Thinking about path integrals …

Been busy this past week running “micro-simulation” models for my day job; “micro-simulation” = build a computer code to simulate a whole population of people, send a swarm of simulated infectious mosquitos after them, and then simulate the process of observing their clinical infections and parasite prevalence rates.  It’s quite similar to running semi-analytical simulations of galaxy formation: the models are so computationally expensive we need to think up clever ways to fit them if we’re going to have any hope of learning their parameters, statistically, from data.

In a brief astro-ph update I noticed some lazy Bayes by Wahhaj et al. who note that their errors are very much non-Gaussian but then proceed to use a Gaussian likelihood function (i.e. proportional to exp[-Chi.sq/2] in physics speak); felt like a case of too blindly following Numerical Recipes.  Also, I was a bit disappointed to see Han et al. shirk high-dimensional MCMC, and instead use rough, simulation-based calibrations, for handling the nuisance parameters of their lensing analysis (their Eqn 22).

But the main thrust of my astronomical thinking this week has been on the topic of the path integral, as used in cosmology (cf. Bertschinger 1987).  It’s my thesis that, although the path integral has helped (via neat ‘tricks’ like perturbation theory) greatly with cosmological statistics in the past, its mathematical clunkiness and general obtuseness (in the eyes of non-physicists) is currently holding back the field of (Bayesian) cosmological inference.  I’d be very interested to hear of any recommendations for papers/notes on the limitations of path integrals, especially in the cosmological context and/or with respect to issues of measure theory.  I feel like there must be a connection between the class of problems that can be handled by path integrals and the class of implicit stochastic process measures that can be constructed from Weiner measure?  Especially since the path integral is defined in the discretisation limit over the field domain in a similar way to which the Radon-Nikodym derivative of two Gaussian measures can be defined (cf. Shepp 1966).  Anyone?

This entry was posted in Astrostatistics, Gaussian Processes, Infinite-Dimensional Inference, Measure Theory, Statistics. Bookmark the permalink.

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