How to Make Good Guesses

An article written by Tim Harford describes the use of Bayes’ rule in order to make good and accurate guesses. Bayes’ rule describes the probability of an event, based on conditions that might be related to the event. There is an exact equation for Bayes’ rule and it is as follows:

P (A|B) = P (B|A) * P (A) / P (B)

Harford explains that when considering an event in which a guess or assumption can be drawn from it, you should take and combine any related information you have about the event. Considering all of this information, you will be more likely to make an accurate guess about the event that is occurring. He explains that psychologists have asserted that people do not make good guesses because they ignore some piece of obvious information altogether. Harford proposes the the information that gets ignored, usually a quantitative number, is the base rate and the effects of neglecting the base rate has been known since the 1950s.

He gives an example that asks him to guess what will happen the UK economy in 2016. Using his reasoning, one would suppose that there is a 10 percent change the UK economy will begin a recession this year. The logic behind this is in the fact that there have been seven recessions in the past 70 years. In this case, the base rate or ignored information is the 10 percent. Harford goes on to explain other ways this reasoning process can be applied. In particular, he talks about its usefulness in the field of screening programs such as DNA tests for potential criminals.

He concludes that it is extremely easy to jump to conclusions about probability. He emphasizes that it is important to take a step back and consider all of the information before you go and make a guess about something. He proposes that you should get in the habit of finding the base rate of any event and use the Bayesian way of thinking whenever you are trying to make a good guess.

ft.com/…/7d01cd92-da87-11e5-98fd-06d75973fe09

 

 

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Decline in Apple Watch Sales, explained by network effects

In this article, the author adopts network effects to explain the causes of decline in sales of Apple Watches.

“In an article by Jay Yarow, he adds a figure from the web that shows interest in the Apple Watch has dropped below that of the iPod. Furthermore, he states that’ People, like myself, have sold their watches. Other folks are find that life without the watch isn’t so bad.”- Cornell University, Networks, Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090

R(x) refers to the intrinsic interest of a consumer with an x reservation price while f(z) refers to the benefit of each consumer from having z fraction of the population using Apple Watch. R(x)f(z) refers to the function that shows consumers who are fond of the benefits offered from purchasing and using apple watches when the users’ population is at large. Therefore, essentially, the decline of apple watches purchases could be explained by people’s realization of apple watch’s useful purposes. Maybe people just don’t find apple watches that worthy to have money spent on, that’s why users’ population declines which causes low intrinsic interest on the product from the public.

https://blogs.cornell.edu/info2040/2015/11/20/network-effects-in-the-market-of-apple-watches/

Pagerank toolbar

We learnt about the essence of PageRank when it comes to wed-surfing. It is a system developed by Larry page and Sergey Brin and its basic idea is that: if a page is important, it will be cited by other important pages. This is the feature that google has within its google toolbar PageRank, it essentially determines what would show up in searching results.

In the second article, it mentions about how Google is planning on removing Toolbar PageRank. This means that individuals using tool or a browser that shows PageRank data from Google, will soon lose their privileges of doing so. Google’s decision, however, doesn’t take away page rank data internally within the ranking algorithm; which means that when people are searching for information on Google, they could still visit sites with high clicking rate, giving them high chance of locating their desirable information. It is just that the external PageRank values are being taken away.

 

Source :

https://websiteadvantage.com.au/Google-Toolbar-PageRank#heading-ToolResult

http://searchengineland.com/google-has-confirmed-they-are-removing-toolbar-pagerank-244230

 

