Diversity score

As a convenience, one might imagine designing a diverse set of 30 substi- 

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The intent of the diversity score is to ensure that methyl-ethyl-propyl-butyl compounds won t all rank near the top and that lower scoring (on other measures) compounds that are structurally novel will be evaluated more favorably. 

An example of a final consensus list can be seen in Fig. 6. In this figure one can see the Q-score and B-score and the computed preliminary consensus score. On the basis of the preliminary consensus, NP-103930 was chosen as the best compound and selected to be the dissimilarity seed. After the maximum dissimilarity calculation, the diversity score was input and the final consensus score was calculated. As one can see from this figure, the first compound in the preliminary run remains the best. The second compound from the preliminary run does not appear in this list as it was very similar to the NP-103930 and was de-prioritized and moved down the list accordingly. Also the 155th compound in the preliminary ranking moved up the 14th rank because it was considered as a structurally novel compound. This, we feel, illustrates the power of this approach. Compounds with the most desirable properties move up the list and compounds with less desirable properties move down the list. 

The designs are then sorted by the diversity scores (log jX Xj), as in Table 3,to critique the tradeoff between bias, synthetic ease, and diversity. The object is to find synthetically feasible biased designs with high diversity and pharmacophore focus, and low molecular weight. Unbiased design 1 was made by taking all 35 substituents from the All candidate bin. Its score of 150.9 is used... 

Table 5 Change in Diversity Score for D-Optimal Libraries of 20 Substituents Forced to Include Increasing Numbers from a Bin of Tyramine Analogs...

Diversity score a statistical value that is calculated via a formula developed by the rating agencies and designed to measure the level of diversity in the asset portfolio, thus minimizing pairwise correlation in terms of each asset s probability of default. 

The correlation between assets in a specified portfolio is an important aspect in CDO risk analysis. Challenges exist in terms of determining what precise correlation values to use these can be correlation between default probabilities, correlation between timing of default, and correlation between spreads. The diversity score value of a portfolio attempts to measure and encapsulate these concepts by way of simplification. The higher the score, presumably the less correlated the default likelihood of each asset becomes. 

Step 3 Calculate Diversity Score. Calculate a diversity score for the portfolio based on the Moody s industry groupings assigned to each asset. The diversity score will provide the important simplifying assumption driving correlation analysis of the portfolio. 

It is important to note that this expected default probability does not say anything about potential correlations among the 100 credits. It is still merely a starting point for assessing the overall risk of the portfolio. Other inputs are required to reach our goal— including the principal correlation proxy for this model diversity score. 

The diversity score takes a pool of different assets which have some actual correlation and reduces them to a smaller pool of assets that are assumed to be homogeneous and uncorrelated. It is hoped that the mean and standard deviation of this model portfolio s performance will match the actual performance of the collateral. 

Effectively, in calculating the diversity score, credits within the same industry are assumed to have some correlation, whereas credits in different industries are assumed to be completely uncorrelated. Each additional member of the portfolio adds to the diversity score, but members that are within the same industry add less and less as the industry concentration grows. For example, 20 assets in 20 different industries might add 20 to the diversity score 20 assets within the same industry, however, might only add 5 to the diversity score. 

Our portfolio, which we assume to be relatively clumped within a few industries, has a diversity score of 49. It is expected to behave as if it were composed of 49 equal-weighted, uncorrelated assets, each of which has the same expected default probability of approximately 0.97%. When defaults occur, we will assume each increment of default is 1/49 of the portfolio rather than 1/100. 

Savy M, Martin-Prevel Y, Traissac P, et al. Dietary diversity scores and nutritional status of women change during the seasonal food shortage in rural Burkina Faso. / Nutr. 2006 136 2625—263Z... 

Fig. 4. Chemical diversity is calculated as the fraction of compounds in a library that singly occupy cells in chemical space, and is shown here for an optimized library of 2000 compounds (a 10 x 20 x 10 combinatorial library) selected by MapMaker (left bar), and for the average of three 2000-member combinatorial libraries formed by selecting reagents at random. The optimized library has a nearly optimal diversity score of 1, whereas picking reagents without optimization would result in about half the screening efficiency, or about half the information (about 50% of the compounds in the random libraries occupy redundant cells).

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