The collection of biological data has been limited by instrumentation, the complexity of the systems themselves, and even the ability of graduate students to stay awake and record the data. However, increasing measurement capabilities and decreasing costs may soon enable the collection of reasonably sampled time course data characterizing biological systems, though in general only a subset of the system's species would be measured. This increase in data volume requires a corresponding increase in the use and interpretation of such data, specifically in the development of system identification techniques to identify parameter sets in proposed models. In this paper, we present the results of identifiability analysis on a small test system, including the identifiability of parameters with respect to different measurements (proteins and mRNA), and propose a working definition for "biologically meaningful estimation". We also analyze the correlations between parameters, and use this analysis to consider effective approaches to determining parameters with biological meaning. In addition, we look at other methods for determining relationships between parameters and their possible significance. Finally, we present potential biologically meaningful parameter groupings from the test system and present the results of our attempt to estimate the value of select groupings. / Master of Science

In previous studies, evidence of thermal wave behavior was found in heterogeneous materials. Thus, the overall goal of this study was to experimentally verify those results, and develop a parameter estimation scheme to estimate the thermal properties of various heterogeneous materials. Two types of experiments (Experiments 1 and 2) were conducted to verify the existence or non-existence of thermal wave behavior in heterogeneous materials. In Experiment 1 sand, ion exchanger, and sodium bicarbonate were used as test materials, while processed meat (bologna) was used in Experiment 2. The measured temperature profiles of the samples were compared with the parabolic and hyperbolic heat conduction model results. The values of thermal diffusivity and thermal conductivity were obtained using the Box-Kanemasu parameter estimation method which is based on the comparison between temperature measurements and the solutions of the theoretical model. Overall, no clear experimental evidence was found to justify the use of hyperbolic heat conduction models rather than parabolic for the materials tested. Further comprehensive experimentation using different heating rates is warranted to definitely identify the accurate type of heat conduction process associated with such materials, and to describe the physical mechanisms which produce wave-like heat conduction in heterogeneous materials. / Master of Science

Inlet distortion research has become increasingly important over the past several years as demands for aircraft flight efficiency and performance has increased. To accommodate these demands, research progression has shifted the emphasis onto airframe-engine integration and improved understanding of engine operability in less than ideal conditions. Swirl distortion, which is considered a type of non-uniform inflow inlet distortion, is characterized by the presence of swirling flow in an inlet. The presence of swirling flow entering an engine can affect the compression systems performance and operability, therefore it is an area of current research. A swirl distortion generation device created by Virginia Tech, identified as the StreamVane, has the ability to produce various swirl distortion flow profiles. In its current state, the StreamVane methodology generates a design swirl distortion at the trailing edge of the device. However, in many applications the plane at which the researcher wants a desired distortion is downstream of the StreamVane trailing edge. After the distortion is discharged from the StreamVane it develops as it moves downstream. Therefore, to more accurately replicate a desired swirl distortion at a given downstream plane, distortion development downstream of the StreamVane must be considered. Currently Virginia Tech utilizes a numerical modeling design tool, designated StreamFlow, that generates predictions of how a StreamVane-generated distortion propagates downstream. However, due to the non-linear physics of the flow problem, StreamFlow cannot directly calculate an accurate inverse solution that can predict upstream conditions from a downstream boundary, as needed to design a StreamVane. To solve this problem, in this research, an efficient estimation process has been created, combining the use of the StreamFlow model with a Markov Chain Monte Carlo (MCMC) parameter estimation tool to estimate upstream flow profiles that will produce the desired downstream profiles. The process is designated the StreamFlow-MC2 Estimation Process. The process was tested on four fundamental types of swirl distortions. The desired downstream distortion was input into the estimation process to predict an upstream profile that would create the desired downstream distortion. Using the estimated design profiles, 6-inch diameter StreamVanes were designed then wind tunnel tested to verify the distortion downstream. Analysis and experimental results show that using this method, the upstream distortion needed to create the desired distortion was estimated with excellent accuracy. Based on those results, the StreamFlow-MC2 Estimation Process was validated. / Master of Science / Inlet distortion research has become increasingly important over the past several years as demands for aircraft flight efficiency and performance has increased. To accommodate these demands, research progression has shifted the emphasis onto airframe-engine integration and improved understanding of engine operability in less than ideal conditions. Swirl distortion, which is considered a type of non-uniform inflow inlet distortion, is characterized by the presence of swirling flow in an inlet. The presence of swirling flow entering an engine can affect the compression system’s performance and operability, therefore it is an area of current research. A swirl distortion generation device created by Virginia Tech, identified as the StreamVane™, has the ability to produce various swirl distortion flow profiles. In its current state, the StreamVane methodology generates a design swirl distortion at the trailing edge of the device. However, in many applications the plane at which the researcher wants a desired distortion is downstream of the StreamVane trailing edge. After the distortion is discharged from the StreamVane it develops as it moves downstream. Therefore, to more accurately replicate a desired swirl distortion at a given downstream plane, distortion development downstream of the StreamVane must be considered. Currently Virginia Tech utilizes a numerical modeling design tool, designated StreamFlow, that generates predictions of how a StreamVane-generated distortion propagates downstream. However, due to the non-linear physics of the flow problem, StreamFlow cannot directly calculate an accurate inverse solution that can predict upstream conditions from a downstream boundary, as needed to design a StreamVane. To solve this problem, in this research, an efficient estimation process has been created, combining the use of the StreamFlow model with a Markov Chain Monte Carlo (MCMC) parameter estimation tool to estimate upstream flow profiles that will produce the desired downstream profiles. The process is designated the StreamFlow-MC2 Estimation Process. The process was tested on four fundamental types of swirl distortions. The desired downstream distortion was input into the estimation process to predict an upstream profile that would create the desired downstream distortion. Using the estimated design profiles, 6-inch diameter StreamVanes were designed then wind tunnel tested to verify the distortion downstream. Analysis and experimental results show that using this method, the upstream distortion needed to create the desired distortion was estimated with excellent accuracy. Based on those results, the StreamFlow-MC2 Estimation Process was validated.

