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Full-Text Articles in Physical Sciences and Mathematics

An Agent-Based Model To Study The Spread And Control Of Epidemics, Ashley Dawn Fuller Jan 2008

An Agent-Based Model To Study The Spread And Control Of Epidemics, Ashley Dawn Fuller

Theses and Dissertations

The world continues to face outbreaks of disease due to natural causes as well as the threat of biological warfare. Mathematical modeling provides an avenue by which to predict and ultimately prevent widespread outbreaks. A wide variety of modeling tools have been used in the study of the spread of diseases, including Ordinary Differential Equations, Partial Differential Equations, and Difference Equations. In this study, an agent-based model is used to study the spread and control of epidemics and is based on Sirakoulis, et al. [1]. The computer program NetLogo [2] is used for simulation. The development and set-up procedures for …


Properties And Recent Applications In Spectral Graph Theory, Michelle L. Rittenhouse Jan 2008

Properties And Recent Applications In Spectral Graph Theory, Michelle L. Rittenhouse

Theses and Dissertations

There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are …


Probe Level Analysis Of Affymetrix Microarray Data, Richard Ellis Kennedy Jan 2008

Probe Level Analysis Of Affymetrix Microarray Data, Richard Ellis Kennedy

Theses and Dissertations

The analysis of Affymetrix GeneChip® data is a complex, multistep process. Most often, methodscondense the multiple probe level intensities into single probeset level measures (such as RobustMulti-chip Average (RMA), dChip and Microarray Suite version 5.0 (MAS5)), which are thenfollowed by application of statistical tests to determine which genes are differentially expressed. An alternative approach is a probe-level analysis, which tests for differential expression directly using the probe-level data. Probe-level models offer the potential advantage of more accurately capturing sources of variation in microarray experiments. However, this has not been thoroughly investigated, since current research efforts have largely focused on the …


A Stratigraphic And Depositional Interpretation Of A Sand Quarry In Middle Georgia, Jessica Taylor Jan 2008

A Stratigraphic And Depositional Interpretation Of A Sand Quarry In Middle Georgia, Jessica Taylor

Theses and Dissertations

Analysis of sediments from two sand quarries in Mauk, Georgia indicate braided stream environment. Sediment samples of both Pleistocene and Cretaceous age were collected, sedimentary features such as trough cross-bedding along with laminar bedding were recorded, and photos were taken to document the scale and stratigraphic sequences of the sediments. Petrified wood was collected throughout the two sand quarries indicating a terrestrial origin. Post-depositional modifications seen at some of sites include load and flame structures. Sediment samples were examined for grain-size distributions and other sediment textures.


Networks And Network Security, Michael Kuralt Jan 2008

Networks And Network Security, Michael Kuralt

Theses and Dissertations

The purpose of this thesis is to increase awareness of network security in the office and at home by educating the public, reinforcing business decisions, and providing guidelines for network security.


An Scir Model Of Meningococcal Meningitis, Kalimah Vereen Jan 2008

An Scir Model Of Meningococcal Meningitis, Kalimah Vereen

Theses and Dissertations

A model for meningitis is developed by adding a class of carriers to the basic SIR model. This model is used to analyze the impact a vaccination program can have on the health of the population of epidemic prone countries. Analysis of the model shows the local stability of the disease free equilibrium, the existence of an endemic equilibrium and computation of the reproduction number, ℜ0 . Using a MATLAB program we simulate a time course of the model using parameters gathered from the World Health Organization. The numerical solution demonstrates that our reproduction number was correct. We thenconcluded that …


Characterization Of Microorganisms Of Interest To Homeland Security And Public Health Utilizing Liquid Chromatography/Mass Spectrometry, Robert A. Everley Jan 2008

Characterization Of Microorganisms Of Interest To Homeland Security And Public Health Utilizing Liquid Chromatography/Mass Spectrometry, Robert A. Everley

