Week 9 Probability and Confidence Level

Question 1

what is the subjective probability equation

Answer 1

P(theory I result) = P(result I theory)P(theory) / P(result)

Question 2

what interpretation can be made from the subjective probability

Answer 2

Similarly if the result is predicted to be unlikely/forbidden by a theory then its observation reduces the degree of belief in the theory and if a result is predicted highly likely then it increases the degree of belief in a theory

Question 3

what can be done if we want to know the true value of a parameter μ having made a measurement with result x and resolution σ

Answer 3

construct a confidence belt

Question 4

what is the procedure for constructing a confidence belt

Answer 4

for a given parameter μ there is a probability distribution function for the measured value x
use this function to construct a confidence belt within an interval of this function

Question 5

what interpretation can be made from a 90% interval confidence belt for μ

Answer 5

the true value of μ has values between μ- and μ+ with 90% probability

Question 6

how do we make confidence belts for Gaussians with constant mean and standard deviation

Answer 6

the x- and x+ interval values are constant so become straight lines and the μ are obtained via the equation
μ-+ = x -+ nσ

Question 7

what do we need to do for constructing confidence belts for Poisson distributions

Answer 7

find the greatest value of N_ that satisfies a given value of λ