Getting into a routine

Weights only this morning: rotator cuff, pull ups (3 sets of 5-5, 2 sets of 10, 1 set of 5); tough getting started, bench: 10 x 135, 2 x 185, 7 x 165, military: 3 x 50 standing (ugly), 15 x 50 seated, 10 x 40 standing, 10 x 180 machine (90 each arm), rows: 3 sets of 10 x 50 single arm, 10 x 110 machine. Goblet squats: sets of 6 with 25, 50, 60, knee stretches, back stuff, headstand, 2:30 front plank, (or hover), side plank (extended arm)

Note: for me, it is easier to do this version of side plank with shoes on; I can do it without shoes but it is more difficult.

This is the version I do.

My knee rehab “sit on my heels”: 4 lb. medicine ball. This explains my issues:

Athletics weekend

Yes, it was snowy outside, and I talked about my walking outside in the sloppy slush soup.

But Saturday I was treated to an unusual 9 inning game double header (sort of) when Bradley defeated Southern Illinois 14-4 (10 run mercy rule in the 7’th) and 7-1 an hour later, to complete the 3 game series sweep. The thing is that SIU is not that bad; BU was just outstanding.

The 14-4 game saw Bradley take a 3-0 lead on the strength of 3 hits, including 2 home runs. SIU came right back with 4 in the top of the second, but that was to be their total scoring. Bradley had 12 hits in 7 innings and scored 5 runs in the 6’th ans 2 in the 7’th to attain the 10 run lead.

My spouse went home in the hour between games (the second game was originally scheduled for Sunday) and I came back for the second, which was 7-1 win.

The few fans that remained for the second game flocked to the sunny areas; I chose a picnic table in the outfield for most of the game. It was more of the same: good pitching and defense by Bradley and a lot of hitting.

Then today, it was time for the Women’s Basketball Team Banquet.

That was well done and fun to attend.

Internet Privacy issues

Well, at one time I considered myself to be internet and social media savvy. But I suppose that I am really not.

I like social media because I can meet people I might not have otherwise met, and I’ve met new friends..people who became IRL friends, in this manner. I’ve also managed to spread the word about events (ball games, foot races, stadiums, books. even math ideas).

BUT, such a reach leads to a cost. In one instance, I ran afoul of a small band of NeoNazis who were attempting to harass a well known columnist. That lead to them spreading fliers in my neighborhood which denounced me (yes, that is free speech). That happened well over a decade ago. There are other instances that lead to my having to expend “in real life” (IRL) energy in ways that I did not want to.

And so, this WILL affect what I post. I will still talk about ideas, controversial or not. THAT is intellectual freedom. But I will make adjustments. Yes, this is vague, and I might…or might not, talk about these issues in greater detail at a later time.

But as as the new generation: they are growing up with such issues and are “adjusting” accordingly. Here is an NPR article about that. Roughly speaking: Employers expect to see an internet/social media history, but they also want to examine said history. So young people are setting up very vanilla to down right banal online profiles to provide the “right image” and then doing things like using fake profiles to actually converse, share more honestly, etc.

I suppose the lesson here is that, unless one is in a position where they can honestly not care about what others think, one has to be as guarded online as they are in real life..perhaps more so?

Off for a wet, sloppy walk outside.

Way too early look at the 2020 General Election

Ok, the 2020 election, barring something that I can NOT realistically foresee, will be between Donald Trump and whoever the Democrats can find. So, my interest is mainly in the Democratic primary. My favorite candidates are Amy Klobuchar, Corey Booker and Kamala Harris (all US Senators) but only Sen. Harris appears to have enough traction to have a realistic shot. But it is early.

One issue I have is that I spend quite a bit of time on Twitter and the Democratic voters I see there represent a small, distinct subgroup of Democrats; they do NOT reflect the Democratic electorate at all. And what I read in articles is often based on such smaller, noisy groups.

And there appears to be rifts. You have a “Bernie” faction and a “NO BERNIE” faction, and neither side appears to care for the other. And among the “NO BERNIE SANDERS” faction you have different groups: the identity politics/”woke group” and the “no socialism” group.

Trump is unpopular..especially so given that the economy is doing ok. So, expanding beyond his current base will be hard to do. BUT, will he have to? Right now, we Democrats appear to be in disarray and I have zero confidence that we’ll unite behind anyone.

So as for right now, I’d have to say that Trump will be reelected (I say that without much confidence).

Interesting few days…

First things first:
Friday’s workout was “weights only”: pull ups: 5 sets of 10, one of 5, bench: 10 x 135, 1 x 190 (not that easy), 10 x 160. military: 7 x 50 standing, 15 x 50 seated, 10 x 40 standing, rows: 3 sets of 10 x 50. Planks (went well), side plank, head stand, goblet squats (6 x 30, 50, 62 “to the sill”)), knee stretches (4 lb. ball is easy)

Today: morning 8.1 course in just under 1:36; nice and easy, perfect running weather.

