Timeline for Calculating uncertainties in low stats radioactive decay data (Poisson Distribution)
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2021 at 23:45 | comment | added | Aksakal | No, in your case intensity is exponentially decaying therefore the variance will not be equal to mean | |
| Jun 3, 2021 at 16:31 | comment | added | Epideme | 1 other thing I wanted to ask... In a precise edit you mentioned it being problematic the mean and variance weren't approximately equal, does this make the graph /fitting above with the GLM w Poisson family less valid? I'm also not completely clear on if it uses a log link or not, I think it does, but I'm still reading through the link, and GLMs are new to me | |
| Jun 2, 2021 at 0:32 | history | edited | Aksakal | CC BY-SA 4.0 |
explained assumption of constant decay during 15s
|
| Jun 1, 2021 at 15:33 | comment | added | Epideme | Oh wow, you're not kidding about the long. I will set about reading that. Thank you. | |
| Jun 1, 2021 at 15:32 | comment | added | Aksakal | dataquest.io/blog/tutorial-poisson-regression-in-r - painfully long explanation here | |
| Jun 1, 2021 at 15:26 | vote | accept | Epideme | ||
| Jun 1, 2021 at 15:26 | comment | added | Epideme | Okay, well... I guess that's good news, I can move on to being frustrated at the next thing. Thank you for such clear and helpful answers. What fitting method do the GLM w/Poisson actually use, do you know? | |
| Jun 1, 2021 at 15:19 | comment | added | Aksakal | The weighting $\pm 1$ will not work for your case. however, your fitting routine already uses Poisson so you are good here. Yes, the output agrees with mine, of course. GLS with Poisson family means that it's all taken care of | |
| Jun 1, 2021 at 15:15 | comment | added | Epideme | I see. I've added my graph which uses a Non-Linear Model Fit from Mathematica for Poisson distributions, but I'm not too sure what the fitting method is. I think it might be Least squares, but not certain. However there's no weighting applied, and I should probably add the +/- 1 on each point. I've just seen you've posted your result, so I'll change my question to do you think this seems valid | |
| Jun 1, 2021 at 15:11 | history | edited | Aksakal | CC BY-SA 4.0 |
added 435 characters in body
|
| Jun 1, 2021 at 15:06 | history | edited | Aksakal | CC BY-SA 4.0 |
added 435 characters in body
|
| Jun 1, 2021 at 15:01 | comment | added | Aksakal | ideally, you want to come up with MLE of Poisson distribution with decaying intensity. however, running a simple nonlinear regression on your data with $1/\hat N$ as weights, and assuming 18s intervals (with 3s mute) I get almost exactly 150s half life | |
| Jun 1, 2021 at 14:45 | comment | added | Aksakal | yes 900s interval is very short relative to half life of 150s. I think in your case WLS should work fine when using $1/N$ as the weight | |
| Jun 1, 2021 at 14:42 | comment | added | Epideme | I see, so uncertainty in a single measurement would be (Taking 74 as the example): 74 +/- 1. And the uncertainty in the counts per second would be 74 +/-Sqrt(74)/(15). Given that you mentioned it not meeting the requirements for a poisson distribution, is there a better way of fitting this you would recommend? The data set does show exponential decay. The half-life is 150s, the experiment is about 900s - would that be considered relatively short enough? My end goal is trying to fit the results validly, and find the half life and uncertainty to see if they agree with the 150s reference | |
| Jun 1, 2021 at 14:37 | history | edited | Aksakal | CC BY-SA 4.0 |
added 214 characters in body
|
| Jun 1, 2021 at 14:31 | history | edited | Aksakal | CC BY-SA 4.0 |
added 214 characters in body
|
| Jun 1, 2021 at 14:24 | history | answered | Aksakal | CC BY-SA 4.0 |