On generalized entropies, Bayesian decisions and statistical diversity

summary:The paper summarizes and extends the theory of generalized $\phi$-entropies $H_{\phi }(X)$ of random variables $X$ obtained as $\phi$-informations $I_{\phi }(X;Y)$ about $X$ maximized over random variables $Y$. Among the new results is the proof of the fact that these entropies need not be concave functions of distributions $p_{X}$. An extended class of power entropies $H_{\alpha }(X)$ is introduced, parametrized by $\alpha \in {\mathbb{R}}$, where $H_{\alpha }(X)$ are concave in $p_{X}$ for $\alpha \ge 0$ and convex for $\alpha <0$. It is proved that all power entropies with $\alpha \le 2$ are maximal $\phi$-informations $I_{\phi }(X;X)$ for appropriate $\phi$ depending on $\alpha$. Prominent members of this subclass of power entropies are the Shannon entropy $H_{1}(X)$ and the quadratic entropy $H_{2}(X)$. The paper investigates also the tightness of practically important previously established relations between these two entropies and errors $e(X)$ of Bayesian decisions about possible realizations of $X$. The quadratic entropy is shown to provide estimates which are in average more than 100 % tighter those based on the Shannon entropy, and this tightness is shown to increase even further when $\alpha$ increases beyond $\alpha =2$. Finally, the paper studies various measures of statistical diversity and introduces a general measure of anisotony between them. This measure is numerically evaluated for the entropic measures of diversity $H_1(X)$ and $H_2(X)$

Measuring diversity in medical reports based on categorized attributes and international classification systems

<p>Abstract</p> <p>Background</p> <p>Narrative medical reports do not use standardized terminology and often bring insufficient information for statistical processing and medical decision making. Objectives of the paper are to propose a method for measuring diversity in medical reports written in any language, to compare diversities in narrative and structured medical reports and to map attributes and terms to selected classification systems.</p> <p>Methods</p> <p>A new method based on a general concept of f-diversity is proposed for measuring diversity of medical reports in any language. The method is based on categorized attributes recorded in narrative or structured medical reports and on international classification systems. Values of categories are expressed by terms. Using SNOMED CT and ICD 10 we are mapping attributes and terms to predefined codes. We use f-diversities of Gini-Simpson and Number of Categories types to compare diversities of narrative and structured medical reports. The comparison is based on attributes selected from the Minimal Data Model for Cardiology (MDMC).</p> <p>Results</p> <p>We compared diversities of 110 Czech narrative medical reports and 1119 Czech structured medical reports. Selected categorized attributes of MDMC had mostly different numbers of categories and used different terms in narrative and structured reports. We found more than 60% of MDMC attributes in SNOMED CT. We showed that attributes in narrative medical reports had greater diversity than the same attributes in structured medical reports. Further, we replaced each value of category (term) used for attributes in narrative medical reports by the closest term and the category used in MDMC for structured medical reports. We found that relative Gini-Simpson diversities in structured medical reports were significantly smaller than those in narrative medical reports except the "Allergy" attribute.</p> <p>Conclusions</p> <p>Terminology in narrative medical reports is not standardized. Therefore it is nearly impossible to map values of attributes (terms) to codes of known classification systems. A high diversity in narrative medical reports terminology leads to more difficult computer processing than in structured medical reports and some information may be lost during this process. Setting a standardized terminology would help healthcare providers to have complete and easily accessible information about patients that would result in better healthcare.</p

Effects of oxygenation and/or SOD on addition to St. Thomas' Hospital cardioplegic solution

博士（医学）神戸大

Information Technologies for Continual Shared Healthcare

In the workshop proceedings there are presented important results of the project „Information technologies for a continual shared healthcare“supported by the grant 1ET200300413 of the Academy of Sciences of the Czech republic. To show results of the project to a vast public the videofilm in Czech and English language, covering several implemented pilots into Czech healthcare, is recored on the attached DVD

Stochastic Modeling of Biodiversity: f-diversity, self f-diversity and Marginal f-diversity

The paper is devoted to stochastic modeling of biodiversities, that are presented as selected f-diversities frequently used in biology and medicine. The most often used in biology and medicine are f-diversities called Number Alles, Gini-Simpson diversity and Shannon diversity. We have introduced two new general concepts, named marginal f-diversity and self f-diversity. The statistical properties of sample estimates of the selected f-diversities are mentioned. Results of simulations of f-diversities, self f-diversities and marginal f-diversities for Number Alles, Gini-Simpson and Shannon type diversities on the example of three alleles with fixed probabilities of occurrence and several sample sizes used are presented

Biomechanics of the Human Skeleton and of Artificial Replacements of its Parts

Nedoma, J., Stehlík, J., Bartoš, M., Denk, F., Džupa, V., Fousek, J., Hlaváček, I., Klézl, Z., Květ, I. Biomechanika lidského skeletu a umělých náhrad jeho částí. (Zvárová J., Nedoma J. eds.) Praha : Karolinum, 2006. 491 s. ISBN 80-246-1227-5. The editors supported co-operation of authors during the development of the book, commented development of the versions of the book and made the final conclusions about the content of the book and its graphical processing