Question
The mode of these distributions can be approximated using MAP estimates. For 10 points each:
[10m] Name these updated distributions generated after considering observed data. In Bayesian inference, these distributions are proportional to the product of the likelihood and the prior distribution.
ANSWER: posterior distribution [or posterior probability]
[10e] Posterior probabilities are these kinds of probabilities that are calculated using Bayes’s theorem. For events A and B, this is the probability of event A occurring given that event B occurred.
ANSWER: conditional probability
[10h] These intervals are generated from the CDFs of posterior distributions. Confidence intervals are frequentist analogs to these intervals, which map where an unobserved parameter may fall at a certain probability.
ANSWER: credible intervals [reject “prediction intervals”]
<Science - Other Science>
Summary
| 2024 Booster Shot (Columbia) | 02/23/2024 | Y | 5 | 8.00 | 60% | 20% | 0% |
| 2024 Booster Shot (Great Lakes) | 03/09/2024 | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2024 Booster Shot (Vanderbilt) | 03/02/2024 | Y | 1 | 10.00 | 100% | 0% | 0% |
| 2024 Booster Shot (WUSTL) | 03/09/2024 | Y | 3 | 10.00 | 67% | 33% | 0% |
| 2024 Booster Shot (Waterloo) | 02/23/2024 | Y | 3 | 13.33 | 67% | 67% | 0% |
Data
| Toronto Tony Jingyu Chen eats quizbowl | Toronto Penguin World War | 10 | 10 | 0 | 20 |
| Waterloo Bust | Waterloo Cali | 10 | 10 | 0 | 20 |
| Ottawa | Toronto Pilk | 0 | 0 | 0 | 0 |