Consider the problem of Bayesian inference, where our goal is to estimate posterior, P (0|D), of...

 

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Consider the problem of Bayesian inference, where our goal is to estimate posterior, P (0|D), of the parameters given a dataset D. P(0|D) = P(D|0)P(0) P (D) Answer the following 1. Explain the challenges in closed-form computation of P(8|D) for a large parameter space. [1] 2. Propose a hill-climbing method to estimate the values of parameter for known prior P(0) and likelihood P(DIO), distributions. [2] 3. Now, let us assume that likelihood of the data is a univariate Gaussian distribution N (, 1) with mean and variance 1. Further, for simplicity let us assume that prior distribution P() is also known to be N(0,1). Generate 20 data points from the standard normal distribution using a random number generator for example numpy Python library and show that the value of u for the generated data, estimated using the method proposed in the answer to the previous part of the question, is 0. [4] Consider the problem of Bayesian inference, where our goal is to estimate posterior, P (0|D), of the parameters given a dataset D. P(0|D) = P(D|0)P(0) P (D) Answer the following 1. Explain the challenges in closed-form computation of P(8|D) for a large parameter space. [1] 2. Propose a hill-climbing method to estimate the values of parameter for known prior P(0) and likelihood P(DIO), distributions. [2] 3. Now, let us assume that likelihood of the data is a univariate Gaussian distribution N (, 1) with mean and variance 1. Further, for simplicity let us assume that prior distribution P() is also known to be N(0,1). Generate 20 data points from the standard normal distribution using a random number generator for example numpy Python library and show that the value of u for the generated data, estimated using the method proposed in the answer to the previous part of the question, is 0. [4]