What are your expectations for 2019?

[Originally posted on December 31th, 2018. Revised a couple sentences on January 2nd, 2019 — sketching under pressure and without proofreading, while the wife is showering, before going to a New Year’s Eve celebration is not really the way to go 😀 ]

As promised in Active inactivity, here is a new blog post, before the end of the year!

Since New Year’s Eve is upon us, I think it is only fair to begin this introduction to De Finetti’s definition of probability with a preparatory introduction to the concept of expectation.

In Statistics, the word expectation has somehow a peculiar meaning, that to me represents an improvement on the everyday meaning of the word; the layman’s definition of the word expectation, according to the Oxford Dictionary is “A strong belief that something will happen or be the case.“. Is this enough for the statistician?

Well, yes and no.

Yes, in the sense that the act of making a statement about the future is somehow maintained, at least for a suitable realization of the abstract definition of probability. No, in the sense that we are not interested in making a generic statement about what we believe that will happen in the future; we want to make a statement that reasonably encompasses everything that could happen, resulting in a statement about the average outcome that I can expect.

Let’s make a simple example: say that you draw a card from a deck, and that you gamble such that you win 10 euros is you get a King, and you lose 10 euros if you get a black card. What do you expect to happen on average?

The relevant useful concept here is that of expectation: each outcome (King, anything but a King) has two numbers associated to it: the probability of obtaining that outcome, and the value or pay-off that you get if that particular outcome happens. For example, there are 4 Kings out of the 52 cards that make the deck, so the probability of obtaining a King is p(K) = \frac{4}{52} \simeq 0.08, whereas the pay-off you get if the outcome happens is V(K)=10, euros. By converse, the probability of obtaining not-a-King is p(nonK) = \frac{48}{52} = 1- \frac{4}{52} \simeq 0.92, and the value you stand to win is V(nonK)=-10, euros (negative, since you would incur in a loss).

To know what you can reasonably expect to happen on average in this situation, it is necessary to think a bit. If the situation was simpler, for example if you stand to win 10 euros regardless of the outcome of the card draw, you can expect that you will win 10 euros. By converse, if you stand to loose 10 euros regardless of the outcome, you can expect that you will loose 10 euros. But in our fictitious situation different outcomes are rewarded with different values; it is then crucial to have a way of estimating a global, average value for what you can expect. Since each pay-off will happen only its corresponding outcome happens, a natural choice is to weight each possible pay-off with the probability that its corresponding outcome will actually happen. It turns out then that, following this line of reasoning, your expectation is given by an average of the pay-offs, weighted by the probability that each outcome happen. For our concrete case, E[gamble] = p(K)\times V(K) + p(nonK)\times V(nonK) = 0.08\times 10 + 0.92\times(-10) =-8.4; in words, the expected value you get out of your gamble is lose 8.4 euros.

You can already use such considerations to find the expected value of any kind of situation in which you can gamble on some well-known outcomes; this works for example for any gamble on a deck of cards, in which you can easily calculate the probability of any outcome by simply counting the cards—or combinations thereof—in the deck).

In order to interpret such statement, and to really get to the bottom of the meaning of expected value, we need to make a small step back and look into how we can define and compute an essential element of the formula for the expectation: probabilities.

However, you will have to wait for the New Year, because my wife has finished showering, and we need to get ready for this night’s party!

See what I did here? Not only have I described briefly the concept of expectation, but I have also given you a way of computing what is the value you expect to get from this blog for the first week of 2019: what is the probability you assign to me writing and publishing the next blog post before January 7th? What is the value you assign to the blog post coming out, and what is the value you assign to the blog post not coming out?

Try to get your probabilities and pay-offs figured out before midnight!

Active inactivity

My introductory post, Welcome to This New Beginning, came on February 19th, 2018. The day of tomorrow will mark 10 months from that moment; should I feel bad about it?

Yes and no.

Let me explain. I had started this project out of frustration and of the need of having a new haven where to rant about what I really care about, but then stuff piled up and I could not put myself to produce content for this blog. The exception being 4 drafts that are still in a very crude form, and that have been expanded at the staggering rate of about 4 or 5 words every couple months.

As I have been preaching to the AMVA4NewPhysics students (in quality of Outreach Offices of the network), the key for a successful blog is building engagement, and engagement is built in perhaps equal parts by interesting, high-quality content and by a frequent and regular update pace. I would not judge quality by the introductory post (nor by the post you are reading now), so all I am left with is the frequency, which is horrendously low.

Yet this has been a very productive year, in which I found stability in a newfound balance between CMS and non-CMS research and between life and work. I have moved to Belgium in July, and am now a researcher in the Institut de recherche en matématique et physique of Université catholique de Louvain; the institute offers an amazing melting pot of experimental physicists, theoreticians, phenomenologists, and generator folks. I am very excited of being here, and am seeing about bringing to light the non-CMS fruits of this melting pot (from the CMS side, I have worked to an update to the observation paper of ttH production, and most importantly to a paper on WZ cross section measurement and search for anomalous triple gauge couplings that is being submitted to JHEP today or tomorrow).

Most importantly, thanks to the new work gig my girlfriend and I moved in together: we actually got married in September in Belgium (followed by a white-dress party with family and friends in Italy)!

So to speak, Belgium is doing great so far: it gave me an exciting job and an exciting wife!

Now that many things have converged, I hope I will really kick-off this blog with an amazing series of posts! I won’t likely follow up immediately on the four drafts I have, because I am getting excited with the idea of writing a series of posts on De Finetti’s definition of probability, so I will most likely start from those. But you never know; the only certainty so far is that I plan to release the next post before the new year, so I will leave you to calculate your posterior for me to actually release the next post in the timescale I advertized 😀