We use extreme value theory to develop point process statistical models relating the probability of extreme winter particulate pollution events in Beijing ("winter haze") to local meteorological variables. The models are trained with the 2009-2017 record of fine particulate matter concentrations (PM2.5) from the U.S. embassy. We find that 850-hPa meridional wind velocity (V850) and relative humidity successfully predict the probability for 24-hr average PM2.5 to exceed 300 mu g/m(3) (95th percentile of the frequency distribution) as well as higher thresholds. We apply the point process models to mid-21st century climate projections from the Coupled Model Intercomparison Project Phase 5 model ensemble under two radiative forcing scenarios (RCP8.5 and RCP4.5). We conclude that 21st century climate change alone is unlikely to increase the frequency of severe PM2.5 pollution events (PM2.5 > 300 mu g/m(3)) in Beijing and is more likely to marginally decrease the probability of such events. Plain Language Summary: We use extreme value theory, a branch of statistics concerned with outliers and unusual events, to develop a model relating the probability of extreme pollution events in Beijing to local weather variables. Haze in Beijing is worst in the winter, so we restrict our study to December, January, and February. We train our models with the 2009-2017 record of fine particulate matter concentrations measured at the U.S. embassy, a pollutant behind many of these haze events. We find that north-south wind velocity and relative humidity successfully predict days when daily mean particulate matter concentrations will exceed a threshold of 300 mu g/m(3). We apply our statistical models to mid-21st century climate projections under two scenarios: business-as-usual emissions and significant reduction in emissions. We find that the frequency of haze events is most likely to decrease because of climate change, driven mainly by a decrease in relative humidity. This result illustrates the importance of including humidity in estimates of future fine particulate matter concentrations.