Spring 2020 Postdoc Seminar Series
March 4, 2020 –
Predicting the response at an unobserved location is a fundamental problem in spatial statistics applications. Traditional methods are model-based, thus there is a risk of model misspecification biases as spatial dependence can be difficult to assess, especially in non-stationary cases. A model-free prediction has been achieved in other contexts using the conformal prediction machinery, which requires the data to be exchangeable. While exchangeability is a mild assumption in some applications, it is apparently incompatible with spatial dependence in general. However, in this talk, I will show that a wide class of spatial processes are locally approximately exchangeable, which suggests that near-valid predictions can be achieved by using conformal prediction on a suitably dense subset of data points closest to the point at which prediction is desired. We prove that the proposed local conformal spatial prediction interval is approximately valid, and numerical examples on both real and simulated data, across a range of non-stationary and non-Gaussian settings, confirm that the predictions are both valid and efficient.
No references provided at this time