Estimation

Question 1

What methods can we use for estimation

Answer 1

• Method of Moments
• Maximum Likelihood
• REML
• Bayesian Methods
  
  • Non-informative priors
  • MC
  • MCMC
  • INLA

Question 2

What is method of moments

Answer 2

In the method of moments we take sample moments and make those ‘equal’ to the theoretical moments from our model.

Question 3

Maximum Likelihood

Answer 3

The likelihood can be thought of as the probability of getting the sample values given a set of parameters.
It is the joint distribution of the sample as a function of the
parameters

Question 4

Restricted Maximum Likelihood (REML)

Answer 4

As is well known MLE in the Normal distribution produces a biased estimator for the variance (although it is unbiased asymptotically)
[Bias means that the expectation of the estimator is not equal to the true the value of the parameter]
One way around this problem is REML.
REML transforms the data/model so that the two parameters are in effect estimated separately and without bias

Question 5

Method of moments process using variogram

Answer 5

• Calculate the sample variogram
• Choose a shape for the variogram
• Fit that variogram to the sample variogram by weighted least squares

Question 6

How do we fit the theoretical variogram to the sample variogram

Answer 6

Least squares

Look at equation sheet for the formula

Question 7

How do we discretise the variogram for least squares estimation

Answer 7

Divide it into bins

Question 8

Options for weighting the bins of the variogram

Answer 8

1. number of pairs in each bin
2. the theoretical variogram
3. equal weights

Question 9

What is Hawkins and Cressie

Answer 9

An estimator for the sample variogram to solve the problems of ‘noise’

See equation sheet for formula