True or false : Grid approximation is a technique to approximate the posterior distribution
True
Tell the steps for the grid approximation
- We select points of theta for which we want to calculate grid
- For all the points, we do prior * likelihood
- We sum all the points to have the total
- You divide each point to the sum
True or false : Grid approximation is not very good tool when there is more than 1 parameter
True
Can you tell me the definition of a 95% confidence interval
- A 95 % confidence interval would contain the true value 95% of the time (No probability)
Can you tell me the definition of a 95% percentile interval / probability interval
A 95% percentile interval would contain the true value with a 95% probability
True or false : HDPI is the best interval we can have
True
Tell the 3 disadvantages with the HDPI
- Harder to compute
- Harder to understand
- It has greater simulation variance
True or false : If the priors are flat, the results of the bayesian methods will be similar to maximum likelihood
True
True or false : We use flat priors when we are uncertain about the parameter values
True
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
true
What are the 2 advantages of standardizing a predictor
- 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
- Glitches that occur with large numbers are avoided. Standardizing is very useful when variables are squared or raised to a power
What is the meaning of centering?
- Centering consists of substracting the mean of the predictor from the predictor. After centering, the estimate is easier to interpret.
- Before centering, intercept = average value of the outcome when the predictors is at its average value
- After centering, intercept = average outcome
Explain to me when we see a spurious relationship
When an irrelevant predictor is correlated to a relevant predictor, we can see a spurious relationship between the response and the irrelevant predictor
Explain to me the purpose of a predictor residual plot
- Run a regression with all predictors except for 1
- Then regress the response on the residuals
- Show the relationship between the response and the omitted predictor after removing the effect of the other predictors
Explain to me what is a counterfactual plot
- In a counterfactual plot, all predictors except for 1 are constant. The plot shows how the response reacts to change in one predictor
True or false : For cases where more than 1 variable has significant impact on the response, counterfactual plot may not be useful
true
Explain to me what is a posterior prediction plot
Show the predicted vs observed values of the response
What is a masked relationship?
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
True or false : Predictors that are too highly correlated result in a good model
False. It result in a poor model
Complete : Generally, correlation with absolute value higher than … will lead to poor result
0.9
True or false : Multicollinearity is part of a family of problems called non-identifiability
True
How do we solve the asymmetry problem for the categorical variables in the bayesian regression?
By putting an indice on the intercept
True or false : When predictors are multicollinear, the model makes poor predictions
False. The model still make good predictions
True or false : Estimates of coefficients for multicollinear models have high variance
True
