Two measurements. Different trust.

[sm1981]

Dear all,

I have two methods to determine a value. Method one, gives me value A with uncertainty sA, and method 2 gives me value B with uncertainty sB. The distance between the values is larger than the addition of their respective uncertainties.

Here is my problem. If I believed both numbers equally, I could calculate the error using standard methods. But I don't believe both numbers equally. I trust measurement A more than do measurement B.

I'm not very familiar with Baysian stastics. Is it possible to assign a final value and uncertainty based on the relative trust I have of the two different methods? If so, how?

Thanks!

(This question comes from my research and is not a HW question. Any literature suggestions would be great.)

 

[zli034]

Say the value you want to study is a random variable, call it X.

Use Bayesian Estimation when you have a prior knowledge of X. By observing a new sample of X, you can use this new sample of X to update your prior knowledge of X. Updated knowledge we call it posterior of X.

The belief you are talking about is not the Bayesian concept.

It is common to have different measurements, and some better than the other. Some measurements are unbiased, and some are not. Some measurements have small variance means they are more precise than the others. Some measurements are more compatable with observed sample. And use Bayesian model to estimate the measurement, we have to have prior model.

Depends on what you want to do, and how big is your sample size, and obtaining a random sample is also important .