Expectation maximization for hard X-ray count modulation profiles

Expectation Maximization

Expectation Maximization

The Expectation Maximization (EM) algorithm [1, 2] is one of the most widely used algorithms in statistics. Suppose we are given some observed data X and a model family parametrized by θ, and would like to find the θ which maximizes p(X |θ), i.e. the maximum likelihood estimator. The basic idea of EM is actually quite simple: when direct maximization of p(X |θ) is complicated we can augment the...

An X-ray polarimeter for hard X-ray optics

Development of multi-layer optics makes feasible the use of X-ray telescope at energy up to 60-80 keV: in this paper we discuss the extension of photoelectric polarimeter based on Micro Pattern Gas Chamber to high energy X-rays. We calculated the sensitivity with Neon and Argon based mixtures at high pressure with thick absorption gap: placing the MPGC at focus of a next generation multi-layer ...

Microquasars: hard X-ray/γ-ray emission

I review some of the basic observational details of jets from X-ray binaries, or ‘microquasars’. It is shown that in both (Z and Atoll) NS and BHC systems radio emission, and therefore jet formation, is correlated with the presence of hard (30–500 keV) X-ray emission. At γ-ray (> 500 keV) energies, the relation is not so clear. Possible physical connections between the presence of a jet, with a...

Week 9: Expectation Maximization

Last week, we saw how we could represent clustering with a probabilistic model. In this model, called a Gaussian mixture model, we model each datapoint x i as originating from some cluster, with a corresponding cluster label y i distributed according to p(y), and the corresponding distribution for that cluster given by a multivariate Gaussian: p(x|y = k) =