直方图与密度图（Julia）

作者

[编辑] 王诗翔

[贡献] Claude Code —— AI 生成，独立 AI 复核；

修改于

2026-10-19

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直方图与核密度估计（KDE）揭示分布的形状——众数、偏度和离散程度，这些是汇总统计量无法呈现的。在生物医学研究中，它们常用于在统计建模之前检查基因表达分布、荧光强度轮廓和质量控制指标。CairoMakie 以统一的风格提供 hist、density 与 ecdfplot。

示例

环境配置

  • 系统要求：跨平台（Linux/MacOS/Windows）
  • 编程语言：Julia
  • 依赖包：CairoMakie、DataFrames、Statistics 
using CairoMakie
using DataFrames
using Statistics
using Random

数据准备

我们模拟一个基因在对照与刺激两种条件下的表达测量。刺激条件是两个细胞亚群的混合，产生直方图与 KDE 旨在揭示的双峰结构。

Random.seed!(11)

n = 800
control = 4.0 .+ 0.8 .* randn(n)
stimulated = vcat(4.2 .+ 0.8 .* randn(n ÷ 2),     # 亚群 A
                  7.5 .+ 0.9 .* randn(n ÷ 2))     # 亚群 B
800-element Vector{Float64}:
 3.865937421494608
 3.974499458766426
 5.381090416248313
 4.110384484371341
 3.7223752847320704
 4.39180807907198
 4.330339266391583
 4.148369000454984
 5.054781277267091
 3.2025996007194766
 ⋮
 5.9133709566761254
 6.211074468067516
 6.648365564220777
 7.991501574926472
 7.918335795750192
 7.957618819674784
 6.908673960979235
 6.625134971802873
 7.20347852264799

可视化

直方图

分箱宽度控制偏差–方差的权衡：分箱太少会隐藏结构，太多则放大噪声。拿不准时，可比较 bins = 15 与更细的分箱设置。

fig = Figure(size = (460, 340))
ax = Axis(fig[1, 1], xlabel = "Gene expression (log2 counts)", ylabel = "Count")
hist!(ax, control; bins = 30, color = :skyblue,
      strokecolor = :white, strokewidth = 0.6)
hidespines!(ax, :t, :r)
fig
图 1: 模拟表达值的直方图

直方图叠加核密度

在计数轴上叠加核密度曲线，既能勾勒分布轮廓，又保留了原始计数信息。

fig = Figure(size = (460, 340))
ax = Axis(fig[1, 1], xlabel = "Gene expression (log2 counts)", ylabel = "Count")
hist!(ax, control; bins = 30, color = :seagreen,
      strokecolor = :white, strokewidth = 0.6)
density!(ax, control; color = (:seagreen, 0.0), strokecolor = :darkgreen,
         strokewidth = 2, offset = 0)
hidespines!(ax, :t, :r)
fig
图 2: 直方图叠加核密度曲线

分组密度曲线比较

对于两组或多组数据，叠加半透明密度曲线可直接看出刺激样本的双峰特征。

fig = Figure(size = (460, 340))
ax = Axis(fig[1, 1], xlabel = "Gene expression (log2 counts)", ylabel = "Density")
density!(ax, control; color = (:steelblue, 0.35), strokecolor = :steelblue, strokewidth = 1.8)
density!(ax, stimulated; color = (:tomato, 0.35), strokecolor = :tomato, strokewidth = 1.8)
hidespines!(ax, :t, :r)
Legend(fig[1, 2], [LineElement(color = :steelblue, linewidth = 2),
                   LineElement(color = :tomato, linewidth = 2)],
       ["Control", "Stimulated"], framevisible = false)
fig
图 3: 对照与刺激条件的密度曲线叠加

经验累积分布函数

ECDF 无需分箱或平滑即可展示每个观测值，是审查队列间分布漂移的理想工具。

fig = Figure(size = (460, 340))
ax = Axis(fig[1, 1], xlabel = "Gene expression (log2 counts)", ylabel = "Proportion")
ecdfplot!(ax, control; color = :steelblue, linewidth = 2)
ecdfplot!(ax, stimulated; color = :tomato, linewidth = 2)
hidespines!(ax, :t, :r)
Legend(fig[1, 2], [LineElement(color = :steelblue, linewidth = 2),
                   LineElement(color = :tomato, linewidth = 2)],
       ["Control", "Stimulated"], framevisible = false)
fig
图 4: 按条件分组经验累积分布函数

参考文献

  1. Makie development team. Makie.jl documentation — hist, density, ecdfplot. https://docs.makie.org/stable/reference/plots/hist
  2. Danisch, S., & Krumbiegel, J. (2021). Makie.jl: Flexible high-performance data visualization for Julia. Journal of Open Source Software, 6(65), 3349.