Reference no: EM131245796
In this problem you will tackle a challenging case when the parameters are degenerate: that is, there is a special combination if x1 and x2 where the model makes the same prediction while simultaneously varying the values of both x1 and x2. In such situations, neural networks trying to learn the likelihood surface may also experience significant difficulties. Obviously, the problem gets even worst when the dimensionality of the parameter space grows beyond two.
In the presence of a model degeneracy, one may encounter a likelihood function such as
L1(X1, X2) = exp (- (1 - x1)2 - 100 (x2 - x12)2) .
(a) Plot In (L1(x1, x2)) over the region x1, x2 ∈ [-5, 5]. The model's degeneracy will show up as lines in the x1-x2 plane where the value of ln L1 does not change.
(b) Modify the code you wrote to solve problem 2 to compute the value of
Z1 = -5∫5 -5∫5 L1(X1, X2) dX1 dX2
(c) Let N = 10k for k = 2,3,4, ... and compute In (Z1) by continually increasing N. Continue increasing N until you can convincingly get at least 2 digits of precision. Quote some values of N and In (Z1).
(d) By any means possible (using your code or some other way entirely), compute Z2 for likelihood function
L2(X1, X2) = 1
What fits the data better, model 1 or model 2?
|
Describe the penalties and fines that exist for offenders
: Suggest a change or ratification of the law and explain how your changes will impact society as well as those convicted of the crime. Summarize the challenges the prosecution faced in a trial from your research and whether you believe they could ..
|
|
What is the speed of the dragster at this point
: A second camera filming the dragster is located on the starting line 120 ft away from the dragster at the start of the race. How fast is this camera turning 2 s after the start of the race?
|
|
Calculate gross profit ratio and current ratio
: Calculate Gross profit ratio, current ratio and debt-equity ratio from the following information: - Net sales = 30,000.- Cost of sales= 20,000 - Net profit= 3000.
|
|
How would you estimate the additional dollar cost
: How would you estimate the additional dollar cost of each additional salesperson? How would you use these cost and revenue estimates to determine whether a sales force increase (or possibly a decrease) is warranted?
|
|
Modify the code you wrote to solve problem
: Plot In (L1(x1, x2)) over the region x1, x2 ∈ [-5, 5]. The model's degeneracy will show up as lines in the x1-x2 plane where the value of ln L1 does not change.
|
|
How much revenue was earned from digital sales
: Tropical music brought in twice as much as urban music, and pop/rock music brought in $7 million more than the others combined. How much revenue was earned from digital sales in each of the three categories?
|
|
Pre and post implementation plan of the new customer systems
: a comprehensive pre and post implementation plan of the new customer systems for the organisation; an implementation plan detailing time, cost and resource schedules. This is a project management document and you must fully demonstrate your skills ..
|
|
Analyze effect of the democratic approach to store operation
: Whole Foods now faces a significant amount of competition. Analyze effects of the democratic approach to store operation and hiring new associates on store performance.
|
|
Calculate the intrinsic value of the firm
: Use the capital asset pricing model (CAPM) to calculate the required rate of return for equity financing purposes;- Calculate the intrinsic value of the firm and stock price using the FCF valuation model.
|