Bayes’ theorem

  By admin | September 26, 2011 - 9:54 am | Management Leave a comment

In probability theory and applications, Bayes’ theorem (alternatively Bayes’ law or Bayes’ decision rule) links a conditional probability to its inverse. That is, it provides the relationship between P(A | B) and P(B | A). It is valid in all common interpretations of probability, and is commonly used in science and engineering.[1] The theorem is named for Thomas Bayes (pronounced /ˈbeɪz/ or “bays”).

To illustrate, suppose J. Doe is a randomly chosen American who was alive on January 1, 2000. According to the United States Center for Disease Control, roughly 2.4 million of the 275 million Americans alive on that date died during the 2000 calendar year. Among the approximately 16.6 million senior citizens (age 75 or greater) about 1.36 million died. The unconditional probability of the hypothesis that our J. Doe died during 2000, H, is just the population-wide mortality rate P(H) = 2.4M/275M = 0.00873. To find the probability of J. Doe’s death conditional on the information, E, that he or she was a senior citizen, we divide the probability that he or she was a senior who died, P(H & E) = 1.36M/275M = 0.00495, by the probability that he or she was a senior citizen, P(E) = 16.6M/275M = 0.06036. Thus, the probability of J. Doe’s death given that he or she was a senior is PE(H) = P(H & E)/P(E) = 0.00495/0.06036 = 0.082. Notice how the size of the total population factors out of this equation, so that PE(H) is just the proportion of seniors who died. One should contrast this quantity, which gives the mortality rate among senior citizens, with the “inverse” probability of E conditional on H, PH(E) = P(H & E)/P(H) = 0.00495/0.00873 = 0.57, which is the proportion of deaths in the total population that occurred among seniors.

Bayes' theorem
Here are some straightforward consequences of (1.1):

Probability. PE is a probability function.[2]
Logical Consequence. If E entails H, then PE(H) = 1.
Preservation of Certainties. If P(H) = 1, then PE(H) = 1.
Mixing. P(H) = P(E)PE(H) + P(~E)P~E(H).[3]

The most important fact about conditional probabilities is undoubtedly Bayes’ Theorem, whose significance was first appreciated by the British cleric Thomas Bayes in his posthumously published masterwork, “An Essay Toward Solving a Problem in the Doctrine of Chances” (Bayes 1764). Bayes’ Theorem relates the “direct” probability of a hypothesis conditional on a given body of data, PE(H), to the “inverse” probability of the data conditional on the hypothesis, PH(E).

(1.2) Bayes’ Theorem.
PE(H) = [P(H)/P(E)] PH(E)

In an unfortunate, but now unavoidable, choice of terminology, statisticians refer to the inverse probability PH(E) as the “likelihood” of H on E. It expresses the degree to which the hypothesis predicts the data given the background information codified in the probability P.

Begin by having a look at the theorem, displayed below. Then we’ll look at the notation and terminology involved.

In this formula, T stands for a theory or hypothesis that we are interested in testing, and E represents a new piece of evidence that seems to confirm or disconfirm the theory. For any proposition S, we will use P(S) to stand for our degree of belief, or “subjective probability,” that S is true. In particular, P(T) represents our best estimate of the probability of the theory we are considering, prior to consideration of the new piece of evidence. It is known as the prior probability of T.

Bayes’ Theorem, sometimes called the Inverse Probability Law, is an example of what we call statistical inference. It is very powerful. In many situations, people make bad intuitive guesses about probabilities, when they could do much better if they understood Bayes’ Theorem.
Recall that the definition of conditional probability is:
[1] P(B|A) = P(A and B)/P(A)
Bayes’ Theorem is used to solve for the inverse conditional probability, P(A|B). By definition,
[2] P(A|B) = P(A and B)/P(B)
Solving [1] for P(A and B) and substituting into [2] gives Bayes’ Theorem:
P(A|B) = [P(B|A)][P(A)]/P(B)

We can use Bayes’ Theorem to find the conditional probability of event A given the conditional probability of event B and the unconditional probabilities of events A and B.

For example, we said that Bernie Williams is a .400 hitter with a runner in scoring position. In other words, P(B|A) = 0.4. We also said that the unconditional probability of Bernie Williams coming up with a runner in scoring position is 0.2, and that the unconditional probability of Bernie Williams getting a hit is 0.3.

Therefore, if you are given the information that Bernie Williams got a hit, you can infer something about the probability that there was a runner in scoring position. Using Bayes’ Theorem,
P(A|B) = [P(B|A)][P(A)]/P(B) = [0.4][0.2]/[0.3] = .267

What this says is that when we are given the information that Bernie Williams got a hit, we should estimate the probability that he came up with a runner in scoring position as .267, which is higher than the unconditional probability of 0.2 that he will come up with a runner in scoring position.

