Aalto BDA course

I've been studying the Aalto university Bayesian data analysis course on my own (slow) pace this spring and early summer. I've mostly watched the excellent course videos and scrolling through the coursebook, but there has been some coding as well.

The exercises are supposed to be made with R, but me being a master hackerman, I chose golang and gonum. While the gonum library is limited compared to what R has, my goal with this course is not to become a statistics expert but rather to relearn what I have forgotten from my university studies. I also value keeping my go skills in tune.

I present you, exercise one. 

 

	package main
	import (
	"fmt"
	"image/color"
	"log"
	"math"
	"sort"
	"golang.org/x/exp/rand"
	"gonum.org/v1/gonum/stat"
	"gonum.org/v1/gonum/stat/distuv"
	"gonum.org/v1/plot"
	"gonum.org/v1/plot/plotter"
	"gonum.org/v1/plot/vg"
	)
	const mu float64 = 0.2
	const sigma float64 = 0.1
	func main() {
	drawBetaDistributionFunction()
	drawRandomHistogram()
	}
	func drawBetaDistributionFunction() {
	p, err := plot.New()
	if err != nil {
	panic(err)
	}
	p.Title.Text = "Beta distribution function"
	alpha := calcAlpha()
	beta := calcBeta(alpha)
	betaDistr := plotter.NewFunction(distuv.Beta{Alpha: alpha, Beta: beta}.Prob)
	p.Add(betaDistr)
	p.X.Min = 0
	p.X.Max = 1
	p.Y.Min = 0
	p.Y.Max = 5
	if err := p.Save(10*vg.Inch, 10*vg.Inch, "func.png"); err != nil {
	panic(err)
	}
	}
	func drawRandomHistogram() {
	p, err := plot.New()
	if err != nil {
	panic(err)
	}
	p.Title.Text = "Beta distribution and random sample histogram"
	alpha := calcAlpha()
	beta := calcBeta(alpha)
	src := rand.New(rand.NewSource(1))
	b := distuv.Beta{Alpha: alpha, Beta: beta, Src: src}
	v := make(plotter.Values, 10000)
	sum := 0.0
	for i := range v {
	r := b.Rand()
	v[i] = r
	sum = sum + r
	}
	sort.Float64s(v)
	h, err := plotter.NewHist(v, 16)
	if err != nil {
	panic(err)
	}
	h.Normalize(1)
	p.Add(h)
	labels, err := plotter.NewLabels(plotter.XYLabels{
	XYs: []plotter.XY{
	{X: 0.8, Y: 4.5},
	{X: 0.8, Y: 4.3},
	{X: 0.8, Y: 4.1},
	{X: 0.8, Y: 3.9},
	{X: 0.8, Y: 3.7},
	{X: 0.8, Y: 3.5},
	},
	Labels: []string{fmt.Sprintf("Sampled Mean: %f\n", sum/10000.0), fmt.Sprintf("True mean: %f\n", b.Mean()), fmt.Sprintf("Sampled Variance: %f\n", stat.Variance(v, nil)),
	fmt.Sprintf("True variance: %f\n", b.Variance()), fmt.Sprintf("Sampled Quantile: %f\n", stat.Quantile(0.95, stat.Empirical, v, nil)),
	fmt.Sprintf("True quantile: %f\n", b.Quantile(0.95))},
	},
	)
	if err != nil {
	log.Fatalf("could not creates labels plotter: %+v", err)
	}
	p.Add(labels)
	betaDistr := plotter.NewFunction(distuv.Beta{Alpha: alpha, Beta: beta}.Prob)
	betaDistr.Color = color.RGBA{R: 255, G: 100, A: 255}
	betaDistr.Width = vg.Points(3)
	p.Add(betaDistr)
	p.X.Min = 0
	p.X.Max = 1
	p.Y.Min = 0
	p.Y.Max = 5
	if err := p.Save(10*vg.Inch, 10*vg.Inch, "hist.png"); err != nil {
	panic(err)
	}
	}
	func calcAlpha() float64 {
	return mu * (((mu * (1 - mu)) / math.Pow(sigma, 2)) - 1)
	}
	func calcBeta(alpha float64) float64 {
	return alpha * (1 - mu) / mu
	}

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