Robotics and Al Midterm, Spring 2019 Name Given the studied Helief Network linking burglary and earthquakes to phone calls from neighbors John and Mary, assume that PIA-B,E)-0.XY where X and Y are the two least significant digits in your student ID Burgla ry.) P(B)-.20 Earthquake-P(E)-.30 Alarm B E P(A) T T 95 TF|.94 T 1.90 F 1.05 70 .04 I a. Show the numerical computation of P(M B-E) using enumeration, where E stands for Earthquake, M for MaryCalls, B for Burglary, and -E stands for Earthgwake False Also, draw the call graph, as in slides b. Show the numerical computation of P(M B.-E) using variable elimination. Draw the call graph with values on arcs, as in slides 4. Use MCMC to estimate the P(JM.-E) based on same belief network from Problem2, with the same random number sequence (PRNG). You should base you estimation on 2 rounds the computation at each step both symbolically and numerically through the network. Show s. Given the library-rat dynamic belief network studied in class examples, with the evidence: U,-U, U (where-U means "not umbrella) a) Evaluate the probability of rain at time 3. deterministic smoothing for the probabilities of each state. Namely, run the forward and backward algorithm Run ong each step on a graph that separately illustrates the application of the transition and sensor model (as in the slides Acing forward computations above the DBN and the backward computations below it. Robotics and Al Midterm, Spring 2019 Name Given the studied Helief Network linking burglary and earthquakes to phone calls from neighbors John and Mary, assume that PIA-B,E)-0.XY where X and Y are the two least significant digits in your student ID Burgla ry.) P(B)-.20 Earthquake-P(E)-.30 Alarm B E P(A) T T 95 TF|.94 T 1.90 F 1.05 70 .04 I a. Show the numerical computation of P(M B-E) using enumeration, where E stands for Earthquake, M for MaryCalls, B for Burglary, and -E stands for Earthgwake False Also, draw the call graph, as in slides b. Show the numerical computation of P(M B.-E) using variable elimination. Draw the call graph with values on arcs, as in slides 4. Use MCMC to estimate the P(JM.-E) based on same belief network from Problem2, with the same random number sequence (PRNG). You should base you estimation on 2 rounds the computation at each step both symbolically and numerically through the network. Show s. Given the library-rat dynamic belief network studied in class examples, with the evidence: U,-U, U (where-U means "not umbrella) a) Evaluate the probability of rain at time 3. deterministic smoothing for the probabilities of each state. Namely, run the forward and backward algorithm Run ong each step on a graph that separately illustrates the application of the transition and sensor model (as in the slides Acing forward computations above the DBN and the backward computations below it
