[Bayesian Survival Analysis]

by

ACKNOWLEDGEMENT

I would take this opportunity to thank my research supervisor, family and friends for their support and guidance without which this research would not have been possible.

DECLARATION

I, [type your full first names and surname here], declare that the contents of this dissertation/thesis represent my own unaided work, and that the dissertation/thesis has not previously been submitted for academic examination towards any qualification. Furthermore, it represents my own opinions and not necessarily those of the University.

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ABSTRACT

The rational management of water resource systems requires an understanding of their response to existing and planned schemes of exploitation, pollution prevention and/or remediation. Such understanding requires the collection of data to help characterize the system and monitor its response to existing and future stresses. It also requires incorporating such data in models of system makeup, water flow and contaminant transport. As the collection of subsurface characterization and monitoring data is costly, it is imperative that the design of corresponding data collection schemes be cost-effective, i.e., that the expected benefit of new information exceed its cost. A major benefit of new data is its potential to help improve one's understanding of the system, in large part through a reduction in model predictive uncertainty and corresponding risk of failure. Traditionally, value-of-information or data-worth analyses have relied on a single conceptual-mathematical model of site hydrology with prescribed parameters. Yet there is a growing recognition that ignoring model and parameter uncertainties render model predictions prone to statistical bias and underestimation of uncertainty. This has led to a recent emphasis on conducting hydrologic analyses and rendering corresponding predictions by means of multiple models. We describe a corresponding approach to data-worth analyses within a Bayesian model averaging (BMA) framework. We focus on a maximum likelihood version (MLBMA) of BMA which (a) is compatible with both deterministic and stochastic models, (b) admits but does not require prior information about the parameters, (c) is consistent with modern statistical methods of hydrologic model calibration, (d) allows approximating lead predictive moments of any model by linearization, and (e) updates model posterior probabilities as well as parameter estimates on the basis of potential new data both before and after such data become actually available. We describe both the BMA and MLBMA versions theoretically and implement MLBMA computationally on a synthetic example with and without linearization.

TABLE OF CONTENTS

ACKNOWLEDGEMENT2

DECLARATION3

ABSTRACT4

CHAPTER 1: INTRODUCTION6

CHAPTER 2: BACKGROUND8

Bayesian decision analysis framework8

Bayesian model averaging (BMA)9

Maximum likelihood Bayesian model averaging (MLBMA)10

CHAPTER 3: EFFECT OF DATA AUGMENTATION ON UNCERTAINTY12

BMA framework12

MLBMA framework13

CHAPTER 4: SYNTHETIC GEO-STATISTICAL EXAMPLE15

CHAPTER 5: APPLICATION OF BESIYAN MODEL24

Application of Bayesian networks in prognostics for a new Integrated Vehicle Health Management concept24

Related works26

Aircraft maintenance26

Future maintenance scenarios27

Integrated Data Management System29

Bayesian networks30

Learning and adaptation32

I - Learning the structure33

II - Learning probabilities in batches33

III - Learning probabilities sequentially33

Bayesian networks for diagnosis34

Bayesian networks for prognosis37

Experimental results40

Experimental setup40

Final model41

Results43

Conclusions and future works45

CHAPTER 6: CONCLUSIONS47

REFERENCES48

CHAPTER 1: INTRODUCTION

The world's water supply is threatened by overexploitation and contamination. To manage this supply in an optimal and sustainable manner, it is necessary to understand the response of water resource systems ...