Questions #1

Question 1

True or false : Grid approximation is a technique to approximate the posterior distribution

Answer 1

True

Question 2

Tell the steps for the grid approximation

Answer 2

1. We select points of theta for which we want to calculate grid
2. For all the points, we do prior * likelihood
3. We sum all the points to have the total
4. You divide each point to the sum

Question 3

True or false : Grid approximation is not very good tool when there is more than 1 parameter

Answer 3

True

Question 4

Can you tell me the definition of a 95% confidence interval

Answer 4

1. A 95 % confidence interval would contain the true value 95% of the time (No probability)

Question 5

Can you tell me the definition of a 95% percentile interval / probability interval

Answer 5

A 95% percentile interval would contain the true value with a 95% probability

Question 6

True or false : HDPI is the best interval we can have

Answer 6

True

Question 7

Tell the 3 disadvantages with the HDPI

Answer 7

1. Harder to compute
2. Harder to understand
3. It has greater simulation variance

Question 8

True or false : If the priors are flat, the results of the bayesian methods will be similar to maximum likelihood

Answer 8

True

Question 9

True or false : We use flat priors when we are uncertain about the parameter values

Answer 9

True

Question 10

True or false : In a model with 1 predictor, if the estimates for the intercept and coefficient of the predictor are highly correlated, centering the predictor may resolve the problem

Answer 10

true

Question 11

What are the 2 advantages of standardizing a predictor

Answer 11

1. It may make interpretation easier. Adding 1 to a standardized variable is equivalent to adding 1 standard deviation. But if we want to interpret on the natural scale, more difficult
2. Glitches that occur with large numbers are avoided. Standardizing is very useful when variables are squared or raised to a power

Question 12

What is the meaning of centering?

Answer 12

1. Centering consists of substracting the mean of the predictor from the predictor. After centering, the estimate is easier to interpret.
2. Before centering, intercept = average value of the outcome when the predictors is at its average value
3. After centering, intercept = average outcome

Question 13

Explain to me when we see a spurious relationship

Answer 13

When an irrelevant predictor is correlated to a relevant predictor, we can see a spurious relationship between the response and the irrelevant predictor

Question 14

Explain to me the purpose of a predictor residual plot

Answer 14

1. Run a regression with all predictors except for 1
2. Then regress the response on the residuals
3. Show the relationship between the response and the omitted predictor after removing the effect of the other predictors

Question 15

Explain to me what is a counterfactual plot

Answer 15

1. In a counterfactual plot, all predictors except for 1 are constant. The plot shows how the response reacts to change in one predictor

Question 16

True or false : For cases where more than 1 variable has significant impact on the response, counterfactual plot may not be useful

Answer 16

true

Question 17

Explain to me what is a posterior prediction plot

Answer 17

Show the predicted vs observed values of the response

Question 18

What is a masked relationship?

Answer 18

When a relationship between a predictor and the response is not significant when it is the only predictor in the regression, but is significant when there is another predictor in the regression. Happening when both predictors are correlated to each other, but one is positively correlated with the response, and the other one is negatively correlated with the response

Question 19

True or false : Predictors that are too highly correlated result in a good model

Answer 19

False. It result in a poor model

Question 20

Complete : Generally, correlation with absolute value higher than … will lead to poor result

Answer 20

0.9

Question 21

True or false : Multicollinearity is part of a family of problems called non-identifiability

Answer 21

True

Question 22

How do we solve the asymmetry problem for the categorical variables in the bayesian regression?

Answer 22

By putting an indice on the intercept

Question 23

True or false : When predictors are multicollinear, the model makes poor predictions

Answer 23

False. The model still make good predictions

Question 24

True or false : Estimates of coefficients for multicollinear models have high variance

Answer 24

True

Question 25

True or false : The coefficients of predictors with positive correlation have negative correlation

Answer 25

True