## Areas of Interest

• Longitudinal Diagnostic Screening for Disease
• Bayesian Statistics
• Nonparametrics
• Markov Chain Monte Carlo Methods
• Collaborative research in science and engineering

A brief description of the first three research areas is given below. If you have questions about my research, feel free to come during my office hours and ask me. I would be happy to explain my research to you.

## Longitudinal Diagnostic Screening for Disease

Diagnostic screening involves testing humans or animals for the presence of disease or infection. Some diagnostic screening tests currently in use are:

• serology tests (like the ELISA test used to detect AIDs)
• tissue cultures (i.e., throat culture used to detect strep throat)
• microscopic examination (like a tissue biopsy to detect cancerous cells)

For some diseases, a perfect, "gold-standard" test does not exist or is too invasive or expensive to use. Hence, the goals of diagnostic screening may include:
quantifying the performance of an imperfect screening test,
diagnosing subjects, and estimating disease prevalence -- possibly
in the absence of a perfect reference test. Interestingly, methods exist to estimate the probability the test will misclassify diseased and undiseased subjects and to estimate the prevalence of a disease, even when the true disease status is unknown due to the lack of a gold-standard test.

To date, most work in the area of diagnostic screening has focused on cross-sectional data (where each subject is tested once). However, longitudinal diagnostic screening data are currently being collected in many studies. My dissertation research involved developing a novel model for longitudinal diagnostic screening outcomes in the no-gold standard case. Additionally, I considered the case where two tests are repeatedly administered to each subject -- one
yielding a continuous response and the other a binary response (positive or negative outcome). For infected subjects, I assume the existence of a changepoint corresponding to time of infection and posit appropriate changes to the model thereafter.

## Bayesian Statistics

Statistical inference can be made either using frequentist or Bayesian methods. Frequentists make inferences using only the data. Bayesians make inference using the data plus other information which is modeled using a "prior" distribution. Bayesians combine the information in the data and the prior in a probabilistically coherent manner using Bayes' Rule. The prior then allows information coming from sources other than the data to be incorporated into the statistical analysis. For example, prior information may come from past studies or from an expert's knowledge (independent of the data).

## Nonparametrics

Often, statistical inference will involve making assumptions about the distribution of the data, i.e. the data have a normal distribution or a gamma distribution. In some cases, assuming the data have a known parametric form is reasonable, whereas in others it is not. Nonparametric methods allow the data to have a very flexible distribution, which may be multimodal, heavy-tailed, or asymmetric. Using nonparametric methods, we can make inferences about the distribution of the data, instead of assuming it follows any specific known form.