Understanding opinions with Bayes’ Theorem

Understanding opinions with Bayes’ Theorem

Remember that one nasty math equation that was presented in class? Well, here is it again and how it is used in the case of people who are dead set on a certain opinion despite overwhelming evidence. You know, that one friend on social media that post article like “our sun is not a star”In this article, the idea behind Bayes’ Theorem is described as seeing how a set of “prior beliefs… change in the face of given evidence.” An example on a supposed cricket match used first to demonstrate. The question of whether a team is using a batting pitch’ or a ‘bowling pitch’ is asked. Given that ‘batting pitch’ has probability 0.61% while a ‘bowling pitch’ only has 0.11%, it can seem that a ‘batting pitch’ is in motion. But Baye’s Theorem says we can not jump to conclusion with out considering ‘prior beliefs’. Consider spectators R and S, where R believes both pitches are 50/50 , while S believes that a ‘bowling pitch’ has a probability of 90%. Both R and S observe the same round of the same match and use Baye’s Theorem, but end up with different probabilities on whether a batting or bowling pitch is in play. Despite the same observations (evidence), both spectators have different conclusions (opinion). Apply this to that one friend on social media, we can partially see why they are against evidence against their opinion. Their prior beliefs greatly influence their current belief. This friend’s opinion could have been the result of some information cascade (maybe they heard it from another friend on social media), so information superior to their current and previous information is needed if you wanted to change their opinion. Read the article below to get all the math details.

 

 

http://www.livemint.com/Consumer/dJyyhAwTsg4PXLSViUg6cJ/Using-Bayes-Theorem-to-understand-extreme-opinions.html

PageRank Algorithm Reveals Soccer Teams’ Strategies

The article I read is about a paper that analyzes football strategies using concepts from network theory to describe the team’s strategies. The article is called, “PageRank Algorithm Reveals Soccer Teams’ Strategies,” using information from a research paper called, “A network theory analysis of football strategies” by Javier Ĺopez Peña and Hugo Touchette.

The article was extremely interesting, because it showed a sports team in a completely different view. Most of the time you think about football you would never think of the team and their strategy as a network. The teams were broken down into terms we use in class, players are nodes in the network, and a pass establishes an edge between each player. The more passes a player receives the thicker the edge, and the more important that player is for the teams strategy. Here is an image from the article that shows the network for two football teams.

Other terms discussed were betweeness, clustering, PageRank which ranks the player on their popularity. The article and the paper go into more detail on the subject and the terms.

Even though this article is 4 years old, I think it is very interesting and helpful in understanding the content. Being able to see the information explained in a different way is a great way to understand the content and information I now can understand and apply the terms in multiple ways.

Here is the Article Page: https://www.technologyreview.com/s/428399/pagerank-algorithm-reveals-soccer-teams-strategies/
Here is the PDF for the research paper: http://arxiv.org/pdf/1206.6904v1.pdf

 

 

Bidding on Airwaves

This past week, the Federal Communications Commission announced that there will be an auction of low-frequency airwaves in the US. These airwaves have been given up by the large broadcast carries. In return, the bidders be bidding for the chance to improves their wireless networks. It is expected that a large amount of money will be exchanged for these airwaves.

In order for these new airwaves to be auctioned off, there will be a reverse auction to start. In this reverse auction, the federal government will be buying the airwaves from the broadcast companies. After the reverse auction is done, a new auction will occur for the airwaves. It is not stated in the article, but you can conclude that the auction will be a  sealed-bid auction. It is a sealed bid auction because the FCC will receive buds from all of the wireless network companies. we do not know if it is a 1st or 2nd price auction. There are over 100 wireless companies bidding for the airwaves. These companies include Verizon, AT&T, and T-Moblie, to name a few.

These “auction like” processes are very common around the US and the world. You see it a lot with construction contractors bidding to have a chance to build a structure for a company.

 

SOURCE: http://www.reuters.com/article/us-fcc-auction-idUSKCN0WV2DO 

Social Networking in Game of Thrones

Recently, a group of Mathematicians who also happen to be huge fans of the popular HBO show Game of Thrones created a Social Network map of the characters in order to determine who the main character of the first book actually is. This is an amazing example of how Social Networking can be applied to almost anything including your favorite television show. The social network shows each characters interaction and actually calculates its PageRank Value and displays all of the information in a great graph.

The article actually goes in depth showing all of the math involved in producing its conclusions. This is extremely interesting to me as a fan of the series and seeing how what we are learning can be applied to almost anything. According to all of the math “Spoiler Alert” Tyrion is the main character according to their algorithms.

 

Social Networks in Game of Thrones