Bayesian estimate of the standard deviation of a Normal distribution with known mean

 

The likelihood function for n observations from a Normal distribution is given by the product of the Normal probability densities for each sample:

 

 

where V is the sample variance

 

With the uninformed prior:

 

 

this gives a posterior distribution of:

 

                              (1)

 

If a variable X = Gamma(a,b), then the variable Y=1/X has the Inverse-Gamma density:

 

                                        (2)

 

Comparing Equations 1 and 2 we see that:

 

 

The last identity comes from here. Rearranging gives:

 

 

See Also

 

ModelRisk

Monte Carlo simulation in Excel. Learn more

Tamara

Adding risk and uncertainty to your project schedule. Learn more

Navigation

FREE MONTE CARLO SIMULATION SOFTWARE

For Microsoft Excel

Download your free copy of ModelRisk Basic today. Professional quality risk modeling software and no catches

Download ModelRisk Basic now

FREE PROJECT RISK SOFTWARE

For Primavera & Microsoft Project

Download your free copy of Tamara Basic today. Professional quality project risk software and no catches.

Download Tamara Basic now
-->