Why is sampling in high dimensions difficult and when can we sample effectively in high dimensions?
When
Speaker
Abstract
Sampling from posterior distributions which are implicitly defined by a computational model and noisy observations is required in many applications in science and engineering. I will give several examples of such sampling problems which I work on and which span the much of the physics of our planet: from the Earth's deep interior, to oceans and clouds. A characteristic of many of the sampling problems that occur in science is that their "dimension" is large. I will discuss what "dimension" can mean in this context and I will show, using simple examples, how that makes sampling difficult (impossible in many cases). I will then describe two situations in which sampling can be done efficiently even if the dimension is huge.