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使用 rstanarm 进行贝叶斯回归建模

Jake Thompson

Psychometrician, ATLAS, University of Kansas

概览

贝叶斯回归简介
定制贝叶斯回归模型
评估贝叶斯回归模型
展示与应用贝叶斯回归模型

频率学派回归回顾

使用普通最小二乘的频率学派回归
kidiq 数据

kidiq

# A tibble: 434 x 4
    kid_score mom_hs mom_iq mom_age
        <int>  <int>  <dbl>   <int>
  1        65      1  121.       27
  2        98      1   89.4      25
  3        85      1  115.       27
  4        83      1   99.4      25
  5       115      1   92.7      27
 # ... with 430 more rows

用母亲 IQ 预测孩子的 IQ 分数

lm_model <- lm(kid_score ~ mom_iq, data = kidiq)

summary(lm_model)

 Call:
 lm(formula = kid_score ~ mom_iq, data = kidiq)
 Residuals:
     Min      1Q  Median      3Q     Max 
 -56.753 -12.074   2.217  11.710  47.691 
 Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
 (Intercept) 25.79978    5.91741    4.36 1.63e-05 ***
 mom_iq       0.60997    0.05852   10.42  < 2e-16 ***
 ---
 Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 Residual standard error: 18.27 on 432 degrees of freedom
 Multiple R-squared:  0.201,  Adjusted R-squared:  0.1991 
 F-statistic: 108.6 on 1 and 432 DF,  p-value: < 2.2e-16

检查模型系数

使用 broom 包仅查看系数

library(broom)

tidy(lm_model)

            term   estimate  std.error statistic      p.value
   1 (Intercept) 25.7997778 5.91741208  4.359977 1.627847e-05
   2      mom_iq  0.6099746 0.05852092 10.423188 7.661950e-23

谨慎理解 p 值的含义

比较频率学派与贝叶斯概率

在乳房 X 光阳性的情况下，女性患癌的概率是多少？
- P(+M | C) = 0.9
- P(C) = 0.004
- P(+M) = (0.9 x 0.004) + (0.1 x 0.996) = 0.1
求 P(C | M+)?
- 0.036

Spotify 数据

songs

 # A tibble: 215 x 7
    track_name    artist_name song_age valence tempo popularity duration_ms
    <chr>         <chr>          <int>   <dbl> <dbl>      <int>       <int>
  1 Crazy In Love Beyoncé         5351   70.1   99.3         72      235933
  2 Naughty Girl  Beyoncé         5351   64.3  100.0         59      208600
  3 Baby Boy      Beyoncé         5351   77.4   91.0         57      244867
  4 Hip Hop Star  Beyoncé         5351   96.8  167.          39      222533
  5 Be With You   Beyoncé         5351   75.6   74.9         42      260160
  6 Me, Myself a… Beyoncé         5351   55.5   83.6         54      301173
  7 Yes           Beyoncé         5351   56.2  112.          43      259093
  8 Signs         Beyoncé         5351   39.8   74.3         41      298533
  9 Speechless    Beyoncé         5351    9.92 113.          41      360440
 # ... with 206 more rows

Ayo berlatih!

使用 rstanarm 进行贝叶斯回归建模