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.

…

A doctor has 1 reliable diagnostic test. Two patients show up to the clinic.

- The patient has a dry cough and fever. A travel history reveals that the patient had returned four days ago from Milan, Italy.
- The patient has a runny nose, and reports having a mild cold over the past few days, which is mostly resolved. A travel history reveals that the patient had returned four days ago from San Francisco, US.

**Who should get the test?**

The doctor looks at the official criteria for determining who to test.

**OFFICIAL GUIDELINES**

If you want to know the severity of an outbreak, you should be careful not to naively look at the final figures of past outbreaks. These final figures are influenced by a variety of factors:

- Virus transmissibility (important)
- Virus lethality (important)
- Containment effectiveness (misleading)
- Healthcare quality and access (misleading)

It is important to account for the effect of human intervention when considering severity. Otherwise, a highly lethal and contagious virus, which is brilliantly contained at an early stage, would appear not severe at all.

A Feb 19 Bloomberg opinion piece, titled “The Economic Hit From Coronavirus Is All in Your…

**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…

*My previous post is highly related to this post:** Why the mortality rate of novel coronavirus is miscalculated, and not important.*

A new study just came out, and I’m sure it’s going to be published in the media soon.

It will state that the mortality rate of novel coronavirus is:

- 18% for severe cases.
- 1–5% for mild to severe cases.
- 1% in total.

On the surface, it looks reassuring for the general public. …

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…

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