Generalized Maximum Entropy

Plastino and Curado [Phys. Rev. E 72, 047103 (2005)] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy showing that the Tsallis entropy yields genuine inverse power laws.

We estimate firm-specific cash flow sensitivities of investment for a panel of manufacturing SMEs, using the generalized maximum entropy-estimator (GME). Since this estimator easily allows for slope heterogeneity, we no longer have to rely on ex-ante sample splitting, which has been common practice in this literature. The results show a wide variation in individual sensitivities in every year, demonstrating the

We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.

The origin of entropy dates back to 19th century. In 1948, the entropy concept as a measure of uncertainty was developed by Shannon. A decade after in 1957, Jaynes formulated Shannon’s entropy as a method for estimation and inference particularly for ill-posed problems by proposing the so called Maximum Entropy (ME) principle. More recently, Golan et al. (1996) developed the Generalized Maximum Entropy (GME) estimator and started a new discussion in econometrics. This paper is divided into two parts. The first part considers the formulation of this new technique (GME). Second, by Monte Carlo simulations the estimation results of GME will be discussed in the context of non-normal disturbances.

Maximum entropy and Bayesian approaches provide superior estimates of a ratio of parameters, as this paper illustrates using the classic Nerlove model of agricultural supply. Providing extra information in the supports for the underlying parameters for generalized maximum entropy (GME) estimators or as an analytically derived prior distribution in Zellner's minimum expected loss (MELO) estimators and Bayesian method of moments

Montado ecosystem in the Alentejo Region, south of Portugal, has enormous agro-ecological and economics heterogeneities. A definition of homogeneous sub-units among this heterogeneous ecosystem was made, but for them is disposal only partial statistical information about soil allocation agro-forestry activities. The paper proposal is to recover the unknown soil allocation at each homogeneous sub-unit, disaggregating a complete data set for the Montado ecosystem area using incomplete information at sub-units level. The methodological framework is based on a Generalized Maximum Entropy approach, which is developed in thee steps concerning the specification of a r order Markov process, the estimates of aggregate transition probabilities and the disaggregation data to recover the unknown soil allocation at each homogeneous sub-units. The results quality is evaluated using the predicted absolute deviation (PAD) and the "Disagegation Information Gain" (DIG) and shows very accept...

Montado ecosystem in the Alentejo Region, south of Portugal, has enormous agro-ecological and economics heterogeneities. A definition of homogeneous sub-units among this heterogeneous ecosystem was made, but for them is disposal only partial statistical information about soil allocation agro-forestry activities. The paper proposal is to recover the unknown soil allocation at each homogeneous sub-unit, disaggregating a complete data set for

Spatial econometrics is a subdiscipline that have gained a huge popularity in the last twenty years, not only in theoretical econometrics but in empirical studies as well. Basically, spatial econometric methods measure spatial interaction and incorporate spatial structure into regression ...

The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called "diagonal ensemble" r DE. Building on the intuition provided by Jaynes' maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to r DE. As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the "thermal ansatz" of Gibbs ensembles.

In this paper we propose a generalised maximum-entropy classification framework, in which the empirical expectation of the feature functions is bounded by the lower and upper expectations associated with the lower and upper probabilities associated with a belief measure. This generalised setting permits a more cautious appreciation of the information content of a training set. We analytically derive the Karush-Kuhn-Tucker conditions for the generalised max-entropy classifier in the case in which a Shannon-like entropy is adopted.

The aim of this paper was to develop a national customer satisfaction index (CSI) in Jordan and to derive its theory using generalized maximum entropy. During the course of this research, we conducted two different surveys to complete the framework of this CSI. The first one is a pilot study conducted based on a CSI basket in order to select the main factors that comprise the Jordanian customer satisfaction index (JCSI). Based on two different analyses, namely nonlinear principal component analysis and factor analysis, the explained ...

We attempt a connection between thermodynamics and zatrikean pregeometry, i.e., a chess-like pregeometry. In zatrikean pregeometry space is represented by the abacus, a discrete chessboard-like structure consisting of a sufficiently large number of plaquettes called geobits. The particles move on the abacus from one geobit to the next following certain rules that resemble the game of chess. The sets of rules imposed on the motions of particles on the abacus are called premetrics. There is a variety of paths (called subabaces) leading from one geobit to another, and there is a class consisting of subabaces with the minimum number of geobits. These are called alyssoids (respectively, class of alyssoids) for the particular premetric, while those alyssoids with minimum length are called geodesics (respectively, class of geodesics) for the particular premetric. The so-called zatrikean geodesic was originally defined in G93 (Section 2) as the geodesic most closely following the line segment joining the two geobits. It is also called algorithmic geodesic since it is drawn with the assistance of four simple algorithms. This is a rectifiable curve; and a connection between rectifiable curves and thermodynamics is already available (DuPain, Kamae and Mendes-France 1986). Consequently, the so-called thermodynamic geodesic is defined as the particular member of the class of geodesics with maximum entropy. Since it does not necessarily correspond to the algorithmic geodesic, a new algorithm is devised that draws the geodesic with maximum entropy. Furthermore, the probability of each member of the class of geodesics can be determined as the difference of its entropy from the entropy of the thermodynamic geodesic.

We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.

"This work stems from a desire to combine ideas arising from two historically different schemes of probabilistic reasoning, each having its own axiomatic traditions, into a single broader axiomatic framework, capable of providing general new insights into the nature of probabilistic inference in a multiagent context.
In the present sketch of our work we first describe briefly the background context, and we then present a set of natural principles to be satisfied by any general method of aggregating the partially defined probabilistic beliefs of several agents into a single probabilistic belief function. We will call such a general method of aggregation a social inference process. Finally we define a particular social inference process, the Social Entropy Process (abbreviated to SEP), which satisfies the principles formulated earlier. SEP has a natural justification in terms of information theory, and is closely related to the maximum entropy inference process: indeed it can be regarded as a natural extension of that inference process to the multiagent context."