Bayes' theorem

Modigliani and Miller (1958) provided a new theory of capital structure, suggesting that a firm’s choice between debt and equity has no impact on the firm’s value. This became known as irrelevance theorem. However, this theory is surrounded by a number of assumptions that can be analyzed in turn. The first assumption from Modigliani and Miller (1958) is that firms operate within a perfect capital market. The perfect capital market is defined by Fabozzi, Neave and Zhou (2012, p 87). Firstly,…

Joint Probability of Non-Independent Events For the joint probability of non-independent events A and B, we need to use a conditional probability. For P(Zargon-AND-Abduct), we cab use P(Zargon|Abduct) or P(Abduct|Zargon). P(Zargon) x P(Abduct|Zargon) = 8 /20 x 3 /8 = 24/160 = 3 /20 P(Abduct) x P(Zargon|Abduct) = 6 /20 x 3 /6 = 18/120 = 3 /20 Here is a different problem. The UFOs are invading, and the military shoots two special UFO missiles. The missiles blow up two of the UFOs. What is…

conditional probability representation. In additional, truth tables and probability are today uses. Bayes Theorem is the final concept in statistics, which is defined as the description of the probability of events based on related conditions. Thomas Bayes developed P (A|B) = P (B|A) (P (A) / P (B) where Pierre-Simon Laplace further the Bayes theorem formula and Sir Harold Jeffreys defined the Bayes Theorem as the theory probability. There are no early uses and is used for probability, odds,…

In his book, “The Signal and the Noise,” Nate Silver discusses many statistical and analytic techniques as they relate to everyday events and phenomenon. For instance Silver writes about topics such as baseball, weather predictions, climate change, the stock market and terrorism to name a few. In each chapter he addresses the issues at hand and describes how statistical analysis can be employed to make the topic easy to understand and often predict certain outcomes. The book is very enjoyable…

whatever other element [13]. The Naive Bayes calculation depends on conditional probabilities. It uses Bayes' hypothesis, a recipe that ascertains a probability by numbering the frequency of qualities and blends of qualities in the recorded data. Bayes' Theorem finds the probability of an event happening given the probability of another event that has as of now happened. In the event that B speaks to the needy event and A speaks to the earlier event, Bayes' hypothesis can be expressed as follows…

In the book “the Signal and the noise”, author Nate Silver talks about prediction from many different angles. Silver explains how prediction is a part of our everyday life and how it affects us. From math to history, inside of a class room or on a court/field, prediction is something we deal with on a day to day basis unconsciously. Silver talks about the benefits of failure and how failure is helpful in the long run with making predictions. Throughout the years we have made progress with…

"base rate" and underweight the new information that based on evidence when compared to Bayesian belief-revision. The change in the individual opinions occurs orderly but very slow and insufficient in its amount according to Bayes' theorem. In other meaning, when Bayes' theorem is used, the individual may update his/her prior beliefs when the evidence available, but this update is very slow. However, the evidence here may be as the "noise" for the judgment. The disadvantage of conservatism is…

Science, one of the most influential subject, has made enormous impacts in Europe during the seventeenth century. Before the seventeenth century, Europe has made minimal progress in science related advancement. On the other hand, the Asian countries have made progress in scientific advancements until the Europeans rise (Goldstone 136). For example, the Chinese developed gun powder, compass, and printing press (Strasser “The Scientific Revolution”). In the seventeenth century, the century which…

The Signal and the Noise by Nate Silver is about making an assessment based on future outcomes. Prediction is indispensable to our everyday lives. The biggest problem with predicting about the future is even though you are forecasting the future the data it is based off is usually from the past. Just because you are able predict the past doesn’t mean you are able to predict the future. Silver demonstrates in this book how many prediction practices have been flawed and suggest ways that might…

What is a Theory from Carnap and Popper Rudolf Carnap and Karl Popper both are philosophers whom tried to question what is a theory. Both of these men look at the same question from different perspectives. How can one decide if a theory is scientific or not. Carnap and Popper both came up with different ways to choose which theories are more important when compared to others. It is definitely possible to agree with both Carnap and Popper’s ways of demarcation as a theory can be both verifiable…