Student Project Presentations (ST 740 )

• Fall semester, 2006
  1. Team members: Suraj Anand
     • Presentation time: Dec. 6, 10:15-10:30
     • Title: A Bayesian Approach to Assess the Risk of QT Prolongation of an Investigational New Drug
       
     • Abstract: An undesirable property associated with some non-antiarrhythmic drugs is their ability to delay cardiac repolarization, more generally known as QT prolongation. The standard approach to investigating a drug for its potential for QT prolongation is to construct a 90% two-sided (or a 95% one-sided) confidence interval (CI), for the difference in mean QTc (a heart-rate corrected version of QT) between drug and placebo at each time point, and to conclude non-inferiority if the upper limits for all these CIs are less than a pre-specified constant. One alternative approach is to base the non-inferiority inference on the largest difference in population mean QTc between drug and placebo. In this project paper, we propose a formal solution to this problem based on a Bayesian framework using a Monte Carlo simulation method. The proposed method has several advantages over some of the other existing methods and it is easy to implement in practice. We use simulated data to assess the appropriateness of this approach and apply the method to a real data set on QTc to make a formal and thorough statistical inference.
       
     • Data Source: Bioequivalence and Statistics in Clinical Pharmacology
       
     • Original Source: Patterson S. and Jones B. (2005). 'Bioequivalence and Statistics in Clinical Pharmacology, Chapman and Hall, CRC Press, London.
       
     • Code used: R code
  2. Team members: Eric Belasco
     • Presentation time: Dec. 6, 10:35-10:50
     • Title: A Bayesian Approach to Analyzing Cattle Feeding Yield Risks
       
     • Abstract: The development of livestock insurance programs as part of the Agricultural Risk Protection Act of 2000 has motivated research investigating risks affecting cattle feeding enterprises. Current research indicates that three cattle yield measures can be jointly modeled through the use of a multivariate lognormal distribution with multiplicative heteroskedasticity under a Tobit formulation. This is largely due to the highly correlated nature of the yield factors and the degree of censoring in the dependent variables. A major concern lies in the modeling of the censored component of the dataset. This research will model yields using a Bayesian approach and compare it to that of a frequentist approach. Also, Bayes Factors will be used to compare this model to one that uses a zero-inflated Gamma distribution.
       
     • Data Source: undisclosed
       
     • Original Source: Belasco, Taylor, Goodwin, and Schroeder. Probabilistic Models of Yield, Price, and Revenue Risk for Fed Cattle Production (unpublished).
       
     • Code used: WinBUGS code
  3. Team members: Carl DiCasoli
     • Presentation time: Dec. 6, 10:55-11:10
     • Title: A Bayesian approach to estimation of survival probability using a posterior distribution based on the Yang-Prentice Model
       
     • Abstract: In this project, we will determine if a Bayesian method for estimating the short-term and long-term hazard ratio is an improvement over two other proposed sets of estimates. These estimates include those from the semi- parametric, Yang-Prentice model and the Kaplan-Meier estimate. In determining both the Kaplan-Meier estimate and the semi-parametric, Yang Prentice model estimates, we have assumed that the sample size is large, and that the response variable (the time to death or hospitalization) between control and treatment groups is independent. Additionally, in the semi-parametric, Yang-Prentice model we have made another assumption, which is to take into account the short- term and long-term hazard ratios, as well as the large sample size. However, the estimates from the Bayesian approach do not depend upon having a large sample size because the model that we will be using is parametric. That is, the Bayesian model assumes that the control group's hazard ratio is coming from a Weibull distribution. If the Bayes estimates produce a good fit when graphing the survival probability against the response as compared to the Kaplan-Meier estimate, then we can conclude that the Bayes procedure is more optimal than either of the frequentist methods since we do not have to take into account the sample size.
       
     • Data Source: datasets
       
     • Original Source: Yang, Song and Prentice, Ross. Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data, Biometrika (2005), 92, 1, pp. 1-17.
       Tsiatis, Anastasios, Zhang, Daowen, and Lu, Wenbin. ST 745, Spring 2006, Analysis of Survival Data, Lecture notes 2, pp. 8-12.
       
