Homework 3

Using the temperature data, read in the file (it is tab-delimited, so you can use sep="\t" in read.table) and first transform Longitude by multiplying by -1 so that when you plot by Long and Lat you get a plot that looks like the geographical layout of the cities in the U.S. (try plot(Long,Lat) to see).
1. Fit a surface to the data using MCMC which you code yourself. Feel free to keep the model simple by fitting a linear trend with unknown coefficients (with independent priors), an unknown overall variance (or precision), and a just a few parameters in the correlation, e.g., a power correlation with fixed power but unknown range (isotropic or separable) and with or without a nugget.
2. Fit a surface using bgp from the tgp package, and compare your results. Note that to get a good plot of the results from bgp, you will want to predict on a grid, for example, by including the argument XX=expand.grid(Long=seq(from=-123,to=-70,length=15),Lat=seq(from=25,to=48,length=15)), and your plot will be even better if you leave out the corners of the grid where no data has been collected (over the oceans).
Using the scallop data, first rotate the data 45 degrees so that a separable correlation structure is reasonable. Using the rotated data, fit a surface using bgp, and a surface using btgp. Use image plots to compare the fits to each other and to a basic interpolation of the data. Comment on your findings.