## To Be Or Not To Be

Physician and medical student suicide is an increasingly recognized area for concern. The film “Do No Harm” will likely be a powerful window into this problem. Milner et al report on the prevalence of doctor and other health professional suicide in Australia. This post is a Bayesian analysis of the data presented in the paper.

The brachistochrone problem is classical example used to illustrate the use of calculus of variations. In some ways it illustrates the trade-off between shortest distance (straight line) and greatest speed for a time minimization problem. The solution curve is a cycloid. In addition to the time minimization, no matter where start on the curve you will reach the end point in the same time.

Categories: Mathematica, Mathematics

## Breaking Sticks

This post is based on a probability puzzle. What is the probability that breaking a straight stick at 2 random points will result in 3 segments that can form a triangle.

Consider the resulting segment lengths: $x_i$, $i \in \{1,2,3\}$. Let the stick length =1.

Now,

$\sum_{j=1}^3 x_j=1$

To form a triangle

$x_i+x_j>x_{6-i-j}, i\neq j$ for all ${i,j}\in \{1,2,3\}$

These constraints reduce to: $x_1+x_2>1/2 , x_1<1/2,x_2<1/2$

You can visualize this as follows. As there are only 2 degrees of freedom, consider only space of $x_1,x_2$. The space of allowable $x_1, x_2$ is the region of the unit square: $x_1+x_2<1$ . Within this space the values of $x_1,x_2$ that form a triangle with lengths $(x_1,x_2,1-x_1-x_2)$ is the region satisfying the constraint above.

The probability is then: (1/8)/(1/2)=1/4.

Just for fun:

The light blue triangle is the region of $x_1,x_2$ that can form triangle and the pink triangle encloses the allowable stick segments.

The triangles on the right have been rescaled to be circumscribed by the unit circle. The relative lengths pertain not the absolute lengths.

## Australian Mortality Data

The Human Mortality Database provides access to world mortality data. This post looks at life expectancy, hazard rates, survival data for Australia from 1921 to 2011 (from the HMD Australian data).

The following plot shows the time course of “approaching” the 2011 life expectancy curve by area between curves referenced to area between 2011 and 1921 curves. There seems to have been “accelerated” progress around 1970’s.

Categories: Mathematica

## Statistical Rethinking

I just finished this book but will be using it as a wonderful resource as I ingest its manifold lessons.

This book is a fearless exposition of Bayesian inference that guides the reader’s understanding as well as providing practical hands-on use of software. The reader is allowed to peak under the hood. This is a gentle but systematic journey facilitated by the author’s R package rethinking.

This book is also a clarion call for transparent, accountable,high quality statistical methods in science and for us to be thoughtful users of the increasingly automated and strong golems we have at our disposal.

Categories: books

## More Fun with R

I am continuing to play with R. I am looking at older data measured and recorded in a different way.

I am (re-)reading Jaynes “Probability”. My first reading was difficult. It seems better the second time.

I post this as prompted by Jaynes’fondness for “desiderata” ( and in the spirit of Star Trek’s50 th anniversary):

Categories: Uncategorized

## Weapons and Lies

I recently finished reading the ebook formats of the above. I am still getting used to this medium.

I found both these books refreshing. The flow of information is increasing in volume and complexity with every passing day. “Big data” is the catch-phrase in many domains. “Weapons of Math Destruction” aims to highlight the limitations and potential unintended (and perhaps intended in some situations) adverse consequences on vulnerable people (on a large scale and leaving people without recourse to correction).

This is not an anti-science book. On the contrary, it is clarion call to data scientists, end-users and people to increase communication and understanding of what models and learning algorithms can and cannot do. The author stresses the importance of iterative refinement and the need to incorporate measures of societal and other less tangible outcomes.

Daniel Levitin’s book was a wonderful companion. This is a very useful and readable guide (and exhortation) to critical thinking when presented political, business and journalist claims. The first part of the book discusses statistical aspects. The author provides numerous examples and visual aids. The importance of critical reasoning and taking the time to practice and learn these skills that we are are not ‘hard-wired’ for (as in Kahneman’s Thinking Fast and Slow, there are a number of references to the work of Tversky and Kahneman in the book).

I think both books are timely. In tandem with the explosion of  “big data”, computational power, and increasingly complex statistical computing and machine learning, there is increasing momentum to deal with “bad science” (conduct, methodology, reporting and dissemination into the public arena).  Asimov’s quotation (used in the Levitin book) seems apt:

“The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom.”

The world faces many complex challenges and there does appear to be an “anti-science” voice emerging (and perhaps inward looking fear and intolerance). These two books (in different ways) help to point us to the path of wisdom to deal with the complex challenges.

Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.- Marie Curie

Categories: books