# Knuth treats acceleration estimates as probability distributions

Markdown copy of https://realalpha.app/s/knuth-treats-acceleration-estimates-as-probability/ on Real Alpha, the best minutes from long interviews with the people building AI. Cite and link the page, not this copy.

- Speaker: [Kevin Knuth](https://realalpha.app/people/kevin-knuth/) · Kevin Knuth is a physics professor at the University at Albany. · Led a multimodal UAP study combining optical, infrared, weather-radar and radiation data.
- Host: [Brian Keating](https://realalpha.app/people/brian-keating/) · Host, Into the Impossible With Brian Keating
- Show: Into the Impossible With Brian Keating
- Episode: [Physics Professor: How Much Power Does a UFO Really Need?](https://realalpha.app/v/EKlLswUgyRI/), Nov 11, 2026
- Moment: 17:54 to 20:25 of the episode (3 min), playing on https://realalpha.app/s/knuth-treats-acceleration-estimates-as-probability/; the episode from there: https://realalpha.app/v/EKlLswUgyRI/?t=1074

## Quote

> “you can't actually estimate a systematic error because you would need to **know what the true value is** to estimate that”
> — [Kevin Knuth](https://realalpha.app/people/kevin-knuth/) at [18:15](https://realalpha.app/v/EKlLswUgyRI/?t=1095) · Into the Impossible With Brian Keating

## Takeaways

1. Estimating systematic error requires knowing the true value.
2. The acceleration result is a probability distribution.
3. An asymmetric distribution gets separate plus and minus uncertainties.

## About this segment

Kevin Knuth explains why he models the radar-derived acceleration as a probability distribution rather than a single exact value. The method shows what the estimate can and cannot say about uncertainty.

From “Physics Professor: How Much Power Does a UFO Really Need?”, Nov 11, 2026. [Watch the full episode](https://realalpha.app/v/EKlLswUgyRI/)

## Transcript

Transcribed by machine (Whisper) from the episode’s audio, so a word may be off here and there.

[18:02](https://realalpha.app/v/EKlLswUgyRI/?t=1082) at 747 speeds, call it 500 miles an hour, pretty much. Let's round up round numbers. And so this thing was tracked over what? I mean, Alaska is not that big. So how are they tracking this thing for that long, getting this data? And what can we ascribe these errors bars to first? Right. Well, when you calculate errors like this, you can't actually estimate a systematic error because you would need to know what the true value is to estimate that, right?

[18:29](https://realalpha.app/v/EKlLswUgyRI/?t=1109) You'd have to have some handle on what the true value is. So you can never really estimate a systematic error. You're calculating a probability distribution of the acceleration, which is what I showed on this previous slide. This is actually what this is giving you. This was done by sampling, which is why it's fuzzy. But this is the probability distribution for the acceleration. That's the answer that Bayesian statistics would give you, right?

[18:53](https://realalpha.app/v/EKlLswUgyRI/?t=1133) And I can report, you know, so what do you want to report? Well, I can report the mode, the peak. I can find the peak. I can fit this to a curve and I found the peak. I can report the mode. I can report the mean. So I can calculate the average value, which is not going to be quite at the same place that the mode is. So you actually have multiple numbers you can report. And then you have your uncertainties, which you can estimate another way.

[19:17](https://realalpha.app/v/EKlLswUgyRI/?t=1157) And uncertainty is a way of estimating the width of the distribution. So what's typically done is once you find the mode, you know where the mode is the peak. Once you know where the peak is, you can look at the curvature of the peak, and basically you're fitting a Gaussian distribution to this, and you take the standard deviation of that Gaussian distribution, fit to the peak. You use that as the measure of the width of this distribution.

[19:41](https://realalpha.app/v/EKlLswUgyRI/?t=1181) Now, in this case, it's asymmetric. It's clearly an asymmetric distribution. So what I did is I actually fit one Gaussian to the left side and a second Gaussian to the right side, And then I use the standard deviation of each Gaussian as the plus or minus. So it has a different plus or minus. whether you're on the plus side or the minus side. And that's basically what's happening here with the accelerations.

[20:08](https://realalpha.app/v/EKlLswUgyRI/?t=1208) So conceptually, what the uncertainty is telling you is it gives you an idea of the precision of your estimation procedure. And that's really what the uncertainty means.