I am actually doing a thesis on proving dependence between causes of mortality by using copula. I have to gather some more information about the effects of independence assumption that is usually used especially in Insurance Context.
Thanks
Statistical independence means that the observation of one of the variables does not change our belief about the other, and hence, the independent variables are mutually non-informative about one-another. This becomes more complicated when dealing with standard IID statistical models, since these are usually based on conditional independence rather than full independence.
An examination of statistical independence used in standard "IID" statistical models can be found in O'Neill (2009) Exchangeability, correlation and Bayes' effect. International Statistical Review 77(2), pp. 241-250. This paper might be useful for what you are studying.
http://onlinelibrary.wiley.com/doi/10.1111/j.1751-5823.2008.00059.x/abstract
I recall an issue of power outage in Alberta in the 1980's.
The electrical system with its transformers stretched hundreds of thousands of miles across the huge province.
There was an electrical outage due to a storm that cost millions of dollars to fix.
A few weeks later and perhaps 50 miles away, another station broke down, again with a repair cost in the millions. If the two events were independent, the insurance company would pay each cost minus a deductible of 0.5 million dollars so the total deductible would be 1 million dollars. If the two events were dependent, then the insurance company would have to pay the total cost minus a single deductible of 0.5 million dollars.
So the difference between dependence and independence is half a million dollars.
Unfortunately, I cannot document my distant memories.
Cause, effect and independence is now-a-days modelled with Bayesian networks. In this theory. There are many resources online that describes the basic ideas. Look for instance at http://www.eng.tau.ac.il/~bengal/BN.pdf
In statistics the concept of independence of variables, events is important. in many situations it is essential to assume that the sample observations are independent. i think in your study, you study the correlation or association between causes of mortality and use of copula instead of dependence.
To add another illustration, in DNA fragment mapping, an important part of inferring overlap is evaluating shared patterns of gel bands. An earlier statistical model (which assumed independence) was subsequently corrected by considering the conditional nature of the problem. It found that probabilities of the earlier model could be wrong by a couple of orders of magnitude. See:
https://en.wikipedia.org/wiki/Sulston_score
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