Probabilistic graphical models in astronomy and astrophysics

How it is used

Astronomy studies objects nobody can touch: stars, exploding stars, galaxies and the large-scale pattern of matter across the sky. Almost everything is inferred from faint signals, and much of what matters is hidden behind what can be measured. A probabilistic graphical model is a way of writing down a whole chain of such dependencies at once. Each quantity becomes a node, each arrow or link says which other quantities it depends on, and probability is attached to every link rather than a single fixed answer. Families of these models include Bayesian networks, which use directed arrows, Markov random fields, where neighbouring nodes influence each other, and maximum-entropy or Potts models, which assign each site one of a few discrete states.

In practice the graph is usually built to mirror the physics. A model of cosmic structure may link the initial conditions of the early universe to the density field today, and then to the galaxies or other tracers actually counted in a survey, with a noisy observation step at the end. A model of a stellar explosion may link the state of the collapsing core to the waveform a detector would record. Researchers then run the chain forwards to make simulated data, or work backwards from real data to the hidden quantities, keeping the spread of possible answers rather than one best guess.

Why researchers use it

Astronomers reach for these models because the quantity they want is rarely the quantity they see. Light and gravitational waves arrive weak, blurred, incomplete and mixed with instrument noise, so any answer has to carry an honest sense of how uncertain it is. A graphical model provides that: because the dependencies are written out explicitly, uncertainty at one node can be carried through to every other. It also lets prior physical knowledge, such as how matter clumps or how a core collapses, sit inside the model rather than being bolted on afterwards.

The graph structure stands in for an assumption that would otherwise be made silently. Treating nearby patches of sky as depending on their neighbours, or sorting the cosmic web into a few discrete kinds of region, encodes a belief about how structure is organised. Because the same model can generate data as well as interpret it, researchers can simulate what a survey or detector would record, use those simulations to train or test other methods, and check whether the assumptions reproduce what is actually observed.

In the record

astronomyReconstructing the early universe's density field with a smoothed map of cosmic structureA mock catalogue of tracer counts was generated with the same forward model later used for inference, starting from a Gaussian initial field with a fixed seed and set bias parameters.astronomyEight machine learning methods sorted supernova gravitational wave signals by nuclear physics modelSimulated gravitational waveforms were generated for four equations of state and about one hundred rotational configurations of one progenitor, then sampled and amplitude-scaled for signal classification.

Limits

The graph is an assumption, not a measurement. If the assumed dependencies or the chosen prior are wrong, the model can return a confident answer that is confidently wrong, and the error is hard to spot because it hides in the structure rather than the data. Models tested on data made by the same forward model may do worse on real observations, which contain instrument effects and physics the model omits. Fitting them over a sky-sized grid of variables is also slow, so researchers simplify, and the simplifications themselves shape the result.

Written by AIxSci: the background from general knowledge, the examples from checked records.