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Dipartimento di Metodi e Modelli per l'Economia, il Territorio e la Finanza

Facoltà di Economia, Sapienza Università di Roma

Giovedì 15 febbraio

Ore 14.00, auletta A, IV piano


*A new approach to spatial entropy measures*

L. Altieri,  D. Cocchi, G. Roli



Entropy is widely employed in many applied sciences to measure the
heterogeneity of observations. Recently, many attempts have been made to
build entropy measures for spatial data, in order to capture the influence
of space over the variable outcomes. The main limit of these developments
is that

all indices are computed conditional on a single distance and do not cover
the whole spatial configuration of the phenomenon under study. Moreover,
most of them do not satisfy the desirable additivity property between local
and global spatial measures. We compare some recent developments in this field
to a new approach which achieves substantial innovations. Firstly,
Shannon’s entropy

may be decomposed into two terms: spatial mutual information, accounting for
the role of space in determining the variable outcome, and spatial
global residual
entropy, summarizing the remaining heterogeneity carried by the
variable itself.
Secondly, both terms satisfy the additivity property, being

sums of partial entropies measuring what happens at different distance
classes. The new entropy measures are shown to be more informative and to
answer a wider set of questions than the current proposals of the
literature. A case study is presented with categorical lattice data,
concerning the spatial heterogeneity

of land use over the Emilia Romagna region.
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