Another occurrence, while building my final math stat exam for my (quarantined!) third year students, of a question on X validated that led me to write down more precisely an argument for the decomposition of densities in exponential families. Albeit the decomposition is somewhat moot *(and lost on the initiator of the question since this person later posted an answer ignoring measures)*, as it all depends on the choice of the dominating measures over X, T(X), and the slices {x; T(x)=t}. The fact that the slice does depend on t requires the measure to accept a potential dependence on t, in which case the conditional density wrt this measure can as well be constant.

## Archive for factorisation

## factorisation theorem on densities

Posted in Statistics with tags cross validated, dominating measure, exponential families, factorisation, final exam, mathematical statistics, sufficient statistics on December 23, 2020 by xi'an## stochastic magnetic bits, simulated annealing and Gibbs sampling

Posted in Statistics with tags factorisation, Gibbs sampling, Nature, optimisation, p-bits, prime numbers, quantum comuting, quantum cryptograpy, Series B, simulated annealing on October 17, 2019 by xi'an**A** paper by Borders et al. in the 19 September issue of Nature offers an interesting mix of computing and electronics and optimisation. With two preparatory tribunes! One [rather overdone] on Feynman’s quest. As a possible alternative to quantum computers for creating probabilistic bits. And making machine learning (as an optimisation program) more efficient. And another one explaining more clearly what is in the paper. As well as the practical advantage of the approach over quantum computing. As for the paper itself, the part I understood about factorising an integer F via minimising the squared difference between a product of two integers and F and using simulated annealing sounded rather easy, while the part I did not about constructing a semi-conductor implementing this stochastic search sounded too technical (especially in the métro during rush hour). Even after checking the on-line supplementary material. Interestingly, the paper claims for higher efficiency thanks to asynchronicity than a regular Gibbs simulation of Boltzman machines, quoting Roberts and Sahu (1997) without further explanation and possibly out of context (as the latter is not concerned with optimisation).