Theses and Dissertations

Liquid chromatography/quadrupole time of flight mass spectrometry (LC/QTOF MS) utilizing electrospray ionization was employed to monitor protein expression in Escherichia coli and Shigella organisms. Automated charge state deconvolution, spectral subtraction and spectral mirroring were used to reveal subtle differences in the LC/MS data. Reproducible intact protein biomarkers were discovered based on their unique mass, retention time and relative intensity. These markers were implemented to differentiate closely related strain types, (e.g. two distinct isolates of E. coli O157:H7) and to correctly identify unknown pathogens. Notable, was the distinction of multiple serotypes of enterohaemorrhagic E. coli which cannot be distinguished by clinical …


Reducing Bacterial Resistance Through Better Antibiotic Prescription Practices, Christine Ouma Jan 2008

Reducing Bacterial Resistance Through Better Antibiotic Prescription Practices, Christine Ouma

Theses and Dissertations

The objective of this study was to find a regression procedure that can better explain the relationship between patterns of antibiotic use and proportions of bacterial resistance. The sample for the study is comprised of 44 University Health System Consortium (UHC) member hospitals, and the data for antibiotic use and proportions of resistance are from the years 2002 to 2005. The hospitals are spread across the Northeast, South, Southwest, Midwest, and Northwest regions of the USA. Based on statistical analysis, MRSA continues to have the highest proportion of resistance among the bacteria examined and has increased significantly since 2002. The …


Magnetic Nanoparticles Based On Iron: Synthesis, Characterization, Design, And Application, Michael David Shultz Jan 2008

Magnetic Nanoparticles Based On Iron: Synthesis, Characterization, Design, And Application, Michael David Shultz

Theses and Dissertations

Magnetic nanoparticles are of great interest for a wide range of applications. This work has focused on three primary forms of iron based nanoparticles and combinations thereof: α-iron, iron oxide, and iron carbide or cementite. The synthesis of several core-shell particles including cementite-iron oxide, α-iron-cementite, and α-iron-iron oxide was accomplished through reverse micelle routes and high temperature decomposition of iron pentacarbonyl in various media. Structural analysis to confirm the structures was performed using extended x-ray absorption fine structure (EXAFS) techniques. A rapid characterization technique was developed utilizing a correlation between Fourier transform infrared spectroscopy and EXAFS to determine the full …


Using Elliptical Fourier Analysis To Compare Size Of Morphospace Occupation Between Modern Edentulous Freshwater Unionoid Mussels And The Fossils At L6516 (Slope County, North Dakota, Usa), With Remarks On Preservation, Mathew E. Burton-Kelly Jan 2008

Using Elliptical Fourier Analysis To Compare Size Of Morphospace Occupation Between Modern Edentulous Freshwater Unionoid Mussels And The Fossils At L6516 (Slope County, North Dakota, Usa), With Remarks On Preservation, Mathew E. Burton-Kelly

Theses and Dissertations

The purpose of this project was to use outline morphometric techniques to determine the number of freshwater mussel taxa present at locality L6516 (“Das Goods”),which is located in Cretaceous strata in the basal Ludlow Member of the Fort Union Formation in Slope County, North Dakota, U.S.A. Secondary goals were to improve the outline morphometric procedures that have been previously used to characterize fossil and extant freshwater mussels, and to describe in more detail the preservation of the edentulous unionoid specimens from the Das Goods area.

Outlines of individual mussel valves were used for morphometric analyses due to lack of preserved …


Geochemical Analysis Of Ironstone Preserved Molluscan Fossils Of The Hell Creek Formation (Cretaceous) And Ludlow Member Of The Fort Union Formation (Paleogene) Of Southwestern North Dakota, Tanya P. Justham Jan 2008

Geochemical Analysis Of Ironstone Preserved Molluscan Fossils Of The Hell Creek Formation (Cretaceous) And Ludlow Member Of The Fort Union Formation (Paleogene) Of Southwestern North Dakota, Tanya P. Justham

Theses and Dissertations

The uppermost Cretaceous Hell Creek Formation and Paleocene Ludlow Member of the Fort Union Formation in easternmost Montana and western North Dakota produce ironstone preserved freshwater molluscan fossils. Ironstone preserved mollusks are associated with ironstone nodules, which have been described as composed of iron carbonate, iron oxide, or manganese oxide by various researchers. To date, the exact composition of the ironstone preservation has not been satisfactorily determined to allow agreement between researchers. Freshwater mollusk fossils, preserved as ironstone external casts, molds, and steinkerns, tend to be highly weathered. The poor preservation of the fossils has resulted in little professional interest, …


