We suggest a parametric modeling approach for nonstationary spatial processes driven by point sources. Baseline near-stationarity, which may be reasonable in the absence of a point source, is modeled using a conditional autoregressive (CAR) Markov random field. Variability due to the point source is captured by our proposed autoregressive point source (ARPS) model. Inference proceeds according to the Bayesian hierarchical paradigm, and is implemented using Markov chain Monte Carlo (MCMC) methods. The parametric approach allows a formal test of effectiveness of the point source. Application is made to a real dataset on electric potential measurements in a field containing a metal pole and the finding is that our approach captures the pole's impact on small-scale variability of the electric potential process.