The importance of accurate data in quantitative modeling is central to the subject raised in the question: using Bayes’s theorem to calculate the probability of the existence of God. Scientific discussion of religion is a popular topic at present, with three new books arguing against theism and one, University of Oxford professor Richard Dawkins’s book The God Delusion, arguing specifically against the use of Bayes’s theorem for assigning a probability to God’s existence. (A Google news search for “Dawkins” turns up 1,890 news items at the time of this writing.) Arguments employing Bayes’s theorem calculate the probability of God given our experiences in the world (the existence of evil, religious experiences, etc.) and assign numbers to the likelihood of these facts given existence or nonexistence of God, as well as to the prior belief of God’s existence–the probability we would assign to the existence of God if we had no data from our experiences. Dawkins’s argument is not with the veracity of Bayes’s theorem itself, whose proof is direct and unassailable, but rather with the lack of data to put into this formula by those employing it to argue for the existence of God. The equation is perfectly accurate, but the numbers inserted are, to quote Dawkins, “not measured quantities but & personal judgments, turned into numbers for the sake of the exercise.”

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How to Develop Market For New Handbags Cleaning Store

  By admin | September 19, 2011 - 4:42 pm | Marketing Leave a comment

There are so many people always ask How To develop Market For New Handbags Cleaning Store. Yes, Their Store is a new one, They have no enough Sources to help themselves. Because they are cleaning Louis Vuitton Neverfull PM They have to depend on themselves. Then How to do that, Here are 3 tips to help you.

1 indication support agreements along with clients. In order to assure clients the actual high-end custom totes in order to dried out cleansing store, store earlier within the payment system could be set up with the putting your signature on associated with support agreements methods to earn clients’ believe in, in order to promote the first client bottom.

two. To make sure high quality associated with support. Custom totes are extremely costly, the actual cleansing procedure when there is defaced, the bigger the quantity of payment. Therefore at first should be produced by on their own or even personally experienced doctor, rigid manage from the cleansing procedure, the actual business associated with thorough procedures. Big purchases following dried out cleansing personnel accountable for recruitment, however should undergo thorough instruction in order to articles.

3 string could be created. As soon as this sort of expert cleansing look for prosperous improvement associated with string procedure, therefore the begin is essential to determine regular methods, through each and every fine detail from the requirements to make sure higher support high quality as well as balance.

Those above are all the Tips i want to Get for you to clean. I think it would help you if you want to run a new handabgs cleaning store

Life-career Rainbow

  By admin | September 19, 2011 - 2:09 pm | Management Leave a comment

Career-development theorists tend to ignore one of the most basic facts of life—that while people are busy making a living, they are living a life. The result is that many theorists describe career development as if it occured in isolation from human development. Isolating life roles creates a false scenario that does not reflect life as people live it. Career interventions emanating from false scenarios have limited usefulness as clients leave career counseling and attempt to implement their work-related decisions within a complex web of life-role activities. When career counselors ignore their clients’ multiple life-role activities, they also ignore the fact that life roles can interact in ways that are supportive, supplementary, complementary, or conflicting. Life roles can enrich life or overburden it.

Donald Super noted that for each person, the social elements that constitute a life are arranged in a pattern of core and peripheral roles. This pattern is defined as the life structure. The life structure organizes and channels the person’s engagement in society. To understand an individual’s career, it is important to know and appreciate the web of life roles that embeds that individual and her or his career concerns.

Understanding the Model:
Life-career Rainbow
The Life Career Rainbow (see figure 1 below) helps us think about the different roles we play at different times in our life.

“Life Roles” are represented by the colored bands of the rainbow, shown in the diagram below. Age is shown by the numbers around the edge of the rainbow. And the amount of time typically taken with each life role is described by the size of the dots in that colored band of the rainbow.

Career Development & Counseling Services – Dr Ed Colozzi

Mind Tools article – Using the Life Career Rainbow.pdf Mind Tools article – Using the Life Career Rainbow.pdf, 667 KB

Lee Iacocca

  By admin | September 7, 2011 - 9:35 am | Celebrity Leave a comment

Lido Anthony “Lee” Iacocca (play /ˌaɪ.əˈkoʊkə/ eye-ə-koh-kə; born October 15, 1924) is an American businessman known for engineering the Mustang, the unsuccessful Ford Pinto, being fired from Ford Motor Company, and his revival of the Chrysler Corporation in the 1980s.[1] He served as President and CEO from 1978 and additionally as chairman from 1979, until his retirement at the end of 1992.

