Number 1 Of These Questions Is From Bayesian Statistical Inf

Number 1of These Question Is From Bayesian Statistical Inference Topi

Number 1of these question is from Bayesian statistical inference topic. so, please use the formula and define the parameters accordingly. please a detailed solution is needed. Number 2 is from Likelihood Ratio Test. the LRT must be derived according to the instruction. Also, the rejection region must be well defined and C for level α = 0.05. please, ensure they are well defined with few comments. A detailed step by step solution is needed. Solution can be uploaded in handwritten form in order to save time and effort as long as it is clear and readable. Lastly, time for collection is 11:00 a.m.

Paper For Above instruction

The assignment encompasses two statistically significant questions: one centered on Bayesian inference and the other on the likelihood ratio test (LRT). The first question requires applying Bayesian statistical principles to a given problem, involving the formulation of prior and posterior distributions, the use of Bayes' theorem, and parameters' interpretation. The second question demands deriving the likelihood ratio test for specified hypotheses, defining the test statistic, establishing the rejection region at a significance level of α = 0.05, and providing a step-by-step detailed solution.

In addressing the Bayesian inference question, it is essential to clearly define all parameters involved and utilize the relevant formulas accurately. This includes prior probability distributions, the likelihood function, and the posterior distribution calculation. A thorough explanation of assumptions, the choice of priors, and the computational steps should be included. The goal is to illustrate the Bayesian updating process from prior to posterior and interpret the results within the context of the problem.

For the likelihood ratio test, the derivation begins with establishing null and alternative hypotheses relevant to the data. The likelihood function under each hypothesis should be formulated explicitly, followed by deriving the likelihood ratio statistic. The test statistic must then be compared to a critical value determined by the chi-square distribution at α = 0.05. The rejection region should be specified clearly, and the decision rule explained explicitly. It is important to include various comments to clarify each step, ensuring transparency and comprehensibility of the procedure.

Furthermore, all calculations should be detailed, and the solution can be presented in handwritten form to facilitate clarity and readability. Time constraints specify that collection of the handwritten work is scheduled for 11:00 a.m., emphasizing the importance of clarity in the presentation.

References

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• Rao, C. R. (1973). Linear Statistical Inference and Its Applications. Wiley.
• Wilks, S. S. (1938). The Large-Sample Distribution of the Likelihood Ratio Test. Annals of Mathematical Statistics, 9(1), 60–62.
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