Rutger van Haasteren (Leiden) is visiting this week to talk about Bayesian inference, gravitational radiation, and pulsar timing. We spent some time talking about some of the details of pulsar timing, including the fact that every pulse looks different, every pulse is measured at low signal-to-noise, but collections of pulses average to a stable and predictable mean. We realized that there is probably a great hierarchical Bayesian description of this process.
The pulse-to-pulse correlations can be amazingly complex (e.g., drifting subpulses, nulls, polarization mode switching, ...), and in the general case the statistics are a blend of intrinsic variability and of diffractive and refractive effects in the interstellar medium. There may be a great hierarchical Bayesian description, but I don't expect to see it during my career.
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