Lab · Updating实验 · 更新
How far should a survey move last year’s notes?一次调查该把去年的笔记推动多远？
A district councillor has last year’s 24 consultation forms on a pedestrian scheme. About 30 percent of those forms supported it. This week 12 street interviews come back, and 8 of the 12 support the scheme. The councillor has to put one share in the Monday note. The dashed curve is last year’s forms, the prior. The dotted line is 8 out of 12. The solid curve is the updated share, the posterior. A heavy stack of last year’s forms barely moves when only 12 new interviews arrive.一位区议员有去年 24 份关于步行街方案的咨询表。其中大约三成表示支持。本周 12 份街访回来了，12 人里有 8 人支持。议员要在周一的说明里写下同一个比例。虚线是去年的表，也就是先验。点线是 12 人中的 8 人。实线是更新后的比例，也就是后验。去年的表如果很重，只来 12 份新访谈时，它几乎不动。
Why this matters.为何重要。 A short survey can feel like news. If last year’s notes are heavy, the briefing should barely move. If the survey grows, the old notes give way.一次短调查会让人觉得是新闻。去年的笔记如果很重，简报几乎不该动。调查变大，旧笔记才让路。
Try this试一试 Keep last year’s forms cautious and heavy, and this week’s interviews few but favorable. Then lighten those forms, or add interviews, and watch the solid curve follow the dotted line.去年的表保持谨慎而且很重，本周的访谈少但比较赞成。再把那些表减轻，或加上访谈，看实线跟着点线走。
Read the chart读这张图
If you misread this读错了会怎样
If the councillor tells the council the solid curve’s peak is what the district wants, the pedestrian scheme can be approved on a mix of last year’s 24 forms and this week’s 12 interviews. A different stack of last year’s forms would have peaked somewhere else.如果议员告诉区议会，实线的峰就是这个区想要的，步行街方案可能会在去年 24 份表和本周 12 份访谈的混合上被通过。换一叠去年的表，峰会在别处。
Enough, and not enough够用，以及不够
Enough to see a heavy pile of last year’s 24 forms hold the share near 30 percent until the number of interviews grows.够用来看见：去年 24 份表如果算得很重，比例会留在三成附近，直到访谈人数变多。
Not enough for Monday’s note to the council. It still has to say who filled last year’s forms, who was stopped on the street and who was missed, and that the update matches how those answers were collected.不够写给区议会的周一说明。说明仍要交代去年的表是谁填的，街上拦住了谁、漏了谁，以及更新的方式和这些答案的收集方式对得上。
Equations, assumptions, and limits方程、假设与限度
The prior is a beta distribution. Its mean is the prior share, and its weight is a count of imaginary past answers. The survey adds that many people in favor and the rest against. The posterior is the beta distribution with those counts folded in. The curves are drawn on the share from 0 to 1.先验是一个贝塔分布。它的均值是先验比例，它的分量是一批想象中的以往回答。调查再加上这么多赞成的人，其余算反对。后验是把这些计数折进去之后的贝塔分布。曲线画在从 0 到 1 的比例上。