Question 4 10 Marks In Order To Predict The Average Dissolved Oxygen Do Concentration Mg L In A Lake Using Water 1 (65.03 KiB) Viewed 25 times
Question 4. (10 marks) In order to predict the average dissolved oxygen (DO) concentration (mg/L) in a lake using water temperature T (°C) as the predictor, the following measurements of DO and T were obtained: T (°C) DO (mg/L) 23.2 4.2 23.4 3.7 24.1 2.5 25.5 2.9 27.2 2.5 Theoretical considerations suggest that the relationship between DO and Tis ᎾᎢ DO = 47eºT where is a parameter to be inferred from the data. Answer the following questions:
Let 0 be the probability of the annual maximum flood exceeding 2500 ML/D. Answer the following questions: a) (5 marks) Assuming a non-informative prior and treating each annual flood as a Bernoulli trial, determine the posterior distribution of 0 with steps of 0.1. You are NOT required to calculate the constant of proportionality. b) (2.5 marks) What is the mode of the posterior distribution of 0? c) (2.5 marks) Assuming a Gaussian approximation, estimate the 95% confidence limits. Given the calculated uncertainty, would it be prudent to use the mode of 0 as a proxy for the true value of 0?
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