process time, utilization and total entity time but increased the idle cost. This KPI are the indicators from the process for the triangular probability most likely value in the process.

Performance evaluation of finite-source Cognitive Radio Networks with impatient customers

The current paper takes into consideration a cognitive radio network with impatient customers, by the help of finite-source retrial queueing system. We consider two different types of customers (Primary and Secondary) assigned to two interconnected frequency bands. A first frequency band with a priority queue and a second one with an orbit, both are respectively dedicated for the Primary Users (PUs) and Secondary Users (SUs). In case the servers are busy, both customers (Licensed and Unlicensed) join either the queue or the orbit. Before joining the orbit, secondary customers receive a random retrial time according to Exponential distribution, which is the holding time before the next retry. Unlicensed users (impatient) are obliged to leave the system once their total waiting time exceeds a given maximum waiting time. The novelty of this work is the investigation of the abandonment and its impact on several performance measures of the system such as the mean response time and waiting time of users, probability of abandonment of SU, etc. Several figures illustrate the problem in question by the help of simulation

Coverage, Rate, and Last Hop Selection in Multi-Hop Communications in Highway Scenarios

The recent 3GPP initiative to extend IAB technology to mobile nodes in recently stated Release 18 opens up new opportunities for services operators in highway scenarios, where the extreme density of base stations (BS) is required to deliver uninterrupted coverage. The latter problem is specifically important for millimeter wave (mmWave) and future sub-terahertz (sub-THz) deployments. However, in such systems, there are inherent trade-offs between the rate provided over the multi-hop chain, the so-called “bridge”, and the inter-site distance. One of the critical factors involved in this trade-off is the choice of the last hop. In this paper, we utilize realistic channel measurements at 300 GHz to develop a framework characterizing the above-mentioned trade-off. Then, we proceed proposing a simple technique to maximize the latter by addressing the “last-hop problem” and compare its performance to the set of alternative solutions. Our numerical results illustrate that bumper location is better in terms of relaying communication distance. Furthermore, the proposed last hop selection strategies allow for extreme performance gains in terms of data rate as compared to the traditional approaches reaching 100% for large ISD and 400–500% for small ISDs. In absolute numbers, the proposed relying with the last hop selection strategy allows for reducing the required BS density along the highways by 15–30% depending on the vehicle density and required level of connectivity

Bayesian Computation with Application to Spatial Models and Neuroimaging

Analysis of Neuroimaging data has experienced great strides over the last few decades. Two key aspects of Neuroimaging data are its high-dimensionality and complex spatio-temporal autocorrelation. Classical approaches are somewhat limited in dealing with these two issues, as a result, Bayesian approaches are being utilized more frequently due to their flexibility. Despite their flexibility, there are several challenges for Bayesian approaches with respect to the required computation. First, the need for an efficient posterior computation method is paramount. Second, even in conjugate models, statistical accuracy in Bayesian computation may be hard to achieve. Since accuracy is of primary concern when studying the human brain, a careful and innovative exploration of Bayesian models and computation is necessary. In this dissertation, we address some of these issues by looking at various Bayesian computational algorithms in terms of both accuracy and speed in the context of Neuroimaging data. The algorithms we study are the Hamiltonian Monte Carlo (HMC), Variational Bayes (VB), and integrated nested Laplace approximation (INLA) algorithms. HMC is a MCMC method that's particularly powerful for sampling in high-dimensional space with highly correlated parameters. It's robust and accurate, yet not as fast as some approximate Bayesian methods, for example, Variational Bayes (VB). However, since there is no theoretical guarantee that the resulting posterior derived from VB is accurate, its performance has to be analyzed on a case-by-case basis. INLA is another extremely fast method based on numerical integration with Laplace approximations but, like VB, there are no generally applicable theoretical guarantees of accuracy. In Chapter II we focus on a particular spatial point process model, namely the log Gaussian Cox Process (LGCP), and consider applications to ecological and neuroimaging data. Inference for the LGCP is challenging due to its non-conjugacy and doubly stochastic property. We develop HMC and VB algorithms for the LGCP model and make comparisons with INLA. In Chapter III, we turn our focus to the general linear model with autoregressive errors (GLM-AR) which is widely used in analyzing fMRI single subject data. We derive an HMC algorithm and compare it with the VB algorithm and the mass univariate approach using the Statistical Parametric Mapping (SPM) software program. In Chapter IV, we extend the original GLM-AR model to a new model where the order of the AR coefficients can varying spatially across the brain and call it GLM with spatially varying autoregressive orders (SVARO). Using simulations and real data we compare our SVARO model with GLM-AR model implemented under both our MCMC sampler and the SPM VB algorithm. Our results shed light on several important issues. While HMC almost always yields the most accurate results, the performance of VB is strongly model specific. INLA is a fast alternative to MCMC methods but we observe some limitations when examining its accuracy in certain settings. Furthermore, our new SVARO model performs better than the GLM-AR model in a number of ways. Not surprisingly, more accurate algorithms generally require more computational time. By systematically evaluating the pros and cons of each method, we believe our work to be practically useful for those researchers considering the use of these methods.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138616/1/tengming_1.pd