Bayesian Estimation of Small Proportions Using Binomial Group Test

Group testing has long been considered as a safe and sensible relative to one-at-a-time testing in applications where the prevalence rate p is small. In this thesis, we applied Bayes approach to estimate p using Beta-type prior distribution. First, we showed two Bayes estimators of p from prior on p derived from two different loss functions. Second, we presented two more Bayes estimators of p from prior on π according to two loss functions. We also displayed credible and HPD interval for p. In addition, we did intensive numerical studies. All results showed that the Bayes estimator was preferred over the usual maximum likelihood estimator (MLE) for small p. We also presented the optimal β for different p, m, and k.

An Ethnographic Study: Becoming a Physics Expert in a Biophysics Research Group

Expertise in physics has been traditionally studied in cognitive science, where physics expertise is understood through the difference between novice and expert problem solving skills. The cognitive perspective of physics experts only create a partial model of physics expertise and does not take into account the development of physics experts in the natural context of research. This dissertation takes a social and cultural perspective of learning through apprenticeship to model the development of physics expertise of physics graduate students in a research group. I use a qualitative methodological approach of an ethnographic case study to observe and video record the common practices of graduate students in their biophysics weekly research group meetings. I recorded notes on observations and conduct interviews with all participants of the biophysics research group for a period of eight months. I apply the theoretical framework of Communities of Practice to distinguish the cultural norms of the group that cultivate physics expert practices. Results indicate that physics expertise is specific to a topic or subfield and it is established through effectively publishing research in the larger biophysics research community. The participant biophysics research group follows a learning trajectory for its students to contribute to research and learn to communicate their research in the larger biophysics community. In this learning trajectory students develop expert member competencies to learn to communicate their research and to learn the standards and trends of research in the larger research community. Findings from this dissertation expand the model of physics expertise beyond the cognitive realm and add the social and cultural nature of physics expertise development. This research also addresses ways to increase physics graduate student success towards their PhD. and decrease the 48% attrition rate of physics graduate students. Cultivating effective research experiences that give graduate students agency and autonomy beyond their research groups gives students the motivation to finish graduate school and establish their physics expertise.