Statistical image analysis and escort histograms in characterization of articular cartilage repair in a skeleton animal model

Statistical image analysis of an ensemble of digital images of histological samples is performed as an auxiliary investigation a result of the recently proposed method of articular cartilage repair utilizing growth plate chondrocytes in a skeleton animal model. A fixed–shift model of maximal likelihood estimates of image histograms applied for monochromatic (grayscale) images or their RGB components confirms the statistically significant effect of the previously proposed medical treatment. The type of staining used to prepare images of histological samples is related to the visibility of the effectiveness of medical treatment. Hellinger distance of escort distributions for maximal likelihood estimates of image histograms of medically treated and control samples is investigated to identify grayscale (or RGB) intensities responsible for statistically significant difference of the estimates. A difference of Shannon entropy quantifying informational content of the histograms allows one to identify staining and image colors which are most suitable to visualize cluster formation typical for articular cartilage repair processes

A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family

In the theory of complex systems, long tailed probability distributions are often discussed. For such a probability distribution, a deformed expectation with respect to an escort distribution is more useful than the standard expectation. In this paper, by generalizing such escort distributions, a sequence of escort distributions is introduced. As a consequence, it is shown that deformed expectations with respect to sequential escort distributions effectively work for anomalous statistics. In particular, it is shown that a Fisher metric on a q-exponential family can be obtained from the escort expectation with respect to the second escort distribution, and a cubic form (or an Amari–Chentsov tensor field, equivalently) is obtained from the escort expectation with respect to the third escort distribution