As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of ...probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity.
The Yule-Simpson paradox refers to the fact that outcomes of comparisons between groups are reversed when groups are combined. Using Essential Sciences Indicators, a part of InCites (Clarivate), data ...for countries, it is shown that although the Yule-Simpson phenomenon in citation analysis and research evaluation is not common, it isn’t extremely rare either. The Yule-Simpson paradox is a phenomenon one should be aware of, otherwise one may encounter unforeseen surprises in scientometric studies.
The current study exhibits a new implication of the Yule-Simpson paradox with public policy repercussions. We construct Laffer curves of local property tax collection based on aggregated data and ...group division to residential land uses in Jerusalem. Results indicate that based on aggregated (dis-aggregated) data, the location of owner-occupiers and renters who pay a relatively high rate tariff will be on the upward-sloping (downward-sloping) part of the Laffer curve. Consequently, statistical test outcomes support Laffer's controversial claim that for the few upper-brackets taxpayers, an efficient collection is associated with tax reduction rather than tax increase.
It is shown, on the examples of concrete publications, that "person-years" category application in multi-factor health risks analysis can lead to false conclusions in the process of observation data ...grouping due to Simpson paradox influence when examinations are performed via demographic or epidemiological techniques. The paradox occurs when heterogeneous strata are being compared. "Person-years" category first appeared in the middle of the 17th century, long before first applications of mathematical tools in statistics and probability theory; it does not fully correspond to up-to-date requirements of epidemiological research. Risk theory should change 17–18 century paradigm as it focuses on conditional probability of unwanted events occurrence and not on a principle of comparing their intensities. It is particularly vital in case when we deal with determining possible damage to health caused by effects exerted by such factors and under such conditions when individual damage cannot be measured objectively but when it is possible to quantitatively determine regularities of changes in stochastic ability to survive for a large group of people or remote consequences occurrence for it. We prove it is necessary to create specialized mathematical tools and hybrid software able to solve a risks assessment task as an inverse one. Mathematical tools of large contingency tables could serve as prototypes of such tools; we can also use multi-factor logistical and Poisson regressions which are usually applied in countable events analysis. We should note that it is also necessary to eliminate a number of methodological drawbacks which are attributable to the said tools.
Dysbiosis, developed upon antibiotic administration, results in loss of diversity and shifts in the abundance of gut microbes. Doxycycline is a tetracycline antibiotic widely used for malaria ...prophylaxis in travelers. We prospectively studied changes in the fecal microbiota of 15 French soldiers after a 4-month mission to Mali with doxycycline malaria prophylaxis, compared to changes in the microbiota of 28 soldiers deployed to Iraq and Lebanon without doxycycline. Stool samples were collected with clinical data before and after missions, and 16S rRNA sequenced on MiSeq targeting the V3-V4 region. Doxycycline exposure resulted in increased alpha-biodiversity and no significant beta-dissimilarities. It led to expansion in Bacteroides, with a reduction in Bifidobacterium and Lactobacillus, as in the group deployed without doxycycline. Doxycycline did not alter the community structure and was specifically associated with a reduction in Escherichia and expression of Rothia. Differences in the microbiota existed at baseline between military units but not within the studied groups. This group-effect highlighted the risk of a Simpson paradox in microbiome studies.
Because police jurisdictions typically rely on different call classification schemes and handle a different mix of calls, it is difficult to compare multi-priority police response time distributions ...between two or more jurisdictions. For the same reasons, it can be challenging to compare response time trends over time, even within a given police jurisdiction. Hypothetical examples illustrate the main analytical challenges. Then, a simple clustering approach, the Jenks natural breaks method, is demonstrated. This approach can be used to objectively compare police response time distributions. The resulting comparisons remain unaffected by differences or changes in call classification rules and cannot be easily manipulated or skewed, either intentionally or inadvertently. Although the discussion is framed within a police context, the proposed analytical approach has the potential to be useful for other emergency services and benchmarking settings.
We say that the signs of association measures among three variables {X, Y, Z} are transitive if a positive association measure between X and Y and a positive association measure between Y and Z imply ...a positive association measure between X and Z. We introduce four association measures with different stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us draw conclusions about the signs of the association measures between X and Z based only on separate studies about {X, Y} and {Y, Z}.
On stochastic dependence Meyer, Joerg M.
Teaching statistics,
03/2018, Letnik:
40, Številka:
1
Journal Article
Recenzirano
Summary
The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, ...some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.
The Yule-Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth introduced the concept of distribution dependence ...between two random variables X and Y, and gave two dependence conditions, each of which guarantees that reversal of qualitatively similar conditional dependences cannot occur after marginalizing over the background variable. Ma, Xie and Geng studied the uniform collapsibility of distribution dependence over a background variable founder stronger homogeneity condition. Collapsibility ensures that associations are the same for conditional and marginal models. In this article, we use the notion of average collapsibility, which requires only the conditional effects average over the background variable to the corresponding marginal effect and investigate its conditions for distribution dependence and for quantile regression coefficients.
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