arXiv is a well-known preprint server for mathematics, computer science, physics, etc. In exchange for weakening the demands of peer review, it encourages people to share articles at a much faster pace than would be possible otherwise. I’ve been a long-time subscriber of their RSS feed, which helps me keep abreast of developments in my field. On a typical day, between 100~150 new preprints are submitted, of which I usually find five or six “interesting.”
So in accordance with this I have added this week an additional “interesting” filter for things that may be of interest to LW. Right now, that seems to mean things about practical Bayesian statistics.
Disclaimer: while I’ve skimmed through the papers listed below, I make no guarantee that they are either correct or interesting. I’m not a domain expert in statistics.
Inverse problems is an important field (i.e., it’s my field) that studies, for example, under what conditions a measurement device is able to function, and how well it functions. Classically the theory has dealt solely with idealized perfect measurements in the absence of error, but since about the 80′s there has been some work done in combining inverse problems with Bayesian updating. Here they study a really general model (that covers e.g., CT imaging) in the presence of white noise. It’s somewhat popular these days to study how the posterior “collapses” in either the high-data or low-noise limit (where the Bayesian result should tend to the classical one), and so this paper studies the model in the high-data limit.
Admittedly this preprint strains my internal definition of “LW-interest,” but it was too cute to pass up. They construct a first-order logical theory of special relativity and ask what the scalar quantities of this theory form a model of. Typically everyone assumes that the real numbers are the “correct” model of physical quantities, but there’s no a priori reason for this to be true, see here. The preprint claims that in more than three dimensions, FOL + SR can model any ordered field. If in addition there exist accelerated observers, a real closed field is required. The most interesting part is that if there is a uniformly accelerated observer, there is no set of first-order axioms characterizing the possible fields of scalars.
The interesting thing about this paper is that it flags down several references describing the analogy between quantum mechanics and Bayesian updating. As the title suggests, they study some discrete- and continuous-time models of a random system that can be probed iteratively. Since QM prevents quantum systems from being completely measured, they work with a model probe that only partially measures the system. After probing the system over and over again, Bayesian updating on the probe data yields more and more complete information, just as one would expect.
This is another Bayesian inverse problems paper, this time dealing with the low-noise limit. The “severely ill-posed inverse problems” of the title covers practical problems like deconvolution and optical tomography. They show posterior consistency for gaussian priors. They also mention a formal analogy between Bayesian updating and Tikhonov regularization, which is the classical method for dealing with this class of inverse problems.
Recent arXiv pre-prints
arXiv is a well-known preprint server for mathematics, computer science, physics, etc. In exchange for weakening the demands of peer review, it encourages people to share articles at a much faster pace than would be possible otherwise. I’ve been a long-time subscriber of their RSS feed, which helps me keep abreast of developments in my field. On a typical day, between 100~150 new preprints are submitted, of which I usually find five or six “interesting.”
So in accordance with this I have added this week an additional “interesting” filter for things that may be of interest to LW. Right now, that seems to mean things about practical Bayesian statistics.
Disclaimer: while I’ve skimmed through the papers listed below, I make no guarantee that they are either correct or interesting. I’m not a domain expert in statistics.
Kolyan Ray, Bayesian inverse problems with non-conjugate priors
Inverse problems is an important field (i.e., it’s my field) that studies, for example, under what conditions a measurement device is able to function, and how well it functions. Classically the theory has dealt solely with idealized perfect measurements in the absence of error, but since about the 80′s there has been some work done in combining inverse problems with Bayesian updating. Here they study a really general model (that covers e.g., CT imaging) in the presence of white noise. It’s somewhat popular these days to study how the posterior “collapses” in either the high-data or low-noise limit (where the Bayesian result should tend to the classical one), and so this paper studies the model in the high-data limit.
Gergely Székely, What properties of numbers are needed to model accelerated observers in relativity?
Admittedly this preprint strains my internal definition of “LW-interest,” but it was too cute to pass up. They construct a first-order logical theory of special relativity and ask what the scalar quantities of this theory form a model of. Typically everyone assumes that the real numbers are the “correct” model of physical quantities, but there’s no a priori reason for this to be true, see here. The preprint claims that in more than three dimensions, FOL + SR can model any ordered field. If in addition there exist accelerated observers, a real closed field is required. The most interesting part is that if there is a uniformly accelerated observer, there is no set of first-order axioms characterizing the possible fields of scalars.
Michel Bauer, Denis Bernard, Tristan Benoist, Iterated Stochastic Measurements
The interesting thing about this paper is that it flags down several references describing the analogy between quantum mechanics and Bayesian updating. As the title suggests, they study some discrete- and continuous-time models of a random system that can be probed iteratively. Since QM prevents quantum systems from being completely measured, they work with a model probe that only partially measures the system. After probing the system over and over again, Bayesian updating on the probe data yields more and more complete information, just as one would expect.
Sergios Agapiou, Andrew M. Stuart, Yuan-Xiang Zhang, Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems
This is another Bayesian inverse problems paper, this time dealing with the low-noise limit. The “severely ill-posed inverse problems” of the title covers practical problems like deconvolution and optical tomography. They show posterior consistency for gaussian priors. They also mention a formal analogy between Bayesian updating and Tikhonov regularization, which is the classical method for dealing with this class of inverse problems.