Estimate the mean number of decays

In summary, the conversation discusses estimating the mean number of decays per period from a table of ~3000 measurements. The use of the Poisson distribution and how to calculate the mean are mentioned, and the speakers' intuition suggests that taking the arithmetic mean of the dataset may be the best estimator. However, they also question if this is always the case and consider other methods such as fitting to the Poisson distribution. The conversation also touches on the practical applications and biases of different estimators.
  • #1
aaaa202
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Homework Statement


I am given a table of ~3000 measurements for the number of decays from some radioactive substance within some period T. I want to estimate the mean number of decays per period.

Homework Equations


Poisson distribution
How to calculate mean.

The Attempt at a Solution


My intuition tells me that the best estimator is simply the to take the arithmetic mean of the dataset. However, given that the data should follow a poisson distribution I am not sure. When is the arithmetic mean the best estimator, and if this is indeed the case, why is it superior to for example fitting to a poisson distribution and then reading of the mean from the fit coefficients?
 
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  • #2
aaaa202 said:
My intuition tells me that the best estimator is simply the to take the arithmetic mean of the dataset.
My experience is practical (radioactive waste management) and my intuition is the same as yours.
I'll be interested to see if our intuition is correct.
 
  • #3
The search for leased biased estimators is fascinating math, but ignores the real world fact that you need to take into account how the answer will be used. An error one way may be more expensive than the same magnitude of error the other.
Also, taking a Bayesian view, I feel the attempt assumes some property of the a priori distribution of rates, symmetric perhaps.
Anyway, start here: https://en.wikipedia.org/wiki/Bias_of_an_estimator#Estimating_a_Poisson_probability
 
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1. What does it mean to "estimate the mean number of decays"?

When we talk about estimating the mean number of decays, we are referring to calculating the average number of particles that undergo radioactive decay in a given sample or substance. This is an important measure in the field of nuclear physics and is often used to make predictions about the stability and decay rates of radioactive materials.

2. How is the mean number of decays calculated?

The mean number of decays can be calculated by taking the sum of all the individual decay events and dividing it by the total number of particles in the sample. This gives us an average value that represents the expected number of decays per unit of time or per unit of substance.

3. What factors can affect the accuracy of the estimated mean number of decays?

There are several factors that can affect the accuracy of the estimated mean number of decays. These include the size and composition of the sample, the type of radioactive material present, and external factors such as temperature, pressure, and radiation shielding.

4. Why is it important to estimate the mean number of decays?

Estimating the mean number of decays is important because it allows us to understand the behavior of radioactive materials and predict their decay rates over time. This information is crucial for various applications such as nuclear power, medical imaging, and environmental monitoring.

5. Can the mean number of decays ever be exactly predicted?

No, the mean number of decays can never be exactly predicted. This is because radioactive decay is a random process and the exact number of particles that will decay in a given sample cannot be known with certainty. However, by using statistical methods and conducting multiple measurements, we can estimate the mean number of decays with a high degree of accuracy.

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