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We know (this is the prior belief ) that by the age of 40, 1% of women will have breast cancer (p(A)) We also have a good test (this is the new evidence) for the presence of breast cancer mammography Eighty percent of women with breast cancer will get positive mammographies (p(X |A), correct hits), while only 96% of women without breast cancer will get positive mammographies (p(X | A), false positives) This is the likelihood that the evidence will be obtained given that our belief is true From these gures it seems obvious that routine screening for breast cancer should be a good thing.

Webmail No discussion about e mail is complete without something on Webmail. Since Hotmail went online with free e mail accounts, the face of the public e mail for consumers has never looked the same. So what is behind a Webmail server Really a Webmail system is just a Web server and an e mail server combined with some executable code in the middle. It doesn't really matter which of the POP or IMAP servers is used to retrieve mail messages down the back. Some even just use the old style UNIX convention and grab the mail directly from the spool directory. Tip Setting up your own personal Webmail system is a trivial task if you have access to your own mail or Web server. Go to Freshmeat (http://www.freshmeat.net/) and search for Webmail. At least 10 different Open Source efforts are available from that one site alone.

So, if all women are screened, then what proportion of those with positive test results will actually have cancer: expressed mathematically as p(A|X) Given that the cancer test seems to be a good one, what would you believe about a woman who had just tested positive for breast cancer Most people believe it is highly likely that she has cancer Application of Bayes theorem shows that this assumption is wrong We can see this very easily if we forget about probabilities Instead, let s consider a group of 10,000 women Before screening, the 10,000 women can be divided into two groups:.

ALSPAC and NSHD provide approved researchers with special datasets for each research project, each of which is kept separate and must be destroyed when the project is completed Other surveys use a combination of approaches depending on the sensitivity of the data being used For example, ELSA provides access to core data through ESDS, but imposes stringent controls on analysis, which involves geographical identifiers (producing special reduced datasets for that purpose), and insists that researchers work in a recognised safe setting when using administrative or highly sensitive data..

erger arbitrageurs make money by writing insurance against failed merger attempts. When a merger is announced, the target s stock price typically appreciates by 20% or more. Yet even with the substantial price increase, the target s stock usually trades at a 1% to 3% discount to the price offered by the acquiring company. The reason for the discount is that there is a nonnegligible probability that the announced merger will fail to be consummated. There are many reasons why a merger might be called off. Government regulators charged with preventing monopolies might determine that the merger would adversely affect competition, and they might le a lawsuit to block the merger. Industry conditions might change, altering the economics of the business combination and causing the target or acquirer to cancel the deal. Shareholders, concerned that the merger is not in their best interest, might vote against the merger. Whatever the reason for aborting the deal, the effect on the target s stock price is usually the same a signi cant decrease, usually on the

one goal is the making of monetary pro ts, as immediately as feasible Needless to say, no such veto exists within ivory towers walls While the quants models must pass the no-nonsense money-seeking test, theorists are free to abstract away as much as they want In other words, while abstraction gets rewarded in academia, it is kept under check in the real world (that s not to say, of course, that banks and hedge funds do not employ unworldly theories, only that it is harder for analytical sobriety to rule unquestioned) In the real world, many times ubercomplex products are not priced directly from a mathematical model, even if one exists, but rather from the quoted market prices of much simpler instruments, with models being used simply as linkage mechanisms between the known and the unknown.