Thompson Sampling has been demonstrated in many complex bandit models, however the theoretical guarantees available for the parametric multi-armed bandit are still limited to the Bernoulli case. Here we extend them by proving asymptotic optimality of the algorithm using the Jeffreys prior for 1-dimensional exponential family bandits. Our proof builds on previous work, but also makes extensive u...

Parametric complexity is a central concept in Minimum Description Length (MDL) model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on Jeffreys’ prior can not be used. Several ways to resolve this problem have been proposed. We condu...

Parametric complexity is a central concept in MDL model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on Jeffreys’ prior can not be used. Several ways to resolve this problem have been proposed. We conduct experiments to compare and...

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses as models for threshold excesses and block maxima, respectively. For each of these distributions we consider Bayesian inference using “reference” prior distributions (in the general sense of priors constructed using formal rules) for the model parameters, specifically a...

Abstract If a prior probability does not exist or is controversial, can we formulate probabilistic inference based only on the properties of the measurement? In the case of plain ‘location’ measurements the answer to this is known. Here we extend that answer to address the general problem of estimating a scalar parameter from a small data sample. That measurement is treated as if resulting from...

Thompson Sampling has been demonstrated in many complex bandit models, however the theoretical guarantees available for the parametric multi-armed bandit are still limited to the Bernoulli case. Here we extend them by proving asymptotic optimality of the algorithm using the Jeffreys prior for 1-dimensional exponential family bandits. Our proof builds on previous work, but also makes extensive u...

When facing small numbers of observations or rare events, political scientists often encounter separation, in which explanatory variables perfectly predict binary events or non-events. In this situation, maximum likelihood provides implausible estimates and the researcher might want incorporate some form of prior information into the model. The most sophisticated research uses Jeffreys’ invaria...

A new study by Jeffreys et al. shows that the rate of recombination in recombination hotspots in humans is not constant through time. This observation adds weight to the idea that hotspots are transient on evolutionary timescales. However, questions remain as to what controls their evolution and how these rapid changes influence broad-scale rates of recombination.

Many interesting divergence measures between conjugate ensembles of nonequilibrium trajectories can be experimentally determined from the work distribution of the process. Herein, we review the statistical and physical significance of several of these measures, in particular the relative entropy (dissipation), Jeffreys divergence (hysteresis), Jensen–Shannon divergence (timeasymmetry), Chernoff...