A bathroom scale does not measure the thing you want to know. Body weight moves by a kilogram or more within a single day for reasons that have nothing to do with a trend — fluid, food, time of day — so any one reading is the underlying weight plus an unknown amount of noise.

HealthTrend estimates the quantity underneath: a latent weight, and the rate at which that weight is changing, in kilograms per week. Both are estimates with a stated uncertainty rather than measurements, and the rate is usually the more useful of the two — it answers “am I progressing” more directly than any single weight value does.

The estimator has no parameter through which a goal could reach it. A target weight is interpreted above the model, never inside it, so the same series produces the same estimate whatever anyone is aiming for.

Each new reading is evidence, not a replacement. The estimate moves part of the way towards it, and how far depends on two things the model tracks: how uncertain the current estimate already is, and how noisy a single reading is assumed to be. A well-determined estimate barely moves for one surprising reading; an uncertain one moves a long way.

Time enters as real elapsed time, not as a count of readings. Two weigh-ins a day apart and two a month apart are treated differently, and a gap of thirty days is handled exactly as thirty one-day steps would be — the same distribution, not an approximation. Weighing yourself irregularly costs precision; it does not break the model.

The trajectory is filtered, not smoothed. Every point on the line reflects only the data available at that instant, so nothing earlier is rewritten when a new reading arrives: it is the estimate you would have had on the day. A retrospective view, which revises the past in light of what came after, is a different calculation and is not what the chart shows.

The band around the line is a 95% interval on the underlying weight — not on what a scale would read tomorrow morning. An interval for a future scale reading would be wider, by the measurement noise, and answers a different question.

It is the model’s own spread, computed from the assumptions below. It is exact only if those assumptions and those parameters are right; it does not include uncertainty about the parameters themselves, and its coverage has never been measured against real recorded data.

HealthTrend states the interval and stops there. It does not turn a spread into a label such as “high confidence” or “low confidence”, because that would be a judgement the numbers do not make and a threshold nobody has defined.

A forecast is the current state carried forward: the estimated weight moves at the estimated rate. Nothing is added to it, and no other information is used.

The interval grows with distance for two separate reasons. The rate is itself only an estimate, and its error compounds over a longer lever arm; and the rate is allowed to drift over the period rather than being held fixed. Together those make a distant forecast honestly vague rather than wrong with a narrow interval.

Horizons are fixed at 7, 30 and 90 days and are measured from a forecast origin. If the last weigh-in was some days ago, those days are real elapsed time in which the trend both moved and became less certain, so they are carried through as well.

The model has no notion of a floor, a ceiling or a return to any usual weight, so it is only locally valid: simulated far enough forward it produces weights no body could have. That is a true property of this class of model, and it is why the product forecasts 90 days rather than years.

These are documented priors, not values fitted to anybody’s data. They are plausible, they are stated in product units and converted, and they determine how hard the estimate smooths — which makes them the single biggest influence on what the analysis screen shows.

These values are read from the analysis service rather than copied into this page, so they cannot drift apart from the ones an analysis actually used.

These are stated because they are load-bearing. None of them has been validated against real recorded data.

• The parameters above are priors, not fitted values. They are plausible and documented, and they determine how hard the product smooths.
• Intervals are exact only for fixed parameters. Coverage on real data is unmeasured.
• There is no robustness to mistyped or freak readings, by design. The filter is linear, so one bad reading displaces the estimate in proportion to the gain, and the displacement decays as a damped oscillation rather than steadily.
• The model has no mean reversion, so it is only locally valid — the reason horizons stop at 90 days.
• Weigh-ins taken minutes apart are treated as independent, which shrinks the interval slightly more than reality warrants.
• A local linear trend cannot represent a flattening or a turn as structure; it tracks them by drifting velocity, which lags.
• The trajectory is filtered, not smoothed: each point reflects only the data available at that instant.
• Calibration has been demonstrated only on data drawn from the model itself, which validates the implementation rather than the choice of model.

The complete specification of the estimator, unsimplified. Everything above is a description of what follows.