Every 4th of July I like to reflect on what it means to be independent. Today I wrote nearly an entire post on production independence, starting with energy independence. But I have decided to post that another day because there is a different type of independence that I have decided is more important at this particular moment in time: independent thinking. It has never been easy to be an independent thinker but it has become considerably more difficult in our always online, always connected ...

The last few Uncertainty Wednesdays had us look at how to model beliefs using probability distributions and then update those with a specific example of using the beta distribution. You may have noticed something odd about the way we updated the parameters of the beta distribution: add 1 to α when we observe heads and add 1 to β when we observe tails. This wipes out any and all ordering information. So let’s say you have a total of 100 observations. With this update rule the only thing that m...

I am spending this 4th of July in Germany, having visited my parents and friends from growing-up near Nuremberg for the last few days. It is late here now and I am seeing all the Happy 4th wishes from the US in my Twitter timeline. That made me think about what I feel like celebrating on this day. And as I wrote last year, it is not so much independence we need in the modern world, but rather interdependence. There is, however, something very much worth celebrating and that is the memorable l...

In the last two installments of Uncertainty Wednesday we looked at the concept of independence and concluded that it was actually quite a strong assumption. Now as one of the comments pointed out, independence is normally introduced in the context of a repeated coin flipping, where it is generally assumed that the outcome of the next coin flip is independent of the prior coin flip. When the independence assumption holds it means that no matter how long a sequence of coin flips I give you, you...

Last Uncertainty Wednesday, I introduced the concept of independence. I ended the post by asking whether independence was likely to be a strong or a weak assumption. To answer this let us look at the possible values for elementary events. And for that purpose I will show a different way of looking at those that I should have probably introduced a long time ago, when I first presented the 2 states, 2 signals model, defined probability, and related the probability of elementary events to compou...

Last week, I provided a recap of what we have covered so far in Uncertainty Wednesday. To go on from here we need to introduce some more concepts that are usually covered earlier but that I believe will make more sense in the framework that we have now established. The first one of these is the concept of independence. Two events are said to be independent if “the occurrence of one does not affect the probability of occurrence of the other.” Now is a good time to remember that in our simplest...

As an immigrant to America, I have enjoyed many 4th of July celebrations over the years. Given the Brexit vote, I woke up today wondering though what it means for a nation to be independent in the world we live in. All the big problems we face as humanity such as climate change, infectious diseases, taxation of multinational corporations are global problems. America can’t solve any of these problems by itself. Neither can any other nation. What we really need is a declaration of In-TER-depend...