Physics doesn't guess the shape of a field. It solves an equation for it. Statistics can do the same: give it your data and the range they live on, and one equation returns the distribution. No model to pick, no kernel to tune.
Most methods start with a choice: a model family, a kernel width, a set of weights. Change the choice and the answer changes. We start from an equation instead. Give it your data and the range they live on, and it returns the distribution. The answer depends on the data, not on the analyst.
| Question | The usual way | With a field equation |
|---|---|---|
| The shape of the distribution | Chosen in advance | Solved from the data |
| Tuning | Kernel widths, weights, bandwidths | Set by the sample, not the analyst |
| Two analysts, same data | Can disagree | Get the same answer |
| Comparing two samples | Simulation, slightly different each run | A formula, the same every time |
The data and the range they live on decide the shape. The bell curve and the other textbook shapes come out as special cases, not as assumptions.
Describe a sample →Fit each sample and measure the distance between the fits, straight from the formulas: the same answer every time, and exactly symmetric.
Compare two distributions →Draw new samples straight from the fitted distribution and check them against real data the generator never saw. Very high dimensions, like shape outlines, are a work in progress.
Draw new samples →When a distribution comes from physics, the numbers that describe it also give its physical quantities, each with an error bar.
See what's coming →NIST's cell image database holds three samples of one cell line and a sample of another. In the shape-populations working paper, the method finds the three replicates to be one population and sets the other line far apart. It agrees with NIST's published analysis, and it corrected two errors in our own earlier analysis of the same cells. The interactive version is coming to the experiments.
About the paper →Experiments on things we're thinking about: the same field model run on physical systems, from molecular energy levels and confined electrons to flow in a duct and the classic tests of gravity. Each shows the computed value beside the published one. They are explorations, not settled claims.
Explore the physics experiments →Nothing to install. Open a session from the button in the lower right of any page, send the link, and work through an experiment with a colleague, a student or a partner lab, in real time.
Open a session on any experiment and send the link. Everyone who joins is in the same room, looking at the same thing.
See each other's cursors. When one person scrolls or moves to another page, everyone comes along.
When anyone sets a parameter or runs a computation, everyone sees the result at the same moment.
Voice is built in, and the conversation carries on as you move from page to page.
Send most interactive charts straight to a shared board, sketch over them, and keep notes in the session chat. The whole session saves as one file you can keep.
Ask about what's on screen. It knows the page and the institute's background documents, and on many experiments it sees the current results too.