We present an analysis of paleoseismic data along the central and southern San Andreas fault that seeks to establish the timing, recurrence, and along-fault correlation of paleoearthquakes. We use Bayesian methods to compute a series of probability density functions (PDFs) that cast paleoearthquake timing in the context of yearly probabilities. To quantify the uncertainties present in the paleoseismic dataset based on stratigraphic interpretations, we use a scenario-based approach in which different, viable, stratigraphic interpretations are used to infer paleoearthquake timing. Using these PDFs, we attempt to correlate earthquakes along the fault through time to image a time series of past fault ruptures. We find that site-to-site correlation is often difficult due to significant uncertainties. Nonetheless, some ruptures could be correlated from site to site. Assuming the paleoseismic record is complete, these inferences may indicate that ruptures begin and terminate more or less randomly in space. The results of our analysis may prove beneficial to future probabalistic seismic hazard assessments of this area and may serve as inputs to studies that seek to quantitatively test rupture models against data in the paleoseismic record.