One of the most famous business people in the world, Iacocca was a passionate advocate of U.S. business exports during the 1980s. He is the author (or co-author) of several books, including Iacocca: An Autobiography (with William Novak), and Where Have All the Leaders Gone?

(born Oct. 15, 1924, Allentown, Pa., U.S.) U.S. automobile executive. He was hired as an engineer by Ford Motor Co. but soon moved to its sales department and was noted for his successful promotion of the sporty yet inexpensive Mustang. He rose rapidly, becoming president of Ford in 1970. His brash manner led to his dismissal by Henry Ford II in 1978. A year later he was hired by the nearly bankrupt Chrysler Corp. He persuaded Congress to lend Chrysler $1.5 billion in 1980 and carried out layoffs, wage cuts, and plant closings to make the company more efficient. He also shifted the company’s emphasis to more fuel-efficient cars and embarked on an aggressive advertising campaign. Within a few years Chrysler was showing record profits, and Iacocca was a national celebrity with a best-selling autobiography, Iacocca (1984). He retired in 1992.

Lee Iacocca was born October 12, 1924 in Allentown , Pennsylvania . He became an American industrialist and is one of the most well known businessman worldwide. Iacocca is the former chairman of Chrysler Corporation and he also became a passionate advocate of U.S. business exports during the 1980s.

After graduating from Leigh University with an industrial engineering degree he was hired by Ford Motor Company and began his career as an engineer. Unhappy as an engineer he changed over to the sales force at Ford and quickly moved up the ladder to product development.

While in product development Iacocca successfully developed many automobiles at Ford, including the Ford Mustang. Ultimately, he became the president of Ford Motor Company but his shaky relationship with Henry Ford II forced him out of the company.

Iacocca was not without a job long as the Chrysler Corporation was in desperate need and going out of business. However, Iacocca rebuilt Chrysler from the ground up, laid off many employees, and sold the plant in Europe . Despite these moves the company was still in dire straights, so Iacocca made an amazing move by asking Congress for a loan. To the surprise to all, he received it.

After receiving the loan, Chrysler released the Dodge Aires and Plymouth Reliant automobiles, which were inexpensive and great on fuel economy since the United States was just coming out of an oil shortage. Then Chrysler came out with the minivan, which till this day is still the leader in minivan sales. Iacocca was also responsible for the acquisition of AMC in 1987, which brought over the money making Jeep division. He eventually stepped down from Chrysler in 1992 and currently works with a company designing electric bikes.

Early life

Lido Anthony Iacocca was born October 15, 1924, in Allentown, Pennsylvania, the son of Italian immigrants Nicola and Antoinette. Iacocca grew up in comfortable surroundings learning the nuts and bolts of business from his father who worked as a cobbler, hot dog restaurant owner and a theater owner. Nicola was a businessman who taught his son about the responsibilities of money and the need for a strong drive and a great vision in order to build a thriving business. Nicola also ran one of the first car rental agencies in the country and passed on his love of the automobile to his son.

Iaccoca’s enlistment in the military during World War II (19139–45) was denied because of his childhood battle with rheumatic fever, a terrible disease that can cause permanent damage to the heart. He earned an undergraduate degree in engineering from Lehigh University and later earned a master’s degree from Princeton University. Even as a teenager, Iacocca decided that he was going to be an automobile company executive and focused his studies in that direction. He secured a much sought-after engineering trainee job at Ford Motor Company in 1946, but put off his start until he completed his master’s degree at Princeton.

At Ford Motor Company

Joining Ford as an engineering trainee in 1946, Iacocca soon entered the fast pace of sales. In 1960, at age thirty-six, he sped into the vice presidency and general managership of the company’s most important unit, Ford Division. In 1964, with others on his staff, he launched the Ford Mustang, which, thanks to brilliant styling and marketing, introduced a new wave of sports cars, set a first-year sales record for any model, gave its name to a generation, and landed its creator’s picture on the covers of Time and Newsweek.

In 1960 Iacocca was named Ford’s vice president of the car and truck group; in 1967, executive vice president; and in 1970, president. Pocketing an annual salary and bonus of $977,000, the flashy executive also earned a reputation as one of the greatest salesmen in U.S. history. Of Iacocca, it has been said that he was always selling, whether products, ideas—or himself.

From Ford to Chrysler

Iacocca was let go from Ford Motor Company in June 1978 by Chairman Henry Ford II for reasons Ford never revealed. Though bitter at being dismissed from Ford, Iacocca was not out of the car business for long. Five months after his dismissal, Iacocca was named president of Chrysler (becoming chairman in 1979) and began transforming the number three automaker from a sluggish moneymaker into a highly profitable business.