Electron Donor Potential Of Eastern North Dakota Shale Formations, Ryan J. Salinas Klapperich Jan 2008

Electron Donor Potential Of Eastern North Dakota Shale Formations, Ryan J. Salinas Klapperich

Theses and Dissertations

Research involving a network of in situ mesocosms (ISM) in North Dakota, Minnesota, and Iowa has revealed significant variation in the denitrification capacity of aquifers in different regions of these states. One aquifer in particular, the Elk Valley Aquifer (EVA) of east-central North Dakota, has the highest concentrations of electron (e) donors (organic carbon -0.4%, pyrite as S -0.4%, and ferrous iron -0.3%) within its sediments and the highest rates of denitrification. The sediments at all of the ISM sites were deposited as outwash during the last Wisconsinan glaciation (-12ka), yet their e· donor concentrations vary. I suggest that the …


Correlation Of Electron Donor Concentrations In Sediments With Sediment Properties: New Providence, Iowa, Bijesh Maharjan Jan 2008

Correlation Of Electron Donor Concentrations In Sediments With Sediment Properties: New Providence, Iowa, Bijesh Maharjan

Theses and Dissertations

The concentrations of electron donors in aquifer sediments are important in understanding the fate and transport of redox-sensitive constituents in ground water, such as nitrate. In this study, 50 sediment samples were collected from below the water table from 11 boreholes at the US Geological Survey Agricultural Chemicals Transport site near New Providence, Iowa. All samples were analyzed for gravel, sand (coarse, medium, and fine), silt, clay, inorganic carbon contents and for the following electron donors: organic carbon, ferrous iron, and inorganic sulfide. A subset of sediment samples was analyzed for organic sulfur, but all of the 14 samples were …


Extending The Information Partition Function: Modeling Interaction Effects In Highly Multivariate, Discrete Data, Paul C. Cannon Dec 2007

Extending The Information Partition Function: Modeling Interaction Effects In Highly Multivariate, Discrete Data, Paul C. Cannon

Theses and Dissertations

Because of the huge amounts of data made available by the technology boom in the late twentieth century, new methods are required to turn data into usable information. Much of this data is categorical in nature, which makes estimation difficult in highly multivariate settings. In this thesis we review various multivariate statistical methods, discuss various statistical methods of natural language processing (NLP), and discuss a general class of models described by Erosheva (2002) called generalized mixed membership models. We then propose extensions of the information partition function (IPF) derived by Engler (2002), Oliphant (2003), and Tolley (2006) that will allow …


Preparation Of Divalent And Trivalent Antigens For Immunogical Studies On Degranulation Of Mast Cells And Preparation Of Ceragenins For Antiviral Studies Against Vaccinia Virus., Dianliang Geng Dec 2007

Preparation Of Divalent And Trivalent Antigens For Immunogical Studies On Degranulation Of Mast Cells And Preparation Of Ceragenins For Antiviral Studies Against Vaccinia Virus., Dianliang Geng

Theses and Dissertations

CHAPTER 1

Aggregation of receptors for IgE (Fc RI) causes mast cells and basophils to release preformed contents of granules, including histamine and a variety of enzymes. This process, called degranulation plays a central role in allergic reactions. Methods to study this process are to create multivalent ligands which can interact with the receptors and, in turn, lead to aggregation of the receptors. We prepared a series of fluorophore-labeled divalent and trivalent antigens to study the degranulation of mast cells. Trivalent antigens proved to be much better stimulators for degranulation of mast cells than divalent antigens. These results indicate that …


Pyridinium Bisretinoids: Synthesis And Photoactivated Cytotoxicity, Junping Gao Dec 2007

Pyridinium Bisretinoids: Synthesis And Photoactivated Cytotoxicity, Junping Gao

Theses and Dissertations

This thesis discusses pyridinium bisretinoid compounds (PBRs), which were prepared for two purposes: 1) to use them as standards for detection of novel fluorophores in human RPE cells, which may be involved in age-related macular degeneration (AMD), and 2) to use them in the development of a targeted and triggered drug delivery system for cancer therapy. We prepared a selection of PBRs using a one-pot biomimetic method; synthesis, mechanisms for formation, and characterization of these compounds is described. We also explored the photoreactivity of three novel PBR compounds and found that these PBRs form oxidation products under blue-light irradiation. The …


