Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables

Good, I. J.

doi:10.1214/aoms/1177704014

Cited by 350 publications

(155 citation statements)

References 30 publications

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“…introduced by Good (1963). This framework is very useful to reach better estimates and its objective is the minimization of the discrepancy between the posterior probability estimates p k and priors of information q k .…”

Section: -The Entropy Approach Backgroundmentioning

confidence: 99%

Estimation of cost allocation coefficients at the farm level using an entropy approach

Fragoso

Carvalho

2013

Journal of Applied Statistics

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This paper aims to estimate the farm cost allocation coefficients from whole farm input costs. An entropy approach was developed under a Tobit formulation and was applied to a sample of farms from the 2004 FADN data base for Alentejo region, Southern Portugal. A Generalized Maximum Entropy model and Cross Generalized Entropy model were developed to the sample conditions and were tested. Model results were assessed in terms of their precision and estimation power and were compared with observed data. The entropy approach showed to be a flexible and valid tool to estimate incomplete information, namely regarding farm costs. The costs per output activity can be obtained either from collecting data directly in farms, or through estimated coefficients of input costs from samples of FADN data base. The second approach seems to be the best solution, since the first approach is expensive and too demanding in resources.There are several works that estimate crop-specific inputs (Just et al., 1983;Shumway et al., 1984; and Miller, 1998a e 1998b). Most of them are based on the relationship between input allocations and production coefficients under the assumption of profit maximization. Traditionally the tools used in these approaches are linear regression techniques (LRT), Bayesian estimation techniques (BES) and linear programming (LP), but their use raises some practical concerns.In the problem of farm cost allocation, it is necessary to ensure the accounting balance between total revenue and total costs. In this situation the disturbance terms of the various input-demand equations are not independent from each other and the system 3 of input-demand equations is singular, which invalidates the use of LRT techniques (Bewley, 1986). Another well known result of the LRT technique is the negative inputdemand coefficients that could be estimated. This can be avoided by using BES techniques or inequality least squares methods (Moxey and Tiffin, 1994). However, the application of these alternative methods is heavy and does not allow incorporating the accounting constraints which need to be treated separately in the system. A flexible alternative that has been widely applied to estimate farm input and output coefficients is the entropy approach. This methodology does not require behavioural assumptions and allows the use of non sample information through the introduction of information priors.This paper aims to apply a flexible methodology that allows estimating the coefficients of farm cost allocation per output activity from the whole farm input costs, taking into account general conditions of Mediterranean areas. An entropy approach is used to make the estimation of coefficients at the farm level based on a farms sample of the FADN data base in the Alentejo region, South of Portugal. A Generalized MaximumEntropy (GME) model and a Cross Generalized Entropy (CGE) model are applied and assessed by looking at the precision of the coefficients extracted from the whole farm data and comparing them with the observed input-o...

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Section: -The Entropy Approach Backgroundmentioning

confidence: 99%

Estimation of cost allocation coefficients at the farm level using an entropy approach

Fragoso

Carvalho

2013

Journal of Applied Statistics

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“…Good [1963] proposed to use the principle of maximum entropy as a heuristic principle for the generation of null hypotheses, with main application to m-dimensional contingency tables. Three versions of this principle are given in his paper.…”

Section: Good's Formulationmentioning

confidence: 99%

“…For the case 7T ijkl = 1/ rcdt, the problem of minimizing I (p : 7T) in (2.4) subject to certain restraints is equivalent to minimizing subject to the same restraints. The latter problem has been considered by Good [1963Good [ , 1965Good [ ,1966.…”

Section: +(C-l )(D-l)(t -1)mentioning

confidence: 99%

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Interaction in multidimensional contingency tables: an information theoretic approach

Ku¹

1968

J. RES. NATL. BUR. STAN. SECT. B. MATH. SCI.

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The problem of interaction in multidime nsional co ntin ge ncy tables is inves ti gated from the viewpoint of information th eory as developed by Kullbac k. The hypothesis of no rth-order interaction is defin ed in the sense of an hypothes is of "generalized " ind ependence of classifications with fix ed rth order marginal restraints. For a three· way table, with given cell probabilities 7Tijk , the minimum discrimination information for a contin ge ncy table with marginals P jj ., P. jk, and P i ... is given by the se t of cell probabilities P 0 k = a jjbj k e ,,·7Ti j k wh ere aij , b j ,., and eik are fun ctions of th e giv e n marginal probabilities, that is, In (p!jJ7T ij") = In a ij + In bj k + In e ,,·, representing no second-order interaction.The minimum di scrimination inl ormation stati sti c, asymptotically distributed as X" with appropriate degrees of freedom is where Xi jk are the observed cell frequencies and Xijk are the " no inte raction" cell frequencies uniquely de termined by a simple co nve rge nt ite rati on process of th e marginals on 7T ijk . For low e r ord e'r marginal restraints the us ual independ ence hypoth eses are ge ne rated when 7Tijk are taken to be the cell probabilities under uniform di stribution. It is shown th at th e set P !j,. satis fi es definitions of no second order interaction in a 2 x 2 x 2 table give n by Bartl ett and no interaction in a r X s X t table by Roy and Kastenbaum, and is also related to that give n by Good. Res ults of application to the analys is of so me "classical " three-dimensional contingency tables are given , together with full details for two four· dimensional examples.

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“…This time the experiment would take longer because there are many more quadratic than linear terms. But we might very well have discovered the principle known to chess players, for at least a century, as "the advantage of two bishops" (Good [5]). This means that although the values of bishops and knights are about equal, a bishop pair is usually more valuable than two knights or than a bishop and a knight.…”

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confidence: 99%

Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables

Cited by 350 publications

References 30 publications

Estimation of cost allocation coefficients at the farm level using an entropy approach

Estimation of cost allocation coefficients at the farm level using an entropy approach

Interaction in multidimensional contingency tables: an information theoretic approach

Book Review: Mechanizing hypothesis formation. Mathematical foundations for a general theory

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