published_or_final_version / abstract / Electrical and Electronic Engineering / Master / Master of Philosophy

No description available.

No description available.

Sensor network plays a significant role in determining the performance of network inference tasks. A wireless sensor network with a large number of sensor nodes can be used as an effective tool for gathering data in various situations. One of the major issues in WSN is developing an efficient protocol which has a significant impact on the convergence of the network. Parameter estimation is one of the most important applications of sensor network. In order to model such large and complex networks for estimation, efficient strategies and algorithms which take less time to converge are being developed. To deal with this challenge, an approach of having multilayer network structure to estimate parameter and reach convergence in less time is estimated by comparing it with known gossip distributed algorithm. Approached Multicast multilayer algorithm on a network structure of Gaussian mixture model with two components to estimate parameters were compared and simulated with gossip algorithm. Both the algorithms were compared based on the number of iterations the algorithms took to reach convergence by using Expectation Maximization Algorithm.Finally a series of theoretical and practical results that explicitly showed that Multicast works better than gossip in large and complex networks for estimation in consensus building strategies.

Contemporary cosmology is a vibrant field, with data and observations increasing rapidly. This allows for accurate estimation of the parameters describing our cosmological model. In this thesis we present new research based on two different types of cosmological observations, which probe the universe at multiple epochs. We begin by reviewing the current concordance cosmological paradigm, and the statistical tools used to perform parameter estimation from cosmological data. We highlight the initial conditions in the universe and how they are detectable using the Cosmic Microwave Background radiation. We present the angular power spectrum data from temperature observations made with the Atacama Cosmology Telescope (ACT) and the methods used to estimate the power spectrum from temperature maps of the sky. We then present a cosmological analysis using the ACT data in combination with observations from the Wilkinson Microwave Anisotropy Probe to constrain parameters such as the effective number of relativistic species and the spectral index of the primordial power spectrum, which we constrain to deviate from scale invariance at the 99% confidence limit. We then use this combined dataset to constrain the primordial power spectrum in a minimally parametric framework, finding no evidence for deviation from a power-law spectrum. Finally we present Bayesian Estimation Applied to Multiple Species, a parameter estimation technique using photometric Type Ia Supernova data to estimate cosmological parameters in the presence of contaminated data. We apply this algorithm to the full season of the Sloan Digital Sky Survey II Supernova Search, and find that the constraints are improved by a factor of three relative to the case where one uses a smaller, spectroscopically confirmed subset of supernovae.

The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

by Ming-long Lam. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 41-43.