Ballpark first forecast based on simple math
Avg # tests per day for the last 8 days = 150,025 . . .
(fun fact: during that period on 4 out of 7 days fewer people were tested than on the previous day)
Avg # of new tests are positive in the last 7 days = 28,197
(fun fact: the days with the lowest % of positive cases were the days when the # of tests increased the most = test more people and the % positive falls)
Because the variation in the # of new tests is so great on a day to day basis, and there's no clear trajectory of increasing or decreasing rates of testing, I'm going to use the avg # of tests per day.
Because the % of new cases seems to be linked more closely to the # of tests than to the date, I"m going to use the avg % of new cases.
Therefore: I going to start off assuming that 150,025 x 7 = 1,050,175 new tests will be done by 4/26
and that 18.6% of those tests will be positive , so 1,050,175 x .186 = 195,332 new positive cases
195,332 + 749,203 (current count) = 944,535 positive cases by EoD 4/26
using the average of 28,197 new positive cases per day in the last 7 days = 197,379
197,379 + 749,203 = 946,582 positive cases by EoD 4/26
What might impact the rate of positive cases:
Decrease due to social distancing
Increase due to delay between exposure & symptoms
"France . . . went into lockdown on the 17th March 2020. . . . The lockdown reduced the reproductive number from 3.3 to 0.5 (84% reduction).. . . "
I'm assuming that the lockdown in the US will have/is having a similar effect.
How do you get 54%, as opposed to 55% or 53%?
re: How do you get 54%, as opposed to 55% or 53%?
he-he, good question! You caught me just making a guess and employing some of my personal rules.
One of my rules is: "Do not forecast strongly against your own best estimate". I estimated 944-947 cases, so I went higher on the bin that those numbers fall within. I wanted my forecast to be higher in that bin than in all others combined.
But my estimates are so close to the upper range of the bin they're in, that I thought it prudent to forecast in the next range up. In the last week there was a variation of 6,312 positive cases between the highest & lowest days.
But that doesn't address your specific question: 55 vs 53. The honest answer was "whim".
Huh. Any other such personal rules you are willing to share?
Other personal rules:
1) Don't go "polar" (0 or 100%) . The last 10% really costs if you're wrong. The best forecasters rarely go polar.
2) Don't flip. After a year I looked at all the forecasts that I had flipped on and discovered that if I had not flipped I would have done better!
3) If really tempted to flip, go to 50% first.
4) Don't forecast strongly against present reality
5) Think like them. Don't be super enamored of your own fantasy or theories. It doesn't matter what you think; what matters is what the decision-makers think.
6) The more people/organizations involved in a decision the longer it will take.
7) When the decision is up to one person--DJT for example--the question can resolve in a blink and it may not conform to any past decisions.
8) Sports are upsetting! High-profile sporting events often result in personal bests & personal worsts, so upsets are possible
9) Nobody is always correct. Carefully ponder the forecasts of wiser forecasters but be true to yourself.
10) Parse the question. Know exactly what it says & doesn't say. Get familiar with the resolution criteria/site
11) Be humble. Be honest. Be generous. Be respectful. Be nice. No name calling.
What are yours?
Some of my rules/habits:
1) Let go. Be free. Don't be attached to forecasts. This also manifests as forecasting "twichily" and often.
2) Would I bet on this? If I have a 90% prediction, would I see a 1:9 bet as fair? This also works the other way; if I'd be willing to take a 1:9 bet to one side, and a 1:4 bet to the other side, then the implied odds are in between ~1:6 (1: sqrt(9*4))
3) Notice when I'm confused. For example:
- I'm confused about this question on the russian referendum: https://www.gjopen.com/questions/1595-before-1-january-2021-will-the-russian-constitution-be-amended-to-allow-vladimir-putin-to-remain-president-after-his-current-term; it seems that the aggregate looks way to high, and that there's nothing really stopping Putin from making the referendum happen next year instead.
- I was confused by this question on the Ghana elections: https://www.gjopen.com/questions/1590-how-many-seats-will-the-new-patriotic-party-win-in-ghana-s-2020-parliamentary-elections, but then the aggregate became more sane.
- The question on Italy's prime ministership also confuses me, given that Conte is rather popular atm. https://www.gjopen.com/questions/1502-will-there-be-a-new-prime-minister-of-italy-before-24-january-2021
4) Don't do ideologies
5) Laplace's rule is your friend.
6) Ask questions. See what models other people have. Or, how I like to call it, "steal other people's superpowers". e.g., your rules seem like useful heuristics; I'll see how they work for me. Thank you.
7) Do a fair bit of my own research. Not necessarily for every forecast, but do it, rather than tracking majority opinion.
@GL2814: I too like Loki :).
Only comment: if I´m sure, I will go polar anyway. That´s the case at GJ 2.0 with many questions right now, and quite a lot here too (worked fine so far). But of course you´re right: if I wanted to be on the leaderboard for the challenges (like you are), that might not be so clever on the long run, because one failure could cost dearly.
So I've been thinking about this. If you have 10 questions and assign 90% to each, and then write 100% instead, then you have a 35% chance of a perfect Brier-score, and you win the challenge. If you instead write your 90%, you are outcompeted by the people who were overconfident in that particular challenge. Similarly, maximizing your probability of being in the top 20 for any particular challenge (or, indeed, your probability of being in the top 2%) is different from maximizing your expected score.
It´s exponetial. If you are wrong 50:50, your brier will be 0.50 on the average every time. If you´re 100% right, it´s brier 0.0. If you are 100% wrong, it will be 2.0. You will need lots of other questions to recover from that, if you are NOT right.