A Unified Framework For Solving Multiagent Task Assignment Problems, Kevin Cousin Dec 2007

A Unified Framework For Solving Multiagent Task Assignment Problems, Kevin Cousin

Theses and Dissertations

Multiagent task assignment problem descriptors do not fully represent the complex interactions in a multiagent domain, and algorithmic solutions vary widely depending on how the domain is represented. This issue is compounded as related research fields contain descriptors that similarly describe multiagent task assignment problems, including complex domain interactions, but generally do not provide the mechanisms needed to solve the multiagent aspect of task assignment. This research presents a unified approach to representing and solving the multiagent task assignment problem for complex problem domains. Ideas central to multiagent task allocation, project scheduling, constraint satisfaction, and coalition formation are combined to …


Study Of The Reproducibility Of Proteomics Methods And Variability Of Fruit Fly Proteomes., Thomas Franklin Culwell Dec 2007

Study Of The Reproducibility Of Proteomics Methods And Variability Of Fruit Fly Proteomes., Thomas Franklin Culwell

Theses and Dissertations

The reliability of biomarker discovery by means of proteomics has been called into question. It was speculated that "background noise" variation resulting from differences in preparation and handling of samples and proteome dynamics may mask subtle, yet important, differences due to the biological condition. Little is understood about complex proteomes and their variability. A critical aspect of proteomic biomarker research that is largely unexplored is the comparative reproducibility of certain methods such as two-dimensional gel electrophoresis and liquid chromatography/mass spectrometry. In particular, with liquid chromatography/mass spectrometry, it is not known whether variability in peptide quantitation is dependent on any of …


A Hybrid Multi-Robot Control Architecture, Daylond J. Hooper Dec 2007

A Hybrid Multi-Robot Control Architecture, Daylond J. Hooper

Theses and Dissertations

Multi-robot systems provide system redundancy and enhanced capability versus single robot systems. Implementations of these systems are varied, each with specific design approaches geared towards an application domain. Some traditional single robot control architectures have been expanded for multi-robot systems, but these expansions predominantly focus on the addition of communication capabilities. Both design approaches are application specific and limit the generalizability of the system. This work presents a redesign of a common single robot architecture in order to provide a more sophisticated multi-robot system. The single robot architecture chosen for application is the Three Layer Architecture (TLA). The primary strength …


Pyridinium Bis-Retinoids A2-Dopamine And A2-Cadaverine: Implications In Age-Related Macular Degeneration And Cancer, Mckenzie Ruth Pew Dec 2007

Pyridinium Bis-Retinoids A2-Dopamine And A2-Cadaverine: Implications In Age-Related Macular Degeneration And Cancer, Mckenzie Ruth Pew

Theses and Dissertations

Age-related macular degeneration (AMD) is the leading cause of blindness in the United States of America. The pyridinium bis-retinoid A2-ethanolamine (A2E) has been implicated to play a role in AMD. We have observed novel pyridinium bis-retinoids through melanolipofuscin and human RPE extractions that may also play a role in the pathology of AMD. We have begun the construction of an amino-retinoid library in order to identify these ocular compounds. The compounds from the amino-retinoid library are also used in a targeted and triggered drug delivery system for treating cancer. Folic acid is coupled with the amino-retinoids to specifically target cancer …


Solid Phase Crystallization Of Vanadium Dioxide Thin Films And Characterization Through Scanning Electron Microscopy, Felipe Rivera Dec 2007

Solid Phase Crystallization Of Vanadium Dioxide Thin Films And Characterization Through Scanning Electron Microscopy, Felipe Rivera

Theses and Dissertations

Crystalline films of vanadium dioxide were obtained through thermal annealing of amorphous vanadium dioxide thin films sputtered on silicon dioxide. An annealing process was found that yielded polycrystalline vanadium dioxide thin films, semi-continuous thin films, and films of isolated single-crystal particles. Orientation Imaging Microscopy (OIM) was used to characterize and study the phase and the orientation of the vanadium dioxide crystals obtained, as well as to diferentiate them from other vanadium oxide stoichiometries that may have formed during the annealing process. There was no evidence of any other vanadium oxides present in the prepared samples. Indexing of the crystals for …


