Lab · Updating练习 · 更新
How far should this week’s chats move last year’s forms?本周这几句，该把去年的反馈表推动多远？
A hall tutor already has last year’s 24 feedback forms on whether to keep the overnight study room open. About 30 percent said yes. This week the tutor asks 12 students, and 8 of the 12 say yes. Monday’s note to the hall has to give one share. The dashed curve is last year’s forms, the prior: what was already on the desk before this week. The dotted line is 8 out of 12. The solid curve is the updated share, the posterior: last year’s forms after the new chats have been allowed to move them. If last year’s pile counts as heavy, 12 new chats barely move it.书院导师已经有去年 24 份反馈表，问的是通宵自修室要不要继续开。大约三成写了要。本周导师又问了 12 名同学，12 人里有 8 人说要。周一给书院的说明里得写下同一个比例。虚线是去年的表，也就是先验：本周的聊天到来之前，桌上已经有的看法。点线是 12 人里的 8 人。实线是更新后的比例，也就是后验：新的回答被允许推动之后，去年那些表现在落在哪里。去年的表如果算得很重，新来的 12 句几乎推不动它。
Why it matters.为什么要紧。 A short round of chats can feel like the answer. If last year’s forms count heavily, Monday’s share should barely move. If you ask more people, the old forms give way.问很少的几个人，会让人觉得答案已经有了。去年的表如果算得很重，周一写下的比例几乎不该动。问的人变多，旧表才让路。
Try this试一试 Keep last year’s forms cautious and heavy, and this week’s chats few but in favor of keeping the room. Then make those forms count for less, or ask more students, and watch the solid curve follow the dotted line.去年的表保持偏低，而且算得很重；本周问的人少，但多数希望继续开。再把那些表的分量减轻，或再多问几个人，看实线跟着点线走。
How to read the chart怎么读这张图
If you read this wrong要是读错了
If the tutor tells the hall that the peak of the solid curve is “what students want,” the room can stay open on a mix of last year’s 24 forms and this week’s 12 chats. A different stack of last year’s forms would have peaked somewhere else.如果导师告诉书院，实线的峰就是“同学想要的”，自修室可能会在去年 24 份表和本周 12 次回答的混合上继续开。换一叠去年的表，峰会落在别处。
What this picture is enough for这张图够说明什么
Enough to see a heavy pile of last year’s 24 forms hold the share near 30 percent until more students are asked.看得出：去年 24 份表如果算得很重，比例会留在三成附近，直到问到的人变多。
Not enough for Monday’s note to the hall. It still has to say who filled last year’s forms, who was asked this week and who was missed, and that this way of updating matches how those answers were collected.还不够拿来写给书院的周一说明。说明仍要交代去年的表是谁填的，本周问了谁、漏了谁，以及这种更新和收集回答的方式对得上。
The equation, and where it stops式子、假设和边界
The prior is a beta distribution: a curve that says where an unknown share might sit. Its center is the share on last year’s forms, and its weight is a count of imaginary past answers — how heavily those forms count. This week adds that many students in favor and the rest against. The posterior is the same kind of curve with those counts folded in. Both curves are drawn on the share from 0 to 1.先验是一个贝塔分布：一条曲线，说这个还不知道的比例大概落在哪里。它的中心是去年表上的比例，它的分量是一批想象中的旧回答，也就是那些表算得多重。本周再加上这么多说“要”的人，其余算“不要”。后验是把这些计数折进去之后的同一类曲线。两条曲线都画在从 0 到 1 的比例上。