     • Code used: WinBUGS code
  4. Team members: Judith Canner
     • Presentation time: Dec. 6, 4:30-4:45
     • Title: Neutral Model of Species Distribution Patterns
       
     • Abstract: Ecologists have long sought to explain species distribution patterns. In Gelfand et al (2003), the authors use a hierarchical Bayesian model to incorporate spatially associated random effects to explain distribution patterns of plants in the Cape Floristic Region in South Africa. In a similar framework, I will analyze species distribution patterns of ants in Southern Appalachia (Smokey Mountains). I will assume that all ant species are biologically similar and will use a Bayesian hierarchical model to test whether habitat characteristics are sufficient to predict species distribution patterns. I will parameterize the model with species presence/absence and site characteristic data (elevation, temperature, litter depth, etc.) from Dunn et al (in press). I will then compare predicted species presence/absence to observed species presence/absence to test if habitat characteristics are sufficient to predict species distribution patterns.
       
     • Data Source: Species Sites and Site Characteristics
       
     • Original Source: Gelfand et al (2003). Explaining Species Distribution Patterns through Hierarchical Modeling. Bayesian Analysis 1(1):1-35.
       
     • Code used: WinBUGS code
  5. Team members: Liz Nelson and Mathew Krachey
     • Presentation time: Dec. 6, 4:50-5:05
     • Title: Bayesian modification to Brownie models applied to Cayuga lake trout
       
     • Abstract: Resource biologists concerned with conservation of exploited animal stocks must assess key population demographics for management plans. One demographic of particular interest is the harvest mortality rate, which can be controlled if the target species is at critically low population levels. The estimation of harvest mortality can be complicated since overall mortality includes both natural and harvest mortality. In addition, harvested stocks are often highly migratory, making population size estimates unreliable. Brownie (1978, 1985) proposed a multinomial model to differentiate natural mortality and harvest mortality in harvested populations through tag return studies. We propose a Bayesian modification of the Brownie model using non-informative priors. Analysis will be based on the 1960-1964 Cayuga lake trout data set provided by Hoenig et al (1998). Model performance will be assessed by comparison with previous studies.
       
     • Data Source: Table 4 of the original source below
       
     • Original Source: Hoenig, J.M., N.J. Barrowman, K.H. Pollock, E.N. Brooks, W.S. Hearn and T. Polacheck. 1998. Models for tagging data that allow for incomplete mixing of newly tagged animals. Can. J. Fish. Aquat. Sci. 55:1477-1483.
       
     • Code used: WinBUGS code
  6. Team members: Yan Zhang and Jin Huang
     • Presentation time: Dec. 6, 5:10-5:25
     • Title: Estimation and Comparison of Empirical Growing Stock Models across three forest types---A Bayesian Approach
       
     • Abstract: The main objective of this project is to fit an empirical model for growing stock volume of three forest types (i.e. loblolly pine, long leaf pine and slash pine) in North Carolina, with stand age and density(trees per acre) as predicting variables. Meanwhile we control for other covariates such as region dummies, site productivity and slope. We plan to estimate the parameters (namely betas) in the Bayesian framework. We also plan to compare whether the betas are significantly different for the three forest types using Bayes Factor.
       
     • Data Source: Forest Inventory and Analysis (FIA) Database
       
     • Original Source: Amacher, Malik and Haight (2005). Not getting burned: The importance of fire preevntion in forest management, Land Economics, 81, 284-302.
       
     • Code used: WinBUGS code
  7. Team members: Arun Krishna, Laine Elliot and Eren Demirhan
     • Presentation time: Dec. 8, 10:15-10:30
     • Title: Bayesian Variable Selection in Linear Models with Zellner's prior
       
     • Abstract: A common method to solve variable selection problems in linear models is minimizing a penalized sum of squares, where most of the methods differ in the penalty function. The earlier methods such as best subset selection, Mallow's C, Bayesian and Akaike Information Criteria use a penalty function where only the number of parameters is penalized. Recent methods are mostly based on penalty functions including the norms of parameter estimates, or combination of them. Ridge Regression, LASSO and Elastic Net can be considered as popular examples of these shrinkage regression models. These problems can be considered under a Bayesian framework where priors of the parameters are represented as proportional to the penalty functions (Ghosh 2006). In this paper, we will talk about a specific approach to performing variable selection by using Zellner's prior, which depends on the design matrix X. We will then compare this method to the recent attempt made by Casella and Moreno (2006) where the variable selection problem was solved by using automatic priors. The data we will use to make this comparison is the "ancient" Hald data (Casella and Moreno, 06) which measures the effect of heat on the composition of cement.
       
