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Bayesian Statistics: Techniques and Models, 1.11 (Q) Lesson 2

Lesson 2 1. Which of the following is one major difference between the frequentist and Bayesian approach to modeling data? The frequentist paradigm treats the data as fixed while the Bayesian paradigm considers data to be random. Frequentist models require a guess of parameter values to initialize models while Bayesian models require initial distributions for the parameters. Frequentist models are deterministic (don't use probability) while Bayesian models are stochastic (based on probability). Frequentists treat the unknown parameters as fixed (constant) while Bayesians treat unknown parameters as random variables. 2. Suppose we have a statistical model with unknown parameter \thetaθ, and we assume a normal prior \theta \sim \\{N}(\mu_0, \sigma_0^2)θ∼N(μ0​,σ02​), where \mu_0μ0​ is the prior mean and \sigma_0^2σ02​ is the prior variance. What does increasing \sigma_0^2σ02​ say about our prior beliefs about \thetaθ? Increasing the variance of the prior narrows the range of what we think \thetaθ might be, indicating greater confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior widens the range of what we think \thetaθ might be, indicating greater confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior widens the range of what we think \thetaθ might be, indicating less confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior narrows the range of what we think \thetaθ might be, indicating less confidence in our prior mean guess \mu_0μ0​.



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Lesson 2 1. Which of the following is one major difference between the frequentist and Bayesian approach to modeling data? The frequentist paradigm treats the data as fixed while the Bayesian paradigm considers data to be random. Frequentist models require a guess of parameter values to initialize models while Bayesian models require initial distributions for the parameters. Frequentist models are deterministic (don't use probability) while Bayesian models are stochastic (based on probability). Frequentists treat the unknown parameters as fixed (constant) while Bayesians treat unknown parameters as random variables. 2. Suppose we have a statistical model with unknown parameter \thetaθ, and we assume a normal prior \theta \sim \\{N}(\mu_0, \sigma_0^2)θ∼N(μ0​,σ02​), where \mu_0μ0​ is the prior mean and \sigma_0^2σ02​ is the prior variance. What does increasing \sigma_0^2σ02​ say about our prior beliefs about \thetaθ? Increasing the variance of the prior narrows the range of what we think \thetaθ might be, indicating greater confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior widens the range of what we think \thetaθ might be, indicating greater confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior widens the range of what we think \thetaθ might be, indicating less confidence in our prior mean guess \mu_0μ0​. Increasing the variance of the prior narrows the range of what we think \thetaθ might be, indicating less confidence in our prior mean guess \mu_0μ0​.


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