Simulation

Understanding whether a variable’s missingness from a dataset is related to the underlying value of the data is a key concept in the field of missing data analysis. We distinguish three broad categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). In his book Statistical Rethinking, McElreath1 gives an amusing example to illustrate this concept: he considers variants of a dog eating homework and how the dog chooses - if at all - to eat the homework. The examples he give show substantial shifts in observed values, which make for a good illustration of the types of problems you might encounter. A lecture corresponding to the example from the book can be found on YouTube. In this post, I will first briefly review the different missing data mechanisms before implementing McElreath’s examples in SAS. ...

In a first semester probability course, students encounter combinatorics and point estimates such as the mean and median of a data set. A common example is the low odds of winning the lottery. When discussing the topic of point estimates, students are exposed to the idea of a “fair bet” or “fair game” - one in which the expected value of the random variable associated with the game is equal to the cost of participation or zero, depending on if a fixed cost is included in the game or tracked separately. This year, the Mega Millions had a jackpot in excess of one billion dollars. This had me thinking - mathematically, this is likely a fair game. But I still would expect to loose out playing it. In this article, I want to explore this idea further using the Mega Millions lottery as a particular example. ...

A look at the distribution of age at death based on social security mortality tables to see how long we can expect to be in retirement for.