Bayesian statistics for business use

Bayesian statistics are being used in business in conjunction with the spread of the Internet.
On the Internet, customers' purchasing and search behavior histories are automatically collected, and Bayesian statistics are overwhelmingly superior to traditional statistics in estimating customer "types" from them.


Currently, many Internet companies are actually using Bayesian statistics.
Among them, Microsoft is famous for using Bayesian statistics in business from early on.
Bayesian statistics have also been introduced to the help function of the Windows OS, and software has also been developed that prioritizes promising guidelines when a user searches for, for example, "child illness symptoms" on the web.


In 1996, former Microsoft CEO Bill Gates announced in a newspaper that his company's competitive advantage was due to Bayesian statistics.
Meanwhile, Google is also known to have utilized Bayesian statistics technology in its search engine's automatic translation system.
Therefore, anyone engaged in business in this century will be at the forefront if they master Bayesian statistics.
This book contains case studies and commentary that will be helpful for business people to use in their daily lives.

Bayesian statistics techniques are being applied in various fields other than IT companies.
For example, in fax machines, Bayesian statistics are used to correct noise in the transmitted image to make it closer to the original image.
Bayesian statistics are also being used in the medical field, such as in ‘automatic diagnosis systems.’
As you will discover as you read this book, the strengths of Bayesian statistics lie in its ability to "make guesses with minimal data, and become more accurate with more data," and its ability to "automatically update guesses in real time in response to incoming information."
Through this, everyone will agree that Bayesian statistics is optimal for cutting-edge business.
--- p.009

It's called 'Bayesian update'.
If we change 'renewal' into the word we commonly use, it is 'update'.
In this book, the above process is called ‘Bayesian estimation’.
Bayesian estimation can be summarized as 'updating the prior probability to the posterior probability based on the observation (information) of the action.'
In this book, estimation in individual cases is called 'Bayesian estimation', and the entire set of such estimation methods is called 'Bayesian statistics'.
--- p.031

In an article I wrote for an entertainment magazine about Bayesian estimation, I used the results of a questionnaire survey.
We asked the editor in advance to conduct a survey on working women's Valentine's Day behavior.
What I wanted to know was, 'What is the probability that women give chocolate to men they like and men they don't like?'
The editor reported on a simple survey conducted on an Internet questionnaire bulletin board targeting working women, offering the options of '0%, 50%, 100%'.
When they processed it statistically, it was found that on average, they gave chocolate to someone they were 'sincere' about 42.5% of the time, and to someone they were 'not' about 22% of the time.
It was surprising that the probability of giving chocolate to someone you truly care about is less than 50%, but the fact that the probability of giving chocolate to someone you don't really care about is as high as 22% made me realize the greatness of the 'habit of giving chocolate out of courtesy'.
--- p.050

At that time, I took out a ball from the jar in front of me and it was black.
This black ball becomes the 'evidence' for the conjecture.
So, from this evidence, can we determine whether this complex is A or B? This is a fairly simple deduction; anyone could conclude that it's B.
The reasoning behind this is obvious enough that it doesn't need any explanation, but to clearly understand 'what is inference', let's describe the inference process in detail.
--- p.077

As we have seen, Bayesian estimation has the advantage of being able to make estimates 'once' in any environment, as there is no significance level setting like in the hypothesis test of Neyman-Pearson statistics.
Unlike the Neyman-Pearson method, it does not make a decision on either A or B, but rather leaves open the possibility of both and presents the ratio of the possibilities.
The job of looking at numbers and making judgments is left to the statistician.
That's why Bayesian estimation is sometimes called the 'president's probability'.
This means that Bayesian estimation is left to the employees, and it is up to the CEO to make a judgment based on the reported figures.
--- p.093

Bayesian estimation is not that new; it simply uses well-known probability formulas (those that high school students learn).
However, in the sense that subjectivity is attached to the prior probability being used, it can be said to be a theory on the borderline between mathematics and philosophy.
As evidence, using Bayesian estimation in special settings produces results that run counter to our common sense.
It may seem like a paradox.
In this lecture, we will introduce two paradoxes related to Bayesian estimation, and hope that through them you will gain a sense of Bayesian estimation from a different perspective than usual.
--- p.106

First, let's set the dictionary type as before, get one piece of information, and then calculate the posterior probability.
Here, we will explain it in the form of 'the computer functionally determines whether the email you received is spam or not', rather than 'the computer functionally determines whether the email you received is spam or not'.
First, before scanning the incoming mail, the computer assigns a prior probability to each type of mail, such as 'whether the mail is spam or regular mail.'
Here, let's apply the 'principle of insufficient reason' and assign 0.5 to each side.
This means that the filter evaluates the incoming mail as '0.5 chance that it is spam, and 0.5 chance that it is regular mail'.
At this time, if there is a probability known to be more credible than this, it is okay to set it as the prior probability.

--- p.133