Homework 4

Due March 2, 2015 in recitation, or before 4 pm by email to weijima@nyu.edu

Q1. Find a suitable nuisance parameter in each scenario. There might be more than one good answer!

a) You are standing outside and trying to infer the air temperature based on how cold your skin feels. You have to take into account that how cold your skin feels is also affected by _____________.

b) An accident investigator is trying to infer how fast a car was going from its braking distance, as measured from the tire tracks. She has to take into account that braking distance is also affected by

___________________. (Assume that the driver fully hit the brakes and didn’t crash.)

c) You are trying to infer your friend’s mood from how talkative he is. You have to take into account that how talkative he is might also be affected by ________________.

can be seen in at least two different ways: as a left-facing cube viewed from

Likelihood

left-facing right-facing

Hypothesized

cube orientation

below cube above cube

below cube above cube

Hypothesized vantage point

above or as a right-facing cube viewed from below closest to the viewer.

, where blue shading to indicates the face

Prior

left-facing right-facing

Hypothesized

cube orientation

below cube above cube

Q2. This Necker cube

Posterior

left-facing right-facing

Hypothesized

cube orientation

a) In the two-variable likelihood diagram above (left), shade the box(es) where the likelihood is high given the image of the Necker cube. Explain.

b) Suppose you live in a world where you view most cube-like objects from above rather than from below.

In the two-variable prior diagram above (center), shade the box(es) where the prior probability is high.

Explain.

c) In the two-variable posterior diagram above (right), use your answers to (a) and (b) to shade the box(es) where the posterior probability is high. Explain.

d) Fill in the blanks: if people indeed perform this inference, they would tend to see the Necker cube as a

__________-facing cube viewed from __________.

Q3. Most people will see the circles in this picture as protrusions (convex objects) lit from above. However, it is also possible to see them as cavities (concave objects) lit from below.

concave convex

Hypothesized

convexity

Prior

concave convex

from below from above

Likelihood

from below from above

from below from above

Hypothesized light direction

a) Would you consider convexity (concave/convex) or light direction (from below / from above) the nuisance parameter? Explain.

b) Does light usually come from above or from below? Explain.

c) Does your answer to (b) say something about a likelihood, a prior, or a posterior? Explain.

d) Given the image, shade in the following diagrams where the likelihood, prior, and posterior are high.

e) How does your answer to…