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Although in principle prior information can significantly improve inference, incorporating incorrect prior information will bias the estimates of any inferential analysis. This fact deters many scientists from incorporating prior information into their inferential analyses. In the natural sciences, where experiments are more regularly conducted, and can be combined with other relevant information, prior information is often used in inferential analysis, despite it being sometimes nontrivial to specify what that information is and how to quantify that information. In the social sciences, however, prior information is often hard to come by and very hard to justify or validate. We review a number of ways to construct such information. This information emerges naturally, either from fundamental properties and characteristics of the systems studied or from logical reasoning about the problems being analyzed. Borrowing from concepts and philosophical reasoning used in the natural sciences, and within an info-metrics framework, we discuss three different, yet complimentary, approaches for constructing prior information, with an application to the social sciences.

Purpose – We propose applying Reardon's approach to the measurement of ordinal segregation to the study of inequality in life chances in the case of ordinal variables. We also propose additional measures of inequality in life chances in such a case.

Methodology – We state the desirable properties of measures of inequality in life chances when the variable under study is ordinal and check which properties are fulfilled by the various indices examined in this chapter.

Findings – All the indices defined in this chapter seem suitable for the analysis of inequality in life chances with ordinal variables but we found some trade-off between indices fulfilling the population composition invariance and those fulfilling the group replication invariance.

Originality – Besides extending the indices suggested by Reardon to the study of inequality of life chances, we propose, to analyze this issue, two additional sets of indices based on the notion of distributional dissimilarity.

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators relative to classical estimators. Finally, the estimators are applied to an illustrative model allocating agricultural disaster payments.