Web Based Resource Management For Multi-Tiered Web Applications, Bryce Daniel Ott Dec 2007

Web Based Resource Management For Multi-Tiered Web Applications, Bryce Daniel Ott

Theses and Dissertations

The currently emerging trend of building more complex web applications to solve increasingly more involved software problems has led to the the need for a more automated and practical means for deploying resources required by these advanced web applications. As web based applications become more complex and involve more developers, greater system redundancy, and a larger number of components, traditional means of resource deployment become painfully inadequate as they fail to scale sufficiently. The purpose of this research is to provide evidence that a more sound and scalable test and deployment process can be employed and that many of the …


The Rate And Timing Of Direct Mountain Front Recharge In An Arid Environment, Silver Island Mountains, Utah, Gregory T. Carling Dec 2007

The Rate And Timing Of Direct Mountain Front Recharge In An Arid Environment, Silver Island Mountains, Utah, Gregory T. Carling

Theses and Dissertations

Direct mountain front recharge (MFR), water table recharge at the base of the mountain front, was evaluated on the arid (<250 mm/yr precipitation) Silver Island Mountains by comparing mountain precipitation to groundwater response. Direct MFR contributions were assessed on two catchments, one bedrock (i.e., mountain block) dominated and the other alluvial fan (i.e., mountain front) dominated. Catchment precipitation and shallow groundwater levels at each catchment outlet were measured for a 24 month period beginning October 2005. This time period captured one complete hydrologic cycle (December 2005-February 2007) for which annual and seasonal direct MFR rates were calculated. Annual direct MFR was calculated using a modified version of the water table fluctuation (WTF) method as 0.015-0.016% of precipitation on both catchments, with seasonal variations of 0% in summer up to 0.023% in winter, spring and fall. Seasonal direct MFR contributions are similar on the bedrock and the alluvial fan dominated catchments, with a notable exception during fall 2006 when direct MFR was twice as effective on the bedrock dominated system than on the alluvial fan dominated system (0.022% and 0.011% of precipitation, respectively). Darcy's law calculations show similarly low annual direct MFR contributions (0.013-0.032% of precipitation) as those calculated by the WTF method. Calculated direct MFR is 10% or less than typical calculated combined MFR (near surface recharge and deep underflow from the mountain block) for similar terrains and climates, and is only 3.5% of the combined MFR for the Silver Island Mountains as calculated by the Maxey-Eakin model. However, based on total recharge to the adjacent playa, it is apparent that the Maxey-Eakin model overestimates combined MFR, and the small calculated direct MFR is at least 50% of combined MFR. Despite some uncertainty in the numerical results, several patterns are evident in the data. The data show that direct MFR occurs in response to small rainfall events throughout much of the year, and that snowmelt is not necessary to produce direct MFR. The data also show that direct MFR responds more quickly and flushes through the system faster on the alluvial fan catchment than on the bedrock catchment.


Effects Of Water Vapor On The Kinetics Of The Methylperoxy Radical Self-Reaction And Reaction With Hydroperoxy, Alecia Mower Dec 2007

Effects Of Water Vapor On The Kinetics Of The Methylperoxy Radical Self-Reaction And Reaction With Hydroperoxy, Alecia Mower

Theses and Dissertations

The gas phase reactions of CH3O2 + CH3O2, HO2 + HO2, and CH3O2 + HO2 in the presence of water vapor have been studied at temperatures between 263 and 303 K using laser flash photolysis coupled with UV time-resolved absorption detection at 220 nm and 260 nm. Water vapor concentration was quantified using tunable diode laser spectroscopy operating in the mid-IR. The HO2 self-reaction rate constant is significantly enhanced by water vapor, consistent with what others have reported, whereas CH3O2 self-reaction and the cross-reaction (CH3O2 + HO2) rate constants are nearly unaffected. The enhancement in the HO2 self-reaction rate coefficient …


Route Validation Using Radio Frequency Identification, William T. Watson Dec 2007

