So, we are back for a new academic year! Over the summer, our group continued reading books on statistics. Our summer readings, both old and new, has inspired a few posts that will be published on the blog soon. We hope you will find them enlightening!

Oh, and by the way, this September is our 21st September since we started Physics of Risk blog (if we include the 2006–2010 period when the posts were written in Lithuanian). 20 years have gone by!

Do you have plans for summer holidays? If not, here is a quick idea presented to you by Woolly Benguin at MathsJam 2023.

As we have already discussed, beta prime distribution arises from a nonlinear transformation of the voter model. Furthermore, recently we have been relying a lot on the said transformation [1, 2, 3]. In those papers, we have been using some results derived for the CIR process as well. Thus, another interesting thing, which my colleague Rytis Kazakevičius has noted, was that the beta prime distribution can be obtained from the ratio of two independent Gamma-distributed random values. Why it is interesting? The stationary distribution of the CIR process is the Gamma distribution!

Have you heard of the beta prime distribution before? Until recently, I hadn't either. My colleague, Rytis Kazakevičius, recently surprised me by pointing out that the distribution we have been repeatedly encountering in nonlinear transformations of the noisy voter model has actually a proper name. It is known as the beta prime distribution. And our history with this distribution, goes back much further.

Recently, Veritasium has posted a video on Newcomb's paradox. This paradox is based on a decision-making problem. Namely, you are presented with two boxes. Box A is transparent and contains a small amount of money, while Box B is opaque. Box B might contain a large amount of money or be empty. Its contents are decided ahead of time by a machine, which has perfect prediction record. If the machine predicts that you will take only Box B, it will put large amount of money inside it. Otherwise, it will keep Box B empty. So, will you take only Box B (and believe in predictor accuracy) or will you take both boxes (and believe in game theory)? For more details on the paradox and its solutions watch the video below.

After watching the video above I wasn't particularly fond of the paradox. Mostly because the paradox seemed to be artificially contrived. After watching minute physics (previously known as One Minute Physics) video I still feel the same way, but surprisingly this paradox prompts us to consider the nature of our own reality. I encourage you to watch it as well.

I especially liked the part about random 5 year old falsely achieving incredible accuracy.