Can someone help me with questions a) and b)? S. waters duri 1974-1999. The webs
ID: 3068799 • Letter: C
Question
Can someone help me with questions a) and b)?
S. waters duri 1974-1999. The website for this book contains the following data: the number of spills in the ith year, N,; the estimated amount of oil shipped through US waters as part of US import/export operations in the ith year, adjusted for spillage in international or foreign waters, bil; and the amount of oil shipped through U.S. waters during domestic shipments in the ith year, bz. The data are adapted from [11]. Oil shipment amounts are measured in billions of barrels (Bbbl) 2.5. There were 46 crude oil spills of at least 1000 barrels from tankers in U.S. waters du The volume of oil shipped is a measure of exposure to spill risk. Suppose we use the Poisson process assumption given by Nlbi, bn Poisson() where A1 bil + a2 bi2. The parameters of this model are and 2 , which represent the rate of spill occurrence per Bbbl oil shipped during import/export and domestic shipments, respectively. a. Derive the Newton-Raphson update for finding the MLEs of 1 and 2. b. Derive the Fisher scoring update for finding the MLEs of 1 and 2 e. Implement the Newton-Raphson and Fisher scoring methods for this problem, provide the MLEs, and compare the implementation ease and performance of the two methods d. Estimate standard errors for the MLEs of 1 and 2. e. Apply the method of steepest ascent. Use step-halving backtracking as necessary f. Apply quasi-Newton optimization with the Hessian approximation update given in (2.49). Compare performance with and without step halving. g. Construct a graph resembling Figure 2.8 that compares the paths taken by methods used in (a)-(0). Choose the plotting region and starting point to best illustrate the features of the algorithms' performanceExplanation / Answer
Q6.
N = 35000 barrels/day
t = 87 days
Barrel = 42 gala)
rate of crude in L/h
Rate = volume / time
Volume = 35000 * 42 = 1470000 gal / day
change time to hours
1 day = 24 h
Rate = 1470000 gal / day * 1 day / 24 h = 61250 gal/h
change gal to l
1 gla = 3.78 l
61250 ga/h * 3.785 L / gal = 231831.25 L/h
Rate in L/h = 231831.25 L/h
b)
N = 40
V = 500 mL each = 0.5 L
Total volume in case = 40*0.5 = 20 Liters
total volume equivalent
Total V = Rate L/h * total hours = 231831.25 L /h * 24 h / d * 87 d = 484063650 L
Total cases = (Total V) / Volume of cases = 484063650 L / 20 L = 24203182.5 cases