从图灵模型在Julia中绘制可信区间

好的，我在Turing.jl中用下面的代码（我复制了McElreath的统计反思）计算出了一元线性模型的可信区间。这个特殊的练习在第4章中。如果有人已经用图灵绘制了这些类型的模型，并能给我一个指导，那就太好了

单变量模型代码：

    using Turing
    using StatsPlots
    using Plots

    height = df2.height

    weight = df2.weight

    @model heightmodel(y, x) = begin
        #priors
        α ~ Normal(178, 100)
        σ ~ Uniform(0, 50)
        β ~ LogNormal(0, 10)

        x_bar = mean(x)
        #model

            μ = α .+ (x.-x_bar).*β
        y ~ MvNormal(μ, σ)
    end

    chns = sample(heightmodel(height, weight), NUTS(), 100000)

    ## code 4.43
    describe(chns) |> display

    # covariance and correlation

    alph = get(chns, :α)[1].data

    bet = get(chns, :β)[1].data

    sigm = get(chns, :σ)[1].data


    vecs = (alph[1:352], bet[1:352])
    arr = vcat(transpose.(vecs)...)'

    ss = [vec(alph + bet.*(x)) for x in 25:1:70]

    arrr = vcat(transpose.(ss)...)'

    plot([mean(arrr[:,x]) for x in 1:46],25:1:70, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))

    weight_s = (df.weight .-mean(df.weight))./std(df.weight)

    weight_s² = weight_s.^2

    @model heightmodel(height, weight, weight²) = begin
        #priors
        α ~ Normal(178, 20)
        σ ~ Uniform(0, 50)
        β1 ~ LogNormal(0, 1)
        β2 ~ Normal(0, 1)
        #model
        μ = α .+ weight.*β1 + weight².*β2
        height ~ MvNormal(μ, σ)
    end

    chns = sample(heightmodel(height, weight_s, weight_s²), NUTS(), 100000)

    describe(chns) |> display

    ### painting the fit

    alph = get(chns, :α)[1].data

    bet1 = get(chns, :β1)[1].data

    bet2 = get(chns, :β2)[1].data



    vecs = (alph[1:99000], bet1[1:99000], bet2[1:99000])
    arr = vcat(transpose.(vecs)...)'


    polinomial = [vec(alph + bet1.*(x) + bet2.*(x.^2)) for x in -2:0.01:2]

    arrr = vcat(transpose.(polinomial)...)'

    plot([mean(arrr[:,x]) for x in 1:401],-2:0.01:2, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))

可信区间单变量：

然而，当我试图用一个多变量函数复制它时，会得出非常奇怪的结果：

多元模型代码：

    using Turing
    using StatsPlots
    using Plots

    height = df2.height

    weight = df2.weight

    @model heightmodel(y, x) = begin
        #priors
        α ~ Normal(178, 100)
        σ ~ Uniform(0, 50)
        β ~ LogNormal(0, 10)

        x_bar = mean(x)
        #model

            μ = α .+ (x.-x_bar).*β
        y ~ MvNormal(μ, σ)
    end

    chns = sample(heightmodel(height, weight), NUTS(), 100000)

    ## code 4.43
    describe(chns) |> display

    # covariance and correlation

    alph = get(chns, :α)[1].data

    bet = get(chns, :β)[1].data

    sigm = get(chns, :σ)[1].data


    vecs = (alph[1:352], bet[1:352])
    arr = vcat(transpose.(vecs)...)'

    ss = [vec(alph + bet.*(x)) for x in 25:1:70]

    arrr = vcat(transpose.(ss)...)'

    plot([mean(arrr[:,x]) for x in 1:46],25:1:70, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))

    weight_s = (df.weight .-mean(df.weight))./std(df.weight)

    weight_s² = weight_s.^2

    @model heightmodel(height, weight, weight²) = begin
        #priors
        α ~ Normal(178, 20)
        σ ~ Uniform(0, 50)
        β1 ~ LogNormal(0, 1)
        β2 ~ Normal(0, 1)
        #model
        μ = α .+ weight.*β1 + weight².*β2
        height ~ MvNormal(μ, σ)
    end

    chns = sample(heightmodel(height, weight_s, weight_s²), NUTS(), 100000)

    describe(chns) |> display

    ### painting the fit

    alph = get(chns, :α)[1].data

    bet1 = get(chns, :β1)[1].data

    bet2 = get(chns, :β2)[1].data



    vecs = (alph[1:99000], bet1[1:99000], bet2[1:99000])
    arr = vcat(transpose.(vecs)...)'


    polinomial = [vec(alph + bet1.*(x) + bet2.*(x.^2)) for x in -2:0.01:2]

    arrr = vcat(transpose.(polinomial)...)'

    plot([mean(arrr[:,x]) for x in 1:401],-2:0.01:2, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))

可信区间单变量：

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在朱莉娅·斯莱克频道（）中，詹斯很好心地给了我答案。这要归功于他——他没有一个SO账户

主要的问题是，我缺乏简单性，试图以错误的方式绘制平均值——我可以补充一句，这种方式效率很低，也很奇怪。每个参数都有一个向量，对应于后验分布的99000次绘制，我试图通过矩阵绘制平均值，但首先定义中值然后绘制它要容易得多，然后你不会像我计算平均值那样出错

旧代码

vecs = (alph[1:99000], bet1[1:99000], bet2[1:99000])
arr = vcat(transpose.(vecs)...)'
[mean(arrr[:,x]) for x in 1:401]

可以写为：

testweights = -2:0.01:2
arr = [fheight.(w, res.α, res.β1, res.β2) for w in testweights]
m = [mean(v) for v in arr]

此外，延斯定义可信区间的方式更加优雅和儒略：

詹斯密码：

quantiles = [quantile(v, [0.1, 0.9]) for v in arr]
lower = [q[1] - m for (q, m) in zip(quantiles, m)]
upper = [q[2] - m for (q, m) in zip(quantiles, m)]

我的代码：

ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))

完整解决方案：

weight_s = (d.weight .-mean(d.weight))./std(d.weight)
height = d.height
@model heightmodel(height, weight) = begin
    #priors
    α ~ Normal(178, 20)´
    σ ~ Uniform(0, 50)
    β1 ~ LogNormal(0, 1)
    β2 ~ Normal(0, 1)
    #model
    μ = α .+ weight .* β1 + weight.^2 .* β2
    # or μ = fheight.(weight, α, β1, β2) if we are defining fheigth anyways
    height ~ MvNormal(μ, σ)
end
chns = sample(heightmodel(height, weight_s), NUTS(), 10000)
describe(chns) |> display
res = DataFrame(chns)
fheight(weight, α, β1, β2) = α + weight * β1 + weight^2 * β2
testweights = -2:0.01:2
arr = [fheight.(w, res.α, res.β1, res.β2) for w in testweights]
m = [mean(v) for v in arr]
quantiles = [quantile(v, [0.1, 0.9]) for v in arr]
lower = [q[1] - m for (q, m) in zip(quantiles, m)]
upper = [q[2] - m for (q, m) in zip(quantiles, m)]
plot(testweights, m, ribbon = [lower, upper])

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请添加您更改的代码的哪一部分，并解释以前的错误