Applied Bayesian Methods

Using R to run a Markov chain Monte Carlo algorithm through OpenBUGS for the study of the relationship of temperature on the growth process of a certain type of tissue. We were given the priors and used R to find the posteriors for our problem. We plotted some posterior distributions for each temperature and did some summary statistics of the posterior distributions. We also used our posterior distributions at 2 different times to find the difference in the number of cells grown at these 2 temperatures.

In the second part, we ran a Bayesian Poisson Regression for a Down Syndrome child born by women in certain age groups on OpenBUGS. Trace plots were presented to show how quickly the samples cycle through the main probability mass after 10,000 iterations. We also used OpenBUGs to find the probability of a child being born with DownSydrome to a mother in the higher age group is more likely of having a child being born with Down Syndrome in a lower age group.

In the third part, we defined a growth curve model in OpenBUGS. After some data manipulation and data analysis, we found that the drug dose level has no significant effect on the intercept of the growth, but the drug dose level has a significant effect on the slope of the growth of rats. ​