Mitchell Boggs on Game Theory in Behavioural Ecology – The Central Equilibrium – Episode 8

Mitchell Boggs kindly talked about game theory in behavioural ecology on my talk show, “The Central Equilibrium”!  He talked about 2 key examples:

  • when animals choose to share or fight for food
  • when parents choose to care for their offspring or seek new mates to produce more offspring

These examples illustrate why seemingly disadvantageous behaviours can persist or even dominate in the animal kingdom.

Mitch recommends a book called “Are We Smart Enough to Know How Smart Animals Are?” by Frans de Waal.

Thanks for being such a great guest, Mitchell!


David Veitch on Rational vs. Irrational Numbers and Countability – The Central Equilibrium – Episode 7

I am so grateful that David Veitch appeared on my talk show, “The Central Equilibrium“, to talk about rational vs. irrational numbers.  While defining irrational numbers, he proved that \sqrt{2} is an irrational number.  He then talked about the concept of bijections while defining countability, and he showed that rational numbers are countable.

David used to work as a bond trader for Bank of America.  He writes a personal blog, and you can follow him on Twitter (@daveveitch).  He recently earned admission into the Master of Science program in statistics at the University of Toronto, and he will begin that program soon.  Congratulations, David!  Thanks for being a guest on my show!

Part 1


Part 2

Benjamin Garden on Simple vs. Compound Interest in Finance – The Central Equilibrium – Episode 5

I am so pleased to publish this new episode of “The Central Equilibrium“, featuring Benjamin Garden.  He talked about simple and compound interest in the context of finance and investment, highlighting the power of compound interest to grow your money and to enlarge debt from credit cards.  We compared the formulas for calculating the accrued amounts under simple and compound interest, and we derived the formula for the Rule of 72, a short-cut to estimate the length of time needed to double your investment under compound interest.

Check out Ben’s blog, Twitter account (@GardenBenjamin), and Instagram account ( to get more advice about managing your money!

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Layne Newhouse on representing neural networks – The Central Equilibrium – Episode 4

I am excited to present the first of a multi-episode series on neural networks on my talk show, “The Central Equilibrium”.  My guest in this series in Layne Newhouse, and he talked about how to represent neural networks. We talked about the biological motivations behind neural networks, how to represent them in diagrams and mathematical equations, and a few of the common activation functions for neural networks.

Check it out!

Video Tutorial – Calculating Expected Counts in Contingency Tables Using Marginal Proportions and Marginal Totals

A common task in statistics and biostatistics is performing hypothesis tests of independence between 2 categorical random variables.  The data for such tests are best organized in contingency tables, which allow expected counts to be calculated easily.  In this video tutorial in my Youtube channel, I demonstrate how to calculate expected counts using marginal proportions and marginal totals.  In a later video, I will introduce a second method for calculating expected counts using joint probabilities and marginal probabilities.

In a later tutorial, I will illustrate how to implement the chi-squared test of independence on the same data set in R and SAS – stay tuned!

Video Tutorial – Rolling 2 Dice: An Intuitive Explanation of The Central Limit Theorem

According to the central limit theorem, if

  • n random variables, X_1, ..., X_n, are independent and identically distributed,
  • n is sufficiently large,

then the distribution of their sample mean, \bar{X_n}, is approximately normal, and this approximation is better as n increases.

One of the most remarkable aspects of the central limit theorem (CLT) is its validity for any parent distribution of X_1, ..., X_n.  In my new Youtube channel, you will find a video tutorial that provides an intuitive explanation of why this is true by considering a thought experiment of rolling 2 dice.  This video focuses on the intuition rather than the mathematics of the CLT.  In a later video, I will discuss the technical details of the CLT and how it applies to this example.


Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is

h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t].

Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the survival function?

h(t) = f(t) \div S(t)

In my new Youtube video, I prove how this relationship can be obtained from the definition of the hazard function!  I am very excited to post this second video in my new Youtube channel.