In Tonga they cook in an 'umu, which is a covered pit lined with hot rocks. They dig a hole and build a hot fire using drift wood. They place volcanic rocks about the size of baseballs on the fire. When the fire burns down, the ashes and coals are removed. It is the hot rocks that actually do the cooking. A layer of banana leaves is placed on the rocks. A variety of food, some wrapped in taro and banana leaves, is placed in layers inside the pit separated by layers of twigs or palm fronds, and usually topped with a small pig. The pit is covered with banana leaves supported by palm fronds or sticks, then covered with burlap or canvas and finally a layer of dirt. The food cooks over the hot rocks for 3-5 hours. I would be careful about cooking a prime rib this way so it doesn't overcook. Maybe you can put an electronic thermometer probe into the meat.
Special attention is given to the way the food is layered. Placing yams or bread fruit beneath a small pig dripping fat, makes them much tastier

. In a similar vein, I would cook a layer of potatoes and other root vegetables where they can catch the drippings off the roast. Tongans cook a lot of things in coconut milk so the 'umus stay pretty steamy. The breadfruit also gives off a lot of moisture. If you aren't cooking any thing with liquid in it, you may want to add a pan of water.
One dessert they make is a half coconut filled with coconut milk and papaya chunks and wapped in a banana leaf. After it bakes in the 'umu it turns to a wonderful thick fruit custard. They also make a dish of octopus or fish (usually mahi mahi or snapper) cooked with coconut milk, hot peppers and citrus leaves in an abalone shell covered with another shell or a banana leaf.
Here is a link to a web page with some incomplete info on building an 'umu. The author suggests that bricks can be used instead of rocks.
http://loseli.tripod.com/umu2.html
edit:I found my copy of what is probably the only English language Tongan cookbook ever published. I was way off on the amount of time required to cook in an 'umu. I originally said 8 hours, but the book says anywhere from 1 1/2 to 5 hours. It also says if you are cooking puaku (pig) you should put hot rocks inside the pig.