In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is consi...

The Maximum Entropy probability density function associated with the testable information on the range and the first and second order moments of the random quantity of interest is derived. The validity of such approach is experimentally demonstrated through comparison between the proposed maximum entropy distribution and the Ushaped distribution. The underlying physical assumptions which must b...

In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the ...

During the MaxEnt 2002 workshop in Moscow, Idaho, Tony Vignaux asked again a few simple questions about using Maximum Entropy or Bayesian approaches for the famous Dice problems which have been analyzed many times through this workshop and also in other places. Here, there is another analysis of these problems. I hope that, this paper will answer a few questions of Tony and other participants o...

Maximum Entropy (MaxEnt) models (Jaynes, 1957) are exponential models that implement the intuition that if there is no evidence to favour one alternative solution above another, both alternatives should be equally likely. In order to accomplish this, as much information as possible about the process you want to model must be collected. This information consists of frequencies of events relevant...

The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one when the ratio is high. The obtained long tail distribution yields correctly the empirical Zipf law, Pareto's 20:80 rule and Benford's l...

We desire to generate monthly rainfall totals for a particular location in such a way that the statistics for the simulated data match the statistics for the observed data. We are especially interested in the accumulated rainfall totals over several months. We propose two different ways to construct a joint rainfall probability distribution that matches the observed grade correlation coefficien...

Spelling check identifies incorrect writing words in documents. For the reason of input methods, Chinese spelling check is much different from English and it is still a challenging work. For the past decade years, most of the methods in detecting errors in documents are lexicon-based or probability-based, and much progress are made. In this paper, we propose a new method in Chinese spelling che...

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are...