     • Data Source: Hald data
       
     • Original Source: Casella, G. and Moreno, E. (2006). Objective Bayesian variable selection, Journal of the American Statistical Association, 101, 157-167.
       
     • Code used: R code
  8. Team members: Dhruv Sharma
     • Presentation time: Dec. 8, 10:35-10:50
     • Title: Variable Selection via Bayesian Optimization
       
     • Abstract: A criterion-based and fully automatic Bayesian variable selection method is proposed for the canonical linear regression model. We consider a full hierarchical model with a conjugate prior with multivariate normal for the regression coefficients and inverse gamma for the error variance. A new loss function is proposed and the Bayes estimator that minimizes the posterior expected loss is obtained under the given setup. The proposed estimator is validated using simulated data and illustrated using the Hald data set. We also compare our results with those using some of the currently available methods.
       
     • Data Source: Hald data
       
     • Original Source: Casella, G. and Moreno, E. (2006). Objective Bayesian variable selection, Journal of the American Statistical Association, 101, 157-167.
       
     • Code used: R code
  9. Team members: Haojun Ouyang and Yuefeng Wu
     • Presentation time: Dec. 8, 10:55-11:10
     • Title: Passenger Car Mileage: A Bayesian Approach
       
     • Abstract: Passenger cars made by different makes and models have different gasoline mileage. Also, the gasoline mileage is influenced by the weight and horsepower of the vehicles. The data set contains the makes, models, engine horsepower, top speed, behicle weight cubic feet of cab space and average miles per gallon. The model we planned to use is y=X*beta+error. We plan to do the Bayesian regression (G-prior) and test for significance of each effect, and compare our results to the ones we will get by using non-Bayesian regression.
       
     • Data Source: DASL: Passenger Car Mileage
       
     • Original Source: R.M. Heavenrich, J.D. Murrell, and K.H. Hellman, Light Duty Automotive Technology and Fuel Economy Trends Through 1991, U.S. Environmental Protection Agency, 1991 (EPA/AA/CTAB/91-02).
       
     • Code used: WinBUGS code
  10. Team members: Kaushal Mishra
      • Presentation time: Dec. 8, 4:30-4:45
      • Title: Estimation of scram rate trends in Nuclear Power Plants using hierarchical Bayesian Model
        
      • Abstract: Nuclear Reactors are equipped with reactor scram (sudden insertion of control rods) systems to ensure rapid shutdown of the system in the event of leaks, failure of power conversion systems, or other operational abnormalities. The U.S. Nuclear Regulatory Commission (NRC) collects data of scram rate for various nuclear power plants to obtain their trend of proper functioning over time and to regulate them if necessary. The source data in this case is the scram rate of 66 commercial nuclear power plants obtained from the annual observed scram data from 1984-1993. The data depicts an increase in the zero scram incidents with time from 1.5% in 1986 to 33% 1993. To analyze this kind of count data with excess zeros a Zero-inflated Poisson (ZIP) distribution on unplanned scrams with appropriate link functions and vague normal and inverse Wishart priors and hyperpriors on regression parameters is being proposed. The results obtained will be compared with the Poisson model. To obtain the posterior estimates of the parameters along with credible interval Markov Chain Monte Carlo (MCMC) technique will be applied using WinBugs.
        
      • Data Source: NRC
        
      • Original Source: Martz H.F., Parker R. L. and Ramuson D. M. (1999) , Estimation of trends in the scram rate at nuclear power plants, Technometrics, 41, 352-364.
        Ghosh S. K., Mukhopadhyay P.and Lu JC. (2006), Bayesian analysis of zero-inflated regression models, Journal of statistical planning and inference, 136, 1360-1375.
        
