10 posts

Trend methods

The fifteen smoothing algorithms, what each one assumes, and when to use it.

1. Why your weight trend barely moves when the scale jumps (EWMA)Your trend line travels a tenth of the way toward each new weigh-in, so a 5.4 lb morning shifts it 0.54 lb. What alpha does, and why a shock halves in 6.6 days.
2. Why your weight trend reads higher than the scale (Hacker's Diet)A trend line that skips the days you missed takes fewer steps down, so it sits above your weight: 186.0 lb against a last reading of 183.0 on one user's log.
3. Why your trend line lags behind the scale (SMA vs EWMA)A trend line lags because it averages weigh-ins you already took. At the shipped defaults a 7-day SMA sits 3 days back and an EWMA at alpha 0.10 sits 9 days back.
4. Why your weekly rate changes every day (the Kalman filter)The Kalman method carries your rate of change as part of its state and updates it with every weigh-in, so the weekly figure moves daily. Measured on 84 weigh-ins.
5. What your trend does on days you skip a weigh-in (interpolation)On a day you did not weigh, the app draws a straight line between your two nearest readings and hands it to the filter — 142 of 226 days on one user's log.
6. What one bad weigh-in does to your trend line (rolling median)One 10 lb error moves a 7-value rolling median 0.4 lb and a 7-value moving average 1.43 lb. Double the error and the mean's miss doubles; the median's does not.
7. Which weight trend method should you use? Fifteen, measuredFor most logs the answer is the shipped default, Robust Adaptive EWMA. The three reasons to override it, and why fifteen methods finish 4.0 lb apart.
8. Is a weekly average weight better than a daily weigh-in?A calendar-week mean ignores more scale noise than any of Peptrend's other fourteen trend methods, and says nothing about today. Measured on one real log.
9. How many weigh-ins before a weight trend means anything?On one real log, two weeks of readings gave a weekly rate that showed a gain in over a quarter of windows. What four and eight weeks of data change, measured.
10. Why your trend line changes last week (LOESS and Savitzky-Golay)Two of Peptrend's trend methods read weigh-ins on both sides of each day, so new readings redraw recent days. On one log, LOESS moved a day 0.62 lb on average.