Publications by Yang Sun
505 Assignment 1
2E1. Which of the expressions below correspond to the statement: the probability of rain on Monday? (1) Pr(rain) (2) Pr(rain|Monday) (3) Pr(Monday|rain) (4) Pr(rain, Monday)/ Pr(Monday) (2)&(4) 2E2. Which of the following statements corresponds to the expression: Pr(Monday|rain)? (1) The probability of rain on Monday. (2) The probability of rain,...
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6E1. List three mechanisms by which multiple regression can produce false inferences about causal effects. #1.Multicollinearity #2.Post-treatment bias #3.Collider bias 6E2. For one of the mechanisms in the previous problem, provide an example of your choice, perhaps from your own research. library(rethinking) ## Loading required package: rstan #...
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5E1. Which of the linear models below are multiple linear regressions? \[\begin{align} {μ_i = α + βx_i} \tag{1}\\ μ_i = β_xx_i + β_zz_i \tag{2} \\ μ_i = β_xx_i + β_zz_i \tag{3} \\ μ_i = α + β(x_i − z_i) \tag{4} \\ μ_i = α + β_xx_i + β_zz_i \tag{5} \\ \end{align}\] #Model 1 --> has only one predictor xi --> not a multi...
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9E1. Which of the following is a requirement of the simple Metropolis algorithm? The parameters must be discrete. The likelihood function must be Gaussian. The proposal distribution must be symmetric. #3 is a requirement of the simple Metropolis algorithm 9E2. Gibbs sampling is more efficient than the Metropolis algorithm. How does it achieve t...
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7E1. State the three motivating criteria that define information entropy. Try to express each in your own words. #The motivating criteria are a measure of uncertainty which (1) should be measured on a continuous scale such that the spacing between adjacent values is consistent, (2) capture the size of the possibility space such that its value sca...
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8E1. For each of the causal relationships below, name a hypothetical third variable that would lead to an interaction effect: Bread dough rises because of yeast. Education leads to higher income. Gasoline makes a car go. #Commercial baking yeast is inactive below 40∘F and dies above 130∘F, so temperature would likely interact with yeast to ...
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11E1. If an event has probability 0.35, what are the log-odds of this event? p <- 0.35 p/(1-p) ## [1] 0.5384615 11E2. If an event has log-odds 3.2, what is the probability of this event? lo <- 3.2 lo/(1+lo) ## [1] 0.7619048 11E3. Suppose that a coefficient in a logistic regression has value 1.7. What does this imply about the proportional change ...
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