We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space f...

Bayesian learning is widely used in many applied datamodelling problems and is often accompanied with approximation schemes since it requires intractable computation of the posterior distributions. In this study, we focus on the two approximation methods, the variational Bayes and the local variational approximation. We show that the variational Bayes approach for statistical models with latent...

Normal approximation confidence intervals are used in most commercial statistical package because they are easy to compute. However, the performance of such procedures could be poor when the sample size is not large or when there is heavy censoring. A transformation can be applied to avoid having confidence interval endpoints fall outside the parameter space and otherwise improves performance, ...

Ising and Potts models are discrete Gibbs random field models originating in statistical physics, which are now widely used in statistics for applications in spatial modeling, image processing, computational biology, and computational neuroscience. However, parameter estimation in these models remains challenging due to the appearance of intractable normalizing constants in the likelihood. Here...

single-valence electron atoms are an important class of atoms. their oscillator strengths are their important properties. knowing the oscillator strengths one can easity calculate the transition probabilities of the spectral lines and hence the lifetimes of energy levels of most atoms. the oscillator strengths of the spectral lines of most atoms are not knoen with sufficient accuracy due to the...