Unequal pair of Dice

Disparities in Health Care Quality

Whether or not you die of a certain disease is just a toss of dice ?
It may be so.
The problem is that your dice might be unfavorably crooked.

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Visualizing stochastic process

How many people per 100,000 die of a certain disease? how many 1s will you observe when rolling 10 dice?
Both have the same structure of statistics; Binomial distribution.
While we can easily imagine a process of counting 1s out of 10 thrown dice, it is almost impossible to imagine observing 100,000 dice, each of which has 10,000 faces.

To visualize this stochastic process, I mapped probability distribution of death from a certain disease to that of "visible" 30-dice case.
For example, in a year, 31.2 black females per 100,00 die from breast cancer while 12.1 asian/ pacific islanders(API) die from the same disease. Estimated probability of death is 0.0312% for black female and 0.0121% for API. In binomial distribution model, probability mass functions for each look like this. The peaks of the curves are at 31.2 and 12.1. their variances are almost the same, 31.19 and 12.09.
As "visible" models of bimonial distribution, take "normal" dice, whose probability of 1 is 16.6% (1/6), and "crooked" dice with probabilities of 35% or 45%. In case of 30 dice, their expected peak(np) are 5, 10.5 and 13.5; their variances (np(1-p)) are 4.16, 6.82 and 7.42 respectively.

In order to map actual(death) distribution curves to visual(dice) simulation curve while the ratio of two death rates is kept same, deviations from expected means are adjusted, in this visual presentation, according to the ratio of two variances.

Crooked dice as I want

Because it is almost impossible to calculate theoretical probability of "crooked" dice, students at Oxford, in 2006, tried a large scale simulation of tossing a rectangular cuboid die to obtain statistical data.

In this visualization, I want to simulate, by using Flash version of physics engine jiglib,  a process of rolling 20 cuboid dice at a time. From some experimental simulations, I found 1)physics engine does not work symmetrically (due to rounding error ?) and 2)Interaction effects between dice are not negligible.(a die often fells another)

So I made a flash object with the same setting as this visualization and embedded it in the sidebar of my blog. While visitors were reading, the embedded flash object sent to my server results of rolling diverse kinds of cuboid dice. Obtained distribution is like this:
As a result, in this presentation, I use a following formula(x:height and y:width are relative to z:depth ):
p(x,y) = 10(x-0.35)(y-0.35)/8(x2+y2+1) , 0.25 < x,y < 2.5

Data

API: Asian or Pacific Islanders
AI/AN: American Indian or Alaska Native

Adjusted by age, gender, age-gender interactions, and All Patient Refined-Diagnosis Related Group (APR-DRG) risk of mortality score. When reporting is by age, the adjustment is by gender and APR-DRG risk of mortality score; when reporting is by gender, the adjustment is by age and APR-DRG risk of mortality score.

Source

Credit

author: Isao Matsunami(Twitter)
tools : Adobe CS5, Papervision3d, jiglibflash(physics engine)