Browsing by Subject "Calibration"

Background

Methods

Results

Conclusions

Our interest is the risk assessment of rare natural hazards, such as

large volcanic pyroclastic flows. Since catastrophic consequences of

volcanic flows are rare events, our analysis benefits from the use of

a computer model to provide information about these events under

natural conditions that may not have been observed in reality.

A common problem in the analysis of computer experiments, however, is the high computational cost associated with each simulation of a complex physical process. We tackle this problem by using a statistical approximation (emulator) to predict the output of this computer model at untried values of inputs. Gaussian process response surface is a technique commonly used in these applications, because it is fast and easy to use in the analysis.

We explore several aspects of the implementation of Gaussian process emulators in a Bayesian context. First, we propose an improvement for the implementation of the plug-in approach to Gaussian processes. Next, we also evaluate the performance of a spatial model for large data sets in the context of computer experiments.

Computer model data can also be combined to field observations in order to calibrate the emulator and obtain statistical approximations to the computer model that are closer to reality. We present an application where we learn the joint distribution of inputs from field data and then bind this auxiliary information to the emulator in a calibration process.

One of the outputs of our computer model is a surface of maximum volcanic flow height over some geographical area. We show how the topography of the volcano area plays an important role in determining the shape of this surface, and we propose methods

to incorporate geophysical information in the multivariate analysis of computer model output.

Among women worldwide, cervical cancer is the third most common cancer with an incidence rate of 15.3 per 100,000 and a mortality rate of 7.8 per 100,000 women. This is largely attributed to the lack of infrastructure and resources in the developing countries to support the organized screening and diagnostic programs that are available to women in developed nations. Hence, there is a critical global need for a screening and diagnostic paradigm that is effective in low-resource settings. Various strategies are described to design an optical spectroscopic sensor capable of collecting reliable diffuse reflectance data to extract quantitative optical contrasts for cervical cancer screening and diagnosis.

A scalable Monte Carlo based optical toolbox can be used to extract absorption and scattering contrasts from diffuse reflectance acquired in the cervix in vivo. [Total Hb] was shown to increase significantly in high-grade cervical intraepithelial neoplasia (CIN 2+), clinically the most important tissue grade to identify, compared to normal and low-grade intraepithelial neoplasia (CIN 1). Scattering was not significantly decreased in CIN 2+ versus normal and CIN 1, but was significantly decreased in CIN relative to normal cervical tissues.

Immunohistochemistry via anti-CD34, which stains the endothelial cells that line blood vessels, was used to validate the observed absorption contrast. The concomitant increase in microvessel density and [total Hb] suggests that both are reactive to angiogenic forces from up-regulated expression of VEGF in CIN 2+. Masson's trichrome stain was used to assess collagen density changes associated with dysplastic transformation of the cervix, hypothesized as the dominant source of decreased scattering observed. Due to mismatch in optical and histological sampling, as well as the small sample size, collagen density and scattering did not change in a similar fashion with tissue grade. Dysplasia may also induce changes in cross-linking of collagen without altering the amount of collagen present. Further work would be required to elucidate the exact sources of scattering contrast observed.

Common confounding variables that limit the accuracy and clinical acceptability of optical spectroscopic systems are calibration requirements and variable probe-tissue contact pressures. Our results suggest that using a real-time self-calibration channel, as opposed to conventional post-experiment diffuse reflectance standard calibration measurements, significantly improved data integrity for the extraction of scattering contrast. Extracted [total Hb] and scattering were also significantly associated with applied contact probe pressure in colposcopically normal sites. Hence, future contact probe spectroscopy or imaging systems should incorporate a self-calibration channel and ensure spectral acquisition at a consistent contact pressure to collect reliable data with enhanced absorption and scattering contrasts.

Another method to enhance optical contrast is to selectively interrogate different depths in the dysplastic cervix. For instance, scattering has been shown to increase in the epithelium (increase in nuclear-to-cytoplasmic ratio) while decrease in the stroma (re-organization of the extra-cellular matrix and changes in of collagen fiber cross-links). A fiber-optic probe with 45° illumination and collection fibers with a separation distance of 330 μm was designed and constructed to selectively interrogate the cervical epithelium. Mean extraction errors from liquid phantoms with optical properties mimicking the cervical epithelium for μa and μs' were 11.3 % and 12.7 %, respectively. Diffuse reflectance spectra from 9 sites in four loop electrosurgical excision procedure (LEEP) patients were analyzed. Preliminary data demonstrate the utility of the oblique fiber geometry in extracting scattering contrast in the cervical epithelium. Further work is needed to study the systematic error in optical property extraction and to incorporate simultaneous extraction of epithelial and stromal contrasts using both flat and oblique illumination and collection fibers.

Various strategies, namely self-calibration, consistent contact pressure, and the incorporation of depth-selective sensing, have been proposed to improve the data integrity of an optical spectroscopic system for maximal contrast. In addition to addressing field operation requirements (such as power and operator training requirement), these improvements should enable the collection of reliable spectral data to aid in the adoption of optical smart sensors in the screening and diagnosis of cervical precancer, especially in a global health setting.

Scientific inquiry about natural phenomena and processes are increasingly relying on the use of computer models as simulators of such processes. The challenge of using computer models for scientific investigation is that they are expensive in terms of computational cost and resources. However, the core methodology of fast statistical emulation (approximation) of a computer model overcomes this computational problem.

