The Wuhan coronavirus (2019-nCoV) is currently spreading throughout China and the world. As of Jan 25, 12am EST, there are 1,354 confirmed cases and 41 confirmed deaths throughout the world. While there are questions about whether these statistics are true or not, people are not appreciating the fact that these statistics are not like the other statistics they encounter, and this is because of the way data is collected.

*Let me demonstrate the difference, with two examples.*

Consider an election, which is not like a disease outbreak. You might want to know what proportion of voters support a certain presidential…

The idea of a black swan dates as far back as the time of the Roman poet Juvenal.

rara avis in terris nigroque simillima cygno — From The Satires, Line 6.165

Translation: A rare bird in these lands, very much like a black swan.

Historically, it was presumed that black swans did not exist. Thus, when Dutch explorers became the first Europeans to see a black swan, it was a big shock — something thought to be impossible suddenly became possible.

The idea was later generalized in a book series and became more commonly known. However, it is still not…

**Investing is a risky endeavour. Take a wrong step, and you could find your cash burned up. So how do you pick the right investments? Should you trust news? Should you trust the brokers? Should you do your own research? Or should you pay someone else to manage your investments?**

Among the more sophisticated investors are those who rely on techniques from mathematics and statistics. These people compare different investment options in terms of return and risk, in order to construct the optimal portfolio.

It’s obvious why people would want to maximise their returns. But why do people try to…

In my last post on insurance, I wanted to calculate a running mean (the mean from the beginning up to the current time t). This was for a time series with 1,000,000 time-steps. In order words, I had to calculate 1,000,000 means. How did I do this?

If you look inside any standard math textbook, you would find something like this.

Using this formula directly, you might then have an algorithm like this:

# X is a time-series with length T.

runningMean = [X[0]]for t in range(1,T):

runningMean.append(sum(X[0:t])/t)

But when you actually run it, the speed of the execution…

Introduction — A simple model of savings

Part I — The benefits of an insurance scheme

Part II — The law of large numbers

Part III — When insurance schemes fail

Appendix — Math for the simulation

**Inspired by Ole Peters (****lecture****) and Nassim Nicholas Taleb.**

This article strings together a surprising series of thoughts which I’ve had over the past year. Expected values, ensemble averages, time averages, empirical vs theoretical mean. Insurance, cooperation, sharing, culture, tradition, conservatism and politics. Risk, correlation, contagion and catastrophe. Portfolio diversification and market delusion. Survival, elimination, and evolution. …

Which genius decided on the rules for social distancing?

This is the official advice from the Australian government on public gatherings during this COVID-19 coronavirus outbreak.

I don’t know how long 1.5 metres is, and I don’t have a ruler on me. Neither do my neighbours, and who knows if the other people around me know the number of centimetres in a metre.

Imagine standing in a queue, and you are standing too close to the person in front. The police catch you, and now you find yourself being questioned and lectured about the importance of the public health measures.

…

**If you are reading this after 2020, please keep in mind that this post was written during the early stages of the COVID-19 pandemic, and hence, may not reflect a reality beyond this time.**

We are currently in February 2020. Over the past month, a deadly virus has been spreading throughout China and the world, sending the infected to the ICU and trapping others in their homes. As authorities try to manage this crisis, they face the challenging issue of containment — sending the infected to quarantine, while allowing the non-infected to go free.

Here is the scenario. You have…

When people teach you about statistical concepts, you usually get a equation which is a formula for some quantity, like the arithmetic mean. Formulas are fine, but they are designed with calculation in mind. Usually, the equation will put the unknown on one side, and all known quantities on the other.

Like this.

Unfortunately, this view does not help students develop a good understanding of concepts like the “average”. And as a result, it is not difficult to find people misapplying statistics, for example, using the arithmetic mean on financial returns data when the geometric mean makes more sense.

By…

**Update (Feb 10): **Some researchers have estimated the case-fatality rate. In my new post, I summarize their research and explain why it’s worse than it looks.

At the start of 2020, murmurs of a mysterious SARS-like coronavirus started to spread in the city of Wuhan, in Hubei, China. Soon enough, the world knew what was going on. This new type of virus, which was given various names such as Wuhan coronavirus, novel coronavirus and 2019-nCoV, brought back memories of the 2003 SARS outbreak which infected around 8000 people and killed 800 worldwide.

These viruses were similar in the way it…

Suppose that you are collecting a sample of ratings data, which can range from 1 to 10. Let’s say that your sample consists of 100 points, and consider two possible samples.

- 10 people give a rating of each possible value from 1 to 10.
- 50 people give a rating of 1, and 50 people give a rating of 10.

The first sample corresponds to a uniform distribution over all 10 possible values.

The second sample corresponds to a bimodal distribution at the extreme values 1 and 10.

Math, stats, data. Influenced by the complex systems perspective. I prefer to take the critical view.