Route Validation Using Radio Frequency Identification, William T. Watson

Theses and Dissertations

In recent years, radio frequency identification (RFID) has been proposed and implemented in a variety of applications where tracking objects, animals or people is desirable. This paper proposes a novel approach to the application of RFID tech- nology in those applications where it is possible to validate a person or an object's passive contact with a given or arbitrary set of fixed points along a predefined route. The notable departure from the typical application of RFID technology is that in this scheme, the transponders are permanently installed while the interrogator is affixed to a person or object that travels the …


Rss Management: An Rss Reader To Manage Rss Feeds That Efficiently And Effectively Pulls And Filters Feeds With Minimal Bandwidth Consumption, Brian Cooper Dec 2007

Rss Management: An Rss Reader To Manage Rss Feeds That Efficiently And Effectively Pulls And Filters Feeds With Minimal Bandwidth Consumption, Brian Cooper

Theses and Dissertations

In the early 2000s, RSS (Really Simple Syndication) was launched into cyber space and rapidly gained fame by existing as the underlying technology that fueled millions of web logs (blogs). Soon RSS feeds appeared for news, multimedia podcasting, and many other types of information on the Internet. RSS introduced a new way to syndicate information that allowed anyone interested to subscribe to published content and pull the information to an aggregator, (RSS reader application), at their discretion. RSS made it simple for people to keep up with online content without having to continuously check websites for new content. This new …


Investigation Of Radio Frequency Discharges And Langmuir Probe Diagnostic Methods In A Fast Flowing Electronegative Background Gas, Nathaniel P. Lockwood Dec 2007

Investigation Of Radio Frequency Discharges And Langmuir Probe Diagnostic Methods In A Fast Flowing Electronegative Background Gas, Nathaniel P. Lockwood

Theses and Dissertations

Discharges in a flowing background gas are used to produce charged and excited species for numerous applications including etching semiconductors and pumping gas discharge lasers (Pinhero and others, 1998). The effect of a flowing background gas on the charged and excited neutral species generation by an RF discharge in a flow tube and the diagnostics of the resulting plasma with a Langmuir probe have been investigated for pressures between 0.001 to 1 Torr and flow velocities up to 1000 m/s. This investigation was performed using a fluid method coupled to a chemical kinetic model and a hybrid Particle-In-Cell/Monte Carlo Collision …


Malicious Mobile Code Related Experiments With An Extensible Network Simulator, Attila Ondi Dec 2007

Malicious Mobile Code Related Experiments With An Extensible Network Simulator, Attila Ondi

Theses and Dissertations

The automated spread of worms such as Code-Red, SQL/Slammer, and Nimda have caused costly problems to computers connected to the Internet. Even users whose machines were not vulnerable to these threats suffered a loss of productivity and experienced great frustration as connectivity and network traffic were negatively impacted during outbreaks. Although the number of new worm attacks reported in the media seems to be declining, it is vital that researchers study the effects of malicious code on the global network to understand how to defend against future threats. The choice of system for studying the spread of worms and viruses …


Scandium Oxide Thin Films And Their Optical Properties In The Extreme Ultraviolet, Guillermo Antonio Acosta Nov 2007

Scandium Oxide Thin Films And Their Optical Properties In The Extreme Ultraviolet, Guillermo Antonio Acosta

Theses and Dissertations

This study reports on the physical and optical characterization of scandium oxide thin films. Thin films of scandium oxide, 20-40 nm thick, were deposited on silicon wafers, quartz slides, and silicon photodiodes by reactively sputtering scandium in an oxygen environment. These samples were characterized using ellipsometry, high-resolution transmission electron microscopy, scanning transmission electron microscopy, and energy dispersive x-ray analysis. A 28.46 nm thick scandium oxide thin film was measured in the Extreme Ultraviolet (EUV) from 2.7 to 50 nm (459.3 to 24.8 eV) using synchrotron radiation at the Advanced Light Source Beamline 6.3.2 at the Lawrence Berkeley National Laboratory. In …


Modeling Transition Probabilities For Loan States Using A Bayesian Hierarchical Model, Rebecca Lee Monson Nov 2007

Modeling Transition Probabilities For Loan States Using A Bayesian Hierarchical Model, Rebecca Lee Monson

Theses and Dissertations

A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can …