We present a lower bound on the Jensen-Shannon divergence by the Jeffrers’ divergence when pi ≥ qi is satisfied. In the original Lin's paper [IEEE Trans. Info. Theory, 37, 145 (1991)], where the divergence was introduced, the upper bound in terms of the Jeffreys was the quarter of it. In view of a recent shaper one reported by Crooks, we present a discussion on upper bounds by transcendental fu...

Jeffreys and Shtarkov distributions play an important role in universal coding andminimumdescription length (MDL) inference, two central areas within the field of information theory. It was recently discovered that in some situations Shtarkov distributions exist while Jeffreys distributions do not. To demonstrate some of these situations we consider in this note the class of natural exponential...

Harold Jeffreys (1891–1989) was a British scientist who mainly contributed to mathematics, statistics, Bayesian probability, geophysics and astronomy, but also published articles on other subjects. (For further biographical information cf. Cook, A. H. (1990). Sir Jeffreys, 2 April 1891 – 18 March 1989. In: Biographical Memoirs of Fellows the Royal Society 36, pp. 301–333. url: https: //royalsoc...

We discuss the relationship between the statistical embedding curvature [1, 2] and the logarithmic regret [11] (regret for short) of the Bayesian prediction strategy (or coding strategy) for curved exponential families and Markov models. The regret of a strategy is defined as the difference of the logarithmic loss (code length) incurred by the strategy and that of the best strategy for each dat...

This Editorial reports an exchange in form of a comment and reply on the article “History Nature Jeffreys–Lindley Paradox” (Arch Hist Exact Sci 77:25, 2023) by Eric-Jan Wagenmakers Alexander Ly.

Objective priors, especially reference priors, have been well-known for geostatistical data since Berger, et al. (2001). A long-standing problem is to develop objective Bayes inference for spatially correlated data with nugget effects. In this paper, objective priors for such cases are systematically studied. In addition to the Jeffreys priors and commonly used reference priors, two types of “e...

Three Bayesian related approaches, namely, variational Bayesian (VB), minimum message length (MML) and Bayesian Ying-Yang (BYY) harmony learning, have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model (GMM). This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conju...