Final Exam STAT 3303: Bayesian Analysis and Statistical Decision Making Due: Thursday, April 30, 2020 (submit on Carmen before 12 pm) INSTRUCTIONS This is an exam and should be treated as such. DO NOT discuss any aspect of this exam with anyone other than your instructor. This includes, but is not limited to, not discussing report structure, coding problems, instructor expectations, how long the exam took you, whether you finished it, etc. You are responsible for ensuring that other students do not have access to your exam. Any violation of these instructions constitutes academic misconduct and will be reported to the university’s Committee on Academic Misconduct. In response to growing concerns about a new strain of influenza (K9C9) that has been identified in humans in 10 countries across the world, medical researchers have developed an inexpensive diagnostic test (named “EZK”). Unfortunately, the EZK diagnostic test is not perfect as it can result in false positives and false negatives. For this exam, you will analyze data related to this new diagnostic test. In an effort to quickly assess the diagnostic ability of EZK, the World Health Organization sponsored a small clinical trial run in each of 10 countries where the K9C9 virus in endemic. Using a highly accurate (very expensive) diagnostic test, 100 randomly selected subjects in each country were tested for K9C9 – this test does not perfectly diagnose infection status of the subjects, but is believed to be far more accurate than the less expensive EZK test. Each subject was then administered the EZK test. As expected, not all of the results of the EZK test agreed with the highly accurate diagnostic results. In the data set flu.txt (available on Carmen), the following variables contain the results of the clinical trial: Infected binary indicator of whether the subject is infected (1) or not infected (0) according the highly accurate diagnostic test EZK binary indicator of whether the subject’s EZK test was positive (1) or negative (0) Country country of residence of the subject, where the countries are labeled A-J Propose a Bayesian hierarchical model for K9C9 status, with Infected as the outcome. After an ap- propriate transformation, model the probability of a subject having the virus as determined by the highly accurate test (Infected) as a parametric function (i.e., a function with unknown parameters) of the results of the EZK test, EZK. Explain how your model can be used to assess the diagnostic ability of the EZK test. Allow model parameters to vary across country using a hierarchical model structure to account for poten- tial genetic variation in the virus (i.e., BOTH the virus and accuracy of the tests may be slightly different across countries). Fit your model using rjag/JAGS and provide appropriate and interesting summaries of your results. In writing your response be sure to: 1. define all variables and interpret model parameters in the context of the problem. 2. specify your model in detail, including conditional independence and prior assumptions (providing your JAGS model files is NOT adequate). 3. provide details on model fitting (what were your starting values, how many iterations did your algo- rithm run, how did you diagnose convergence of the model fitting algorithm). 4. provide interpretations of the results of your statistical analysis in the context of the problem. These are the formatting guidelines: • Your report should be typed. You may use R Markdown if you wish, but DO NOT include any code in the main body of your report. • Carefully proofread and spell check your report. Write in complete sentences and in paragraphs, not bulleted lists. • Define all mathematical notation in the text of the report. • Make sure all figures/tables are straightforward to understand, have captions, and are referenced in the text. • Include commented R/JAGS code in an appendix. • You may assume that the reader is familiar with Bayesian statistics, but not that they are familiar with the content of STAT 3303. For example, do not refer to specific examples that have been discussed in lecture or homework. Your report should be no longer than five pages double-spaced, including figures and tables. (Text, figures, and tables that are after five pages may not be considered by the instructor.) Your appendix with R/JAGS code does not count toward the five page limit. Submit your final exam report as a single PDF file on Carmen before the deadline. 2