      • Code used: WinBUGS code
  11. Team members: Alexander Griffing
      • Presentation time: Dec. 8, 4:50-5:05
      • Title: A Bayesian approach to cryptogram language estimation
        
      • Abstract: Hiding written text by permuting the meanings of the letters is a basic method of cryptography. I plan to develop a Bayesian method of estimating the language in which the original text was written given the encrypted text. First, language models for several languages that use the roman alphabet will each be built using a non-informative Dirichlet prior for the letter probabilities which will be updated using a training subset of text from Project Gutenberg, a free online text repository. The final model will be a non-informative mixture of these language models. Second, samples will be taken from a test subset and MCMC will be used to estimate the posterior language distribution for these sample texts. The estimates will be compared to the true text languages.
        
      • Data Source: Project Gutenberg and Index of coincidence
        
      • Original Source: Chen and Goodman (1998) and Hasinoff (2003)
        
      • Code used: C code

  

• Fall semester, 2005
  1. Team members: Hugh Crews, Emily Hohmeister, Rebecca Horowitz
     • Presentation time: Nov 28th, 2005, 10:15 - 10:35
     • Title: The Silver Lining: A Bayesian Approach to Analyzing Cloud Seeding Data
       
     • Abstract: In Simpson (1975), data from both seeded and unseeded clouds were analyzed in a Bayesian setting. The amount of rainfall was assumed to follow a skewed Gamma distribution with the same shape parameter for both seeded and unseeded clouds. The prior used was a vague prior. Simpson (1972) provided results indicating that the use of the gamma distribution is appropriate. Another possibility suggested in Simpson (1972) is the Rayleigh distribution. We plan to use the Rayleigh distribution and test for a multiplicative effect, comparing our results and assumptions to those of the gamma distribution. We can compare these distributions using the Bayes factor as well as plots. We will also compare the results from a Bayesian setting with a frequentist approach.
       
     • Data Source: DASL Clouds data set
       Original Source: Simpson, Alsen and Eden (1975). A Bayesian analysis of a multiplicative treatment effect in weather modification, Technometrics, 17, 161-166.
       Additional Source: Simpson, J. (1972). Use of the gamma distribution in single cloud rainfall analysis, Monthly Weather Review, 100, 309-312.
     • WinBUGS code: WinBUGS code
  2. Team members: Chia-Cheng Chen, Tsuei-Long Chen and Mingyan Huang
     • Presentation time: Nov 28th, 2005, 10:40 - 11:00
     • Title: Prediction of US Temperatures and Bayesian Model Determination.
     • Abstract: The purpose of this project is to find a way so that we could predict the average January minimum temperature in degrees Fahrenheit of any U.S. cities when the information of the latitude and longitude for that city was given. We could first check plots of Lat vs. Long, JanTemp vs. Lat, and JanTemp vs. Long (Lat stands for Latitude, Long stands for Longitude, and JanTemp stands for average January minimum temperature) to see if there is any information from these plots. Then, consider three competing models that could show the relationships among JanTemp, Lat, and Long. Finally, use the method of Bayesian model selection to check which model is adequate. Therefore, based on the chosen model, we could have a better prediction of temperature of any U.S. cities.
       
     • Data Source: DASL US temperatues data set
  3. Team members: Xiaohua Gong and Shufang Liu
     • Presentation time: Nov 30, 2005, 10:15-10:35
     • Title: Bayesian Logistic Regression for Spam Email Classification
     • Abstract: In this study, we built a model to predict whether an email is normal or spam according to some mostly common occuring words in the emails. We use the spam dataset as our training dataset. To estimate the parameters, namely beta, we adopted a Bayesian framework where under the assumption of gaussian prior for the parameters beta, we obtain the MAP (maximum a posteriori) estimate of beta. To choose an appropriate prior variance of beta that is needed for MAP estimation, we took the cross validation approach to select the values of prior variance that minimized the cross validation error. Cross validation error for the chosen value of prior variance is reported as an estimate of the testing error of our model.
     • Data Source: Spam Data Info and the spam data set
     • Final report: Gong & Liu report and LaTex file
     • Slides: Gong & Liu's presentation slides
  4. Team members: Martin Heller
     • Presentation time: Nov 30, 2005, 10:40-11:00
     • Title: Bayesian functional data analysis when the coefficients are random
     • Abstract: Of interest is finding a probability density of functions determining the daily electrical consumption for buildings in a research park. Cubic splines were chosen to model the data because of their ability to emulate a wide variety of functions. Random coefficient models in a Bayesian context will be used to get an estimate of the posterior distribution.
     • Data Source: undisclosed

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