Additive Gaussian noise channel 𝑌𝑖 = 𝐴 + 𝑍𝑖 for 𝑖 = 1,2,....,1000 where 𝑍𝑖's are i.i.d. zero mean Gaussian random variables with variance 𝜃, i.e. 𝑍𝑖~𝒩(0, 𝜃). The signal 𝐴, and the noises 𝑍𝑖 ’s are independent.
The maximum likelihood estimate of the variance 𝜃 using the first N samples where 𝑁 ∈ {10,100,1000}. For each case, calculate the absolute error between the estimated and the true value of 𝜃, i.e. |𝜃 − 𝜃𝑡𝑟𝑢𝑒| where 𝜃𝑡𝑟𝑢𝑒 = "0.25".
Maximum-a-posteriori (MAP) estimator of 𝜃 using the following scale inverse chisquare prior. MAP estimates of 𝜃 using the first N samples, where 𝑁 ∈ {10,100,1000}. Setting the prior parameters such that Tao = 0.25 and v = 100.