Complex phenomena and processes are often described not by a single computer model, but by a system of computer models or simulators. Direct emulation of a system of simulators may be infeasible for computational and logistical reasons.

This thesis proposes a statistical framework for fast emulation of systems of computer models and demonstrates its potential for inferential and predictive scientific goals.

The first chapter of the thesis introduces the Gaussian stochastic process (GaSP) emulator of a single simulator and summarizes ideas and findings in the rest of the thesis. The second chapter investigates the possibility of using independent GaSP emulators of computer models for fast construction of emulators of systems of computer models. The resulting approximation to a system of computer models is called the linked emulator. The third chapter discusses the irrelevance of attempting to model multivariate output of a computer model, for the purpose of emulation of that model. The linear model of coregionalization (LMC) is used to demonstrate this irrelevance, from both a theoretical perspective and from simulation studies. The fourth chapter introduces a framework for calibration of a system of computer models, using its linked emulator. The linked emulator allows for development of independent emulators of submodels on their own separately constructed design spaces, thus leading to effective dimension reduction in explored parameter space. The fifth chapter addresses the use of some non-Gaussian emulators, in particular censored and truncated GaSP emulators. The censored emulator is constructed to appropriately account for zero-inflated output of a computer model, arising when there are large regions of the input space for which the computer model output is zero. The truncated GaSP accommodates computer model output that is constrained to appear in a certain region. The linked emulator, for systems of computer models whose individual subemulators are either censored or truncated, is also presented. The last chapter concludes with an exposition of further research directions based on the ideas explored in the thesis.

The methodology developed in this thesis is illustrated by an application to quantification of the hazard from pyroclastic flow from the Soufri\`{e}re Hills Volcano on the island of Montserrat; a case study on prediction of volcanic ash transport and dispersal from the Eyjafjallaj{\"o}kull volcano, Iceland in April 14-16, 2010; and calibration of a vapour-liquid equilibrium model, a submodel of the Aspen Plus \textcopyright~chemical process software for design and deployment of amine-based $\mathrm{CO_2}$ capture systems.

This research presents new calibration techniques for the characterization of atomic force microscopy cantilevers. Atomic force microscopy cantilevers are sensors that detect forces on the order of pico- to nanonewtons and displacements on the order of nano- to micrometers. Several calibration techniques exist with a variety of strengths and weaknesses. This research presents techniques that enable the noncontact calibration of the output sensor voltage-to-displacement sensitivity and the cantilever stiffness through the analysis of the unscaled thermal vibration of a cantilever in a liquid environment.

A noncontact stiffness calibration method is presented that identifies cantilever characteristics by fitting a dynamic model of the cantilever reaction to a thermal bath according to the fluctuation-dissipation theorem. The fitting algorithm incorporates an assumption of heavy fluid loading, which is present in liquid environments.

The use of the Lorentzian line function and a variable-slope noise model as an alternate approach to the thermal noise method was found to reduce the difference between calibrations preformed on the same cantilever in air and in water relative to existing techniques. This alternate approach was used in combination with the new stiffness calibration technique to determine the voltage-to-displacement sensitivity without requiring contact loading of the cantilever.

Additionally, computational techniques are presented in the investigation of alternate cantilever geometries, including V-shaped cantilevers and warped cantilevers. These techniques offer opportunities for future research to further reduce the uncertainty of atomic force microscopy calibration.

X-ray micro-CT is widely used for small animal imaging in preclinical studies of cardiopulmonary disease, but further development is needed to improve spatial resolution, temporal resolution, and material contrast. This study presents a set of tools that achieve these improvements. These tools include the mathematical formulation and computational implementation of algorithms for calibration, image reconstruction, and image analysis with our custom micro-CT system. These tools are tested in simulations and in experiments with live animals. With these tools, it is possible to visualize the distribution of a contrast agent throughout the body of a mouse as it changes over time, and produce 5-dimensional images (3 spatial dimensions + time + energy) of the cardiac cycle.

Problems involving computer model emulation arise when scientists simulate expensive experiments with computationally expensive computer models. To more quickly probe the experimental design space, statisticians build emulators that act as fast surrogates to the computationally expensive computer models. The emulators are typically Gaussian processes, in order to induce spatial correlation in the input space. Often the main scientific interest lies in inference on one or more input parameters of the computer model which do not vary in nature. Inference on these input parameters is referred to as ``calibration,'' and these inputs are referred to as ``calibration parameters.'' We first detail our emulation and calibration model for an application in high-energy particle physics; this model brings together some existing ideas in the literature on handling multivariate output, and lays out a foundation for the remainder of the thesis.

In the next two chapters, we introduce novel ideas in the field of computer model emulation and calibration. The first addresses the problem of model comparison in this context, and how to simultaneously compare competing computer models while performing calibration. Using a mixture model to facilitate the comparison, we demonstrate that by conditioning on the mixture parameter we can recover the calibration parameter posterior from an independent calibration model. This mixture is then extended in the case of correlated data, a crucial innovation for this comparison framework to be useful in the particle collision setting. Lastly, we explore two possible non-exchangeable mixture models, where model preference changes over the input space.

The second novel idea addresses density estimation when only coarse bin counts are available. We develop an estimation method which avoids costly numerical integration and maintains plausible correlation for nearby bins. Additionally, we extend the method to density regression so that full a full density can be predicted from an input parameter, having only been trained on coarse histograms. This enables inference on the input parameter, and we develop an importance sampling method that compares favorably to the foundational calibration method detailed earlier.