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