From 77b3625d2e1cba843d2ee9934247ba1160589f19 Mon Sep 17 00:00:00 2001 From: wizardforcel <562826179@qq.com> Date: Thu, 18 Jan 2018 19:58:45 +0800 Subject: [PATCH] ch11pic --- 11.md | 34 ++++++++++++++++++++++++++++++++++ img/11-1.png | Bin 0 -> 10807 bytes img/11-10.png | Bin 0 -> 17650 bytes img/11-11.png | Bin 0 -> 10486 bytes img/11-12.png | Bin 0 -> 14123 bytes img/11-13.png | Bin 0 -> 10486 bytes img/11-14.png | Bin 0 -> 14102 bytes img/11-15.png | Bin 0 -> 16199 bytes img/11-16.png | Bin 0 -> 10486 bytes img/11-17.png | Bin 0 -> 9188 bytes img/11-18.png | Bin 0 -> 12908 bytes img/11-2.png | Bin 0 -> 20410 bytes img/11-3.png | Bin 0 -> 19251 bytes img/11-4.png | Bin 0 -> 70470 bytes img/11-5.png | Bin 0 -> 20378 bytes img/11-6.png | Bin 0 -> 18813 bytes img/11-7.png | Bin 0 -> 18868 bytes img/11-8.png | Bin 0 -> 61284 bytes img/11-9.png | Bin 0 -> 14102 bytes 19 files changed, 34 insertions(+) create mode 100644 img/11-1.png create mode 100644 img/11-10.png create mode 100644 img/11-11.png create mode 100644 img/11-12.png create mode 100644 img/11-13.png create mode 100644 img/11-14.png create mode 100644 img/11-15.png create mode 100644 img/11-16.png create mode 100644 img/11-17.png create mode 100644 img/11-18.png create mode 100644 img/11-2.png create mode 100644 img/11-3.png create mode 100644 img/11-4.png create mode 100644 img/11-5.png create mode 100644 img/11-6.png create mode 100644 img/11-7.png create mode 100644 img/11-8.png create mode 100644 img/11-9.png diff --git a/11.md b/11.md index 3328442..8b5f260 100644 --- a/11.md +++ b/11.md @@ -113,6 +113,8 @@ scores_and_sections scores_and_sections.select('Midterm').hist(bins=np.arange(-0.5, 25.6, 1)) ``` +![](img/11-1.png) + 分数的第 85 个百分位数是多少? 为了使用`percentile`函数,创建包含期中分数的数组`scores`,并找到第 85 个百分位数: ```py @@ -253,6 +255,8 @@ sf_bins = np.arange(0, 700000, 25000) sf2015.select('Total Compensation').hist(bins=sf_bins) ``` +![](img/11-2.png) + 虽然大部分值都低于 300,000 美元,但有一些还是比较高的。 例如,首席投资官的总薪资不多是 65 万美元。 这就是为什么横轴延伸到了 700,000 美元。 ```py @@ -291,6 +295,8 @@ our_sample = sf2015.sample(500, with_replacement=False) our_sample.select('Total Compensation').hist(bins=sf_bins) ``` +![](img/11-3.png) + ```py est_median = percentile(50, our_sample.column('Total Compensation')) est_median @@ -320,6 +326,7 @@ est_median 为什么这是一个好主意? 按照平均定律,原始样本的分布可能与总体相似,所有“二次样本”的分布可能与原始样本相似。 因此,所有二次样本的分布也可能与总体相似。 +![](img/11-4.png) ### 二次样本的中位数 @@ -330,6 +337,8 @@ resample_1 = our_sample.sample() resample_1.select('Total Compensation').hist(bins=sf_bins) ``` +![](img/11-5.png) + ```py resampled_median_1 = percentile(50, resample_1.column('Total Compensation')) resampled_median_1 @@ -386,6 +395,8 @@ resampled_medians.hist() plots.scatter(pop_median, 0, color='red', s=30); ``` +![](img/11-6.png) + 重要的是要记住,红点是固定的:110,305.79 美元,总体的中位数。 经验直方图是随机抽取的结果,将相对于红点随机定位。 请记住,所有这些计算的重点是估计人口中位数,它是红点。我们的估计是所有随机生成的样本中位数,它们的直方图你在上面看到了。 我们希望这些估计量包含参数 - 如果没有,它们就脱线了。 @@ -416,6 +427,8 @@ plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=3, zord plots.scatter(pop_median, 0, color='red', s=30, zorder=2); ``` +![](img/11-7.png) + 我们例子中,估计量的“中间 95%”的区间捕获了参数。 但是,这是一个偶然吗? 要查看区间包含参数的频率,我们必须一遍又一遍地运行整个过程。具体而言,我们将重复以下过程 100 次: @@ -493,6 +506,8 @@ intervals.where('Left', are.below(pop_median)).where('Right', are.above(pop_medi 任何基于抽样的方法都有可能脱线。基于随机抽样的方法的优点是,我们可以量化它们可能脱线的频率。 +![](img/11-8.png) + 为了总结模拟所示的内容,假设你通过以下过程来估计总体中位数: 从总体中随机抽取一个大样本。 @@ -575,6 +590,8 @@ ratios ratios.select('Ratio BW/GD').hist() ``` +![](img/11-9.png) + 一眼望去,直方图看起来相当对称,密度在 4opd 到 4.5opd 的区间内是最大的。 但仔细一看,就可以看出一些比例相当大。 比率的最大值刚好超过 0.78opd,几乎是通常值的两倍。 ```py @@ -640,6 +657,8 @@ resampled_medians.hist(bins=15) plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); ``` +![](img/11-10.png) + 这个直方图和区间就像我们在前一节中绘制的直方图和区间,只有一个很大的区别 - 没有显示参数的红点。 我们不知道这个点应该在哪里,或者它是否在区间中。 我们只是有一个估计区间。 这是估计量的 95% 置信区间,因为生成它的过程在 95% 的时间中产生了良好的区间。 那肯定是在随机猜测! @@ -654,6 +673,8 @@ plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); baby.select('Maternal Age').hist() ``` +![](img/11-11.png) + ```py np.mean(baby.column('Maternal Age')) 27.228279386712096 @@ -705,6 +726,8 @@ resampled_means.hist(bins=15) plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); ``` +![](img/11-12.png) + 原始样本的均值(27.23 岁)同样接近区间中心。 这并不奇怪,因为每个自举样本都是从相同的原始样本中抽取的。 自举样本的均值大约对称分布原始样本(从其中抽取)的均值的两侧。 还要注意,即使所采样的年龄的直方图完全不是对称的,二次样本的均值的经验直方图也是大致对称的钟形: @@ -713,6 +736,8 @@ plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); baby.select('Maternal Age').hist() ``` +![](img/11-13.png) + 这是概率统计的中心极限定理的结果。 在后面的章节中,我们将看到这个定理是什么。 ### 80% 置信区间 @@ -728,6 +753,8 @@ resampled_means.hist(bins=15) plots.plot(make_array(left_80, right_80), make_array(0, 0), color='yellow', lw=8); ``` +![](img/11-14.png) + 这个 80% 置信区间比 95% 置信区间要短得多。 它只是约定 27.0 岁到约 27.4 岁。 虽然这是估计量的较窄区间,你知道这个过程在 80% 的时间内产生良好的区间。 之前过程产生了较宽的区间,但是我们对产生它的过程拥有更高的置信度。 @@ -803,6 +830,8 @@ resampled_proportions.hist(bins=15) plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); ``` +![](img/11-15.png) + ### 自举法的注意事项 自举法是一个优雅而强大的方法。在使用之前,记住一些要点非常重要。 @@ -880,6 +909,8 @@ baby = Table.read_table('baby.csv') baby.select('Maternal Age').hist() ``` +![](img/11-16.png) + 抽样年龄的一小部分在`(26.9, 27.6)`的区间内,你可能会预计总体中的百分比很小。 区间只是估计一个数字:总体中所有年龄的平均值。 但是,除了仅仅告诉我们这个参数有多大之外,用置信区间来估计一个参数确实有重要的用处。 @@ -945,6 +976,7 @@ hodgkins = hodgkins.with_column( hodgkins ``` +![](img/11-17.png) | height | rad | chemo | base | month15 | drop | | --- | --- | --- | --- | --- | --- | @@ -995,6 +1027,8 @@ resampled_means.hist() plots.plot(make_array(left, right), make_array(0, 0), color='yellow', lw=8); ``` +![](img/11-18.png) + 总体均值的 99% 置信区间是约 17 到约 40。区间不包含 0。因此,我们拒绝原假设。 但是请注意,我们所做的不仅仅是简单得出结论:总体均值不是 0,我们估计了均值的幅度是多大。这比仅仅说“不是 0”更有用。 diff --git a/img/11-1.png b/img/11-1.png new file mode 100644 index 0000000000000000000000000000000000000000..9fef7ffee706ff5a444e0a22164c965c8b5f6047 GIT binary patch literal 10807 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