Past 3 days: I got to see great lectures on “privacy and the digital age”, “topology, big data and financial networks” and the statistics of bracketology. Then after dinner with the speaker and other colleagues,
I caught the last 4-5 innings of Bradley’s 8-0 win over Southern Illinois. And I got to see Alex, a former student who is blossoming into a successful professional:

Star baseball pitcher and award winning student…that is quite the combination.

Bayesian Statistics: what is it about?

First of all, if you are unfamiliar with Bayes’ Law, here is a very nice video that explains both the formula AND the concept. Yes, the end of the video goes into social commentary (and makes some interesting points) but the math before it is very good.

If you’ve already familiar with those ideas, you can start here.

Let’s start with an example from sports: basketball free throws. At a certain times in a game, a player is awarded a free throw, where the player stands 15 feet away from the basket and is allowed to shoot to make a basket, which is worth 1 point. In the NBA, a player will take 2 or 3 shots; the rules are slightly different for college basketball.

Each player will have a “free throw percentage” which is the number of made shots divided by the number of attempts. For NBA players, the league average is .672 with a variance of .0074.

Now suppose you want to determine how well a player will do, given, say, a sample of the player’s data? Under classical (aka “frequentist” ) statistics, one looks at how well the player has done, calculates the percentage (p ) and then determines a confidence interval for said p : using the normal approximation to the binomial distribution, this works out to \hat{p} \pm z_{\frac{\alpha}{2}} \sqrt{n}\sqrt{p(1-p)}

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Yes, I know..for someone who has played a long time, one has career statistics ..so imagine one is trying to extrapolate for a new player with limited data.

That seems straightforward enough. But what if one samples the player’s shooting during an unusually good or unusually bad streak? Example: former NBA star Larry Bird once made 71 straight free throws…if that were the sample, \hat{p} = 1 with variance zero! Needless to say that trend is highly unlikely to continue.

Classical frequentist statistics doesn’t offer a way out but Bayesian Statistics does.

This is a good introduction:

But here is a simple, “rough and ready” introduction. Bayesian statistics uses not only the observed sample, but a proposed distribution for the parameter of interest (in this case, p, the probability of making a free throw). The proposed distribution is called a prior distribution or just prior. That is often labeled g(p)

Since we are dealing with what amounts to 71 Bernoulli trials where p = .672 so the distribution of each random variable describing the outcome of each individual shot has probability mass fuction p^{y_i}(1-p)^{1-y_i} where y_i = 1 for a make and y_i = 0 for a miss.

Our goal is to calculate what is known as a posterior distribution (or just posterior) which describes g after updating with the data; we’ll call that g^*(p) .

How we go about it: use the principles of joint distributions, likelihood functions and marginal distributions to calculate g^*(p|y_1, y_2...,y_n) = \frac{L(y_1, y_2, ..y_n|p)g(p)}{\int^{\infty}_{-\infty}L(y_1, y_2, ..y_n|p)g(p)dp}

The denominator “integrates out” p to turn that into a marginal; remember that the y_i are set to the observed values. In our case, all are 1 with n = 71 .

What works well is to use the beta distribution for the prior. Note: the pdf is \frac{\Gamma (a+b)}{\Gamma(a) \Gamma(b)} x^{a-1}(1-x)^{b-1} and if one uses p = x , this works very well. Now because the mean will be \mu = \frac{a}{a+b} and \sigma^2 = \frac{ab}{(a+b)^2(a+b+1)} given the required mean and variance, one can work out a, b algebraically.

Now look at the numerator which consists of the product of a likelihood function and a density function: up to constant k , if we set \sum^n_{i=1} y_i = y we get k p^{y+a-1}(1-p)^{n-y+b-1}
The denominator: same thing, but p gets integrated out and the constant k cancels; basically the denominator is what makes the fraction into a density function.

So, in effect, we have kp^{y+a-1}(1-p)^{n-y+b-1} which is just a beta distribution with new a^* =y+a, b^* =n-y + b .

So, I will spare you the calculation except to say that that the NBA prior with \mu = .672, \sigma^2 =.0074 leads to a = 19.355, b= 9.447

Now the update: a^* = 71+19.355 = 90.355, b^* = 9.447 .

What does this look like? (I used this calculator)

That is the prior. Now for the posterior:

Yes, shifted to the right..very narrow as well. The information has changed..but we avoid the absurd contention that p = 1 with a confidence interval of zero width.

We can now calculate a “credible interval” of, say, 90 percent, to see where p most likely lies: use the cumulative density function to find this out:

And note that P(p < .85) = .042, P(p < .95) = .958 \rightarrow P(.85 < p < .95) = .916 . In fact, Bird’s lifetime free throw shooting percentage is .882, which is well within this 91.6 percent credible interval, based on sampling from this one freakish streak.

Embarrassed but still trying

To the Riverplex via a 2.5 mile segment and 7.6 home. It was windy going out. On the way back a young person smiled at me and said “great job”…I think that I was losing steam. And I KNOW I looked terrible. But I smiled and said “thank you.” My yoga teacher upped the ante in class…gave us a flowing, high energy, lots of plank/side plank movements. And my knees…side block is easy..not *quite* to sitting on one flat yoga block.

Weight: 186…getting there.