## Applied Nate Silver – 3

Another week and a bit more data, plus some actual observations about Nate Silver’s methodology, which it turns out I’m not really using properly. But let’s start with the money graph:

Last week’s money graph extrapolated to 229.3 for this week but I knew that was too optimistic so I did some other prediction techniques and averaged the results but still thought it was too high so I completely ignored the math and picked 230.2 as my “projection” and it turns out my “intuitive” idea was closer to reality than objectively using the statistics only. For fundamental reasons I think I’m going to be doing this all the more, so here’s my “cooked” prediction for next week (halfway between my “pessimist” “guess” and actual numerical projection):

# 227.3

(I’ll declare a “moral victory” if I just make 228.0 since that gets me out of “obese” category into merely overweight)

Meanwhile let’s look at the issue I raised last week, which is the scale variability on even trying to get each new weekly point:

Actually it looks like my samples are bimodal but guessing that based on five points is silly, but OTOH, my estimate is obviously going to fall in the middle where there are no measured points. My “estimate” is based on average((min+max)/2, ave, med) and actually came out slightly higher than my normal “consensus” guess (that I’ve used in previous weeks). So this is where 229.9 came from on the first graph.

But now I have two weeks where I have multiple samples per weekly value so perhaps my regression is getting a little better now:

So this is where the “optimistic”projection comes from, namely predicting exactly the same trendline into next week which I think is unlikely based on fundamentals. But before we go to the fundamentals let’s go to the graph that is the real purpose of this exercise and back to some discussion of Nate’s methodology:

My goal of the whole personal exercise is to reach 200lbs (then possibly consider going for 185lbs which seems really unreachable as that is going back about 40 years). So when is this going to happen? If I can maintain the trendline for the past seven weeks then I’ll reach the goal in week 19, or 11 more weeks. For a whole bunch of reasons this, I think, is unrealistic, and while (at the moment, until new data) would be the projection, I just know it’s not going to happen.

Lots of events will get in the way, most noticeably the holidays. For the past seven weeks I’ve been able to focus on this process with few distractions, but in the next few weeks there will be many distractions (meaning more eating, less exercise). So realistically I think reaching the new year at only 227.0 will be a “victory” and then my new starting point for a determined push.

But the more significant problem is that all the various daily caloric intake requirement  calculators are based on current weight (not entirely clear what the underlying reasons would be, presumably lugging around fat takes energy). So as I drop I need less calories, or needling less, I will be running a smaller “deficit” (with current exercise and eating levels) and thus burn less fat. When I started my daily requirements were 3442 (seems like a lot, but that’s what calculator says) and now it would be 3285 and as I near target it will be 3040 or basically about 2800/week less. Now given a pound of flab is worth about 3500 calories that really means, given I maintain current intake and exercise, that my weekly loss with drop to somewhere around 1.5-1.8, or over the 11 weeks the projection makes probably somewhere around 5-8lbs worse than the trendline.

So that implies something on the order, let’s say of 4 weeks, and I’m going to lose 2 weeks in the remainder of this month, so I’d now project hitting 200lb target at something like

# week 25

or something like the beginning of June (which is better than my original estimate of by my birthday in August). So I might reset to a more aggressive goal in the 190 range by my birthday but that’s going to take a boatload of determination.

And we’ll see where this all goes, about 4 weeks from now will be a good time to do another thorough projection and goal setting.

Now given my titling this series of posts with Nate’s name I think he’d denounce what I’m doing here. I’m making linear predictions using “frequentist” methods, not the Bayesian approach he uses. Plus I’m making point predictions rather than probabilities.

OK, got it, I see what I’m doing wrong, but I’m not sure how to recast this particular problem into his framework.

## need some help here, Nate!

What does it really mean to be using probability? I suppose the way to do this is to refocus my “prediction” into what is probability I will reach 200lbs in week25? (or any other timeframe, or any other weight target).

Now that’s the easy part, to reframe the question. The harder part is to actually figure out how to apply the Bayes formula (or my favorite, stochastic simulation) to get the probability. Obviously the updating with new data (the critical part of Nate’s method) is easy since I’ll continue to accumulate weekly data (whether it moves in correct direction or amount, or not).

But in some sense, like the 2012 election, my outcomes are really binary – either I will make it or not (or Obama will get elected or not). This isn’t baseball or gambling where I will repeat this experiment many times and thus probability is meaningful.

So that’s my next bit of homework, to actually turn this around and get into this framework.