Graphical Models: Assignment 6
Due April 3, 2017
- Consider the fragment shown below of a Markov model for cold
- Construct a junction tree for this BN with belief tables for the cliques and separators.
- Absorb both directions to obtain clique and separator marginals
for each clique.
- Enter a finding of sneezing on Day 2. Absorb
both directions to obtain clique and separator marginals for each
- Agent Hydziz I. Dennity's contact classification model
the PersonType, Gender, and HairLength random variables (as well as
other random variables not considered in this assignment). Agent
Dennity defines a completely connected Bayesian network for these three
random variables, as shown in the figure below, and assigns a uniform
prior distribution for each of these local
distributions: PersonType (1 distribution with four states), Gender
given PersonType (4
distributions with 2 states each), and HairLength given PersonType and
distributions with 2 states each). What is the prior distribution
for the probability that a contact is a government agent?
- To estimate the probability distributions in his contact
classification model, Agent Dennity collected a sample of 200
individuals whose type and features were known. The sample was
collected in such a way that Agent Dennity is confident
in treating the observations as a random sample from the population of
Depravians. The data he collected is provided here.
- Find the posterior distribution for each of the local
distributions in Agent Dennity's Bayesian network. State the type
of distribution and the parameters.
- Find the mean and variance of each probability in Agent Dennity's Bayesian network.
- Find a 90% interval for each probability. That is, find
the 5th and 95th percentile of each probability. (Hint:
You can do this with Excel's BETAINV function or R's qbeta function.)
Problem 3, but assume that (i) the gender
distribution for government agents is the same as the gender
distribution for dissidents; (ii) the hair length distribution is the
same for all women; (iii) the hair length distributions are the same
for male government agents, male government supporters, and apolitical
males. Compare these results to Problem 3 and comment on the
differences. If you were advising Agent Dennity on whether to
estimate the probabilies using the method of Problem 3 or Problem 4,
what would you recommend? Justify your recommendation.