Error Estimate from Value

• If we expand near its minimum with---for convenience---just one theoretical parameter, .

  

• where is our estimate of .

• Then probability distribution of is just

  

  i.e., is Standard Deviation of estimate.

• Returning to Equation (35), we find that if we put (i.e., at its one standard deviation value),

• is increased by 1.

• This increase ``rule'' is common method of finding ``error'' in estimate even when the Taylor expansion equation is not a good approximation.