Hello (New World!), 

My name is Edwin, I’m a 22 year-old French student in applied mathematics. In particular, I study probability, statistics and risk theory. We learn interesting things but there is still one question I feel stupid about: Is statistics, actually, useful? I mean not theoretically but in the real life. Many friends of mine asked me this, and I vainly struggle in answering with understandable and cogent examples. I can’t get rid of the stereotypes such as the over optimistic forecasts of GDP gross given by government neither of the very easy statistics which are about collecting data rather than proper data analyses.


Because, mathematics should never be like that... (source:http://lovestats.wordpress.com/dman/)

This question is the reason of this blog, I would like to explain by examples how statistics and probability could offer a useful perception of our environment. Indeed, according to the Oxford Dictionary, perception is the ability to see, hear, or become aware of something through the senses, or in a second meaning, the way in which something is regarded, understood, or interpreted. This is how probability and statistics are useful. They give a perception of our environment, which might be wrong, as well as our sight can suffer from an optical illusion, but the perception may help us to understand and become aware of phenomena of our environment.

To answer “the” question I will try to use examples as easy as possible so that not only the conclusions but also the process are understandable. As you will certainly see, I like sport, finance and risk issues, and I will use many examples from these areas to answer the question. I will use the software R to illustrate the different topics. Although, I’m not a great programmer, feel free to use my programs if you think they could be useful.  They are certainly not as efficient as possible and, again, feel free to comment any of my programs if you have any ideas to improve the program or the method.

Finally, before blogging for the first time in my life, I’d like to thank all the people who settle in my mind the unfathomable question of the utility of statistics. In particular Claire, Justine, Arthur, Clement and Rudy (even though the three last ones certainly know better than I do how useful is statistics) for the countless, long and unfinished delicious discussions we had about statistics and probability. Claude for his unconditional but fair question: “You like mathematics, but what kind of work can you do with mathematics?” and many other people, who, I am sure will recognize they have left their print on this blog.

Edwin.
Posted by
Location: University of Cambridge, Cambridge, UK
Labels: blog introduction
0

Add a comment

The financial market is not only made of stock options. Other financial products enable market actors to target specific aims. For example, an oil buyer like a flight company may want to cover the risk of increase in the price of oil. In this case it is possible to buy on the financial market what is known as a "Call" or a "Call Option".

A Call Option is a contract between two counterparties (the flight company and a financial actor). The buyer of the Call has the opportunity but not the obligation to buy a certain  quantity of a certain product (called the underlying) at a certain date (the maturity) for a certain price (the strike).

I found a golden website. The blog of Esteban Moro. He uses R to work on networks. In particular he has done a really nice code to make some great videos of networks. This post is purely a copy of his code. I just changed a few arguments to change colors and to do my own network.

To create the network, I used the  Barabási-Albert algorithm that you can find at the end of the post on the different algorithms for networks. Igraph is the library which has been used.
3

As you have certainly seen now, I like working on artificial neural networks. I have written a few posts about models with neural networks (Models to generate networks, Want to win to Guess Who and Study of spatial segregation).

Unfortunately, I missed so far a nice and pleasant aspect of networks : its graphical approach. Indeed, plots of neural networks are often really nice and really useful to understand the network.

Sometimes such a graph can point out some characteristics of the network.
1

I already talked about networks a few times in this blog. In particular, I had this approach to explain spatial segregation in a city or to solve the Guess Who? problem. However, one of the question is how to generate a good network. Indeed, I aim to study strategy to split a network, but I need first to work with a realistic neural network. I could have downloaded data of a network, but I'd rather study the different models proposed to generate neural networks.

The function apply() is certainly one of the most useful function. I was scared of it during a while and refused to use it. But it makes the code so much faster to write and so efficient that we can't afford not using it. If you are like me, that you refuse to use apply because it is scary, read the following lines, it will help you. You want to know how to use apply() in general, with a home-made function or with several parameters ? Then, go to see the following examples.
1

Have you ever played the board game "Guess who?". For those who have not experienced childhood (because it might be the only reason to ignore this board game), this is a game consisting in trying to guess who the opponent player is thinking of among a list of characters - we will call the one he chooses the "chosen character". These characters have several characteristics such as gender, having brown hair or wearing glasses.

If you want to choose randomly your next holidays destination, you are likely to process in a way which is certainly biased. Especially if you choose randomly the latitude and the longitude. A bit like they do in this lovely advertising (For those of you who do not speak French, this is about a couple who have won the national gamble prize and have to decide their next travel. The husband randomly picks Australia and the wife is complaining : "Not again!").
4

My previous post is about a method to simulate a Brownian motion. A friend of mine emailed me yesterday to tell me that this is useless if we do not know how to simulate a normally distributed variable.

My first remark is: use the rnorm() function if the quality of your simulation is not too important (Later, I'll try to explain you why the R "default random generation" functions are not perfect). However, it may be fun to generate a normal distribution from a simple uniform distribution.

The Brownian motion is certainly the most famous stochastic process (a random variable evolving in the time). It has been the first way to model a stock option price (Louis Bachelier's thesis in 1900).

The reason why is easy to understand, a Brownian motion is graphically very similar to the historical price of a stock option.
1

The merge of two insurance companies enables to curb the probability of ruin by sharing the risk and the capital of the two companies.

For example, we can consider two insurance companies, A and B. A is a well known insurance company with a big capital and is dealing with a risk with a low variance. We will assume that the global risk of all its customers follow a chi-square distribution with one degree of freedom.
Blog Archive
Blog Archive
Translate
Translate
Loading