How was Chrysler turned around? By downsizing (to make smaller) expenses to a much lower break-even point; by winning approval of $1.5 billion in federal loan guarantees; by selling off profitable units such as the tank division; and by introducing timely products. In addition, Chrysler welcomed, for the first time in U.S. corporate history, a union president to a board of directors. In 1984 the company posted profits of $2.4 billion (higher than in the previous sixty years combined), and in 1985 it bought Gulf-stream Aerospace Corporation for $637 million and E. F. Hutton Credit Corporation for $125 million.

In the early 1980s Chrysler issued the K-car and what would later become its best seller—the minivan. Just as the Mustang reestablished the sports car for Ford, the minivan would be loved by the young family in need of room and efficiency and revitalize Chrysler. In 1983 Chrysler paid the government back its loans and Iacocca became a star, a symbol of success and the achievement of the American dream.

Along with spearheading Chrysler’s rise, Iacocca took leadership roles in many noteworthy causes, most notably the chairmanship of the President’s Statue of Liberty-Ellis Island Centennial Commission, which was set up to raise funds for and to oversee restoration of the two monuments in New York City. While Iacocca gained a worldwide reputation through business leadership, television commercials, and association with the Statue of Liberty, he gained much additional exposure through his 1984 autobiography (a book written by someone about their life). Iacocca: An Autobiography, the best-selling nonfiction hardcover book in history, had two million copies in print by July 1985.

Folk hero

By the mid-1980s Iacocca had achieved folk-hero status. The Saturday Evening Post described him as “the sex symbol of America” and Reader’s Digest as “the living embodiment of the American dream.” Talk of Iacocca-for-president became increasingly widespread, and a 1985 poll of 1988 presidential preferences showed that the cocky industrialist trailed Vice President George Bush (1924–) by only three percentage points (41 to 38 points).

The late 1980s and early 1990s were not as kind to Iacocca. His public image, like Chrysler’s earnings, began to fall. At a time when the American people, in the grip of a recession (a temporary slowing of the economy), criticized the huge paychecks of executives whose companies were hurting, Iacocca who had once achieved a publicity coup (takeover) when, for a time, he only accepted one dollar a year from Chrysler, was paid a 1987 salary of $18 million. In addition, Iacocca, criticized Japanese trading practices, blaming them for the ills that American car manufacturers had suffered. Critics stated that the American public believed that Japanese cars were superior

With the fuel crisis of the 1970s, Americans were looking for automobiles that were more fuel efficient and inexpensive than previous models. As a result, Iacocca introduced small compact cars from Chrysler that the American public embraced. These small models, along with the minivan, were ideas that had been rejected by Ford. The smaller Chrysler models were a hit and the minivan became the essential family vehicle as soon as it was introduced only a few years later.

Iacocca eventually left Chrysler in 1993, but not before acquiring AMC, the parent company of the Jeep brand. The Jeep Grand Cherokee had been in Lee Iacocca’s sights for a long time and he helped Chrysler acquire the rights prior to his departure.

Besides contributing to the American automotive industry, Lee Iacocca also wrote a series of books detailing his life and work. He has also been a long-time supporter of diabetes research ever since his first wife, Mary McCleary, died of complications from diabetes in 1983. Although he has officially retired from Chrysler, Iacocca continues to write and speak on behalf of the company and contributes to websites and editorials concerning politics and the state of America.

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Pyramid Principles

  By admin | August 23, 2011 - 8:54 am | Management Leave a comment

Barbara Minto’s Pyramid Principle is a hierarchically structured thinking and communication technique that can be used to precede good structured writing. The Minto Pyramid Principle assumes that you already know how to write good sentences and paragraphs. It concentrates instead on the thinking process that should precede the writing.

She presents ‘rules’ for structuring any piece of writing:

  1. Ideas at any level in the pyramid must always be summaries of the ideas grouped below them.
  2. Ideas in each grouping must always be the same kind of idea.
  3. Ideas in each grouping must always be logically ordered.

Reader Reveiws From Amazon.com

It is VERY slow going, but you *do* get the impression that this is an important skill to have. The tips are good, and the examples are easy to comprehend. I dont think they should wait until you’re in business to learn this. They should teach the Principle in highschool!… if you could stay awake long enough to learn it.

Like one reviewer said, “the book on structuring documents is not well structured”. I was trying to create a presentation on this book. After I summarized all the chapters in a PowerPoint, I could hardly connect one chapter to the other sequentially. This book needs a makeover.