An answer to https://dsp.stackexchange.com/questions/74078/hypothesis-testing-with-binary-pattern/74137#74137

sequence_test.jl

### A Pluto.jl notebook ###
# v0.12.21

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 1301ad3c-9098-11eb-377b-655794eedeb7
using Distributions, DSP, StatsPlots, StatsBase, PlutoUI

# ╔═╡ b63ef62c-9097-11eb-0d6a-b9c24d0b13f4
import Pkg

# ╔═╡ bd82f474-9097-11eb-0d2f-3fbe5cdcbf76
Pkg.add("DSP")


# ╔═╡ 843f6622-909a-11eb-1a0f-195649300b81
md"""

flipfrac = $( @bind flipfrac Slider(0:0.05:1, show_value=true) )

"""

# ╔═╡ c4af9504-9097-11eb-2661-397f406c4ad7
noisy = let ff = flipfrac
	n=1000
	flip_frac = ff
	raw_a = repeat([1,0,0], n)
	flipind = rand(n*3) .< flip_frac
	noisy_a = copy(raw_a)
	noisy_a[flipind] .= sample([0,1], sum(flipind))
	noisy_a = noisy_a .- mean(noisy_a)
end

# ╔═╡ c6a4901e-9097-11eb-0e9c-c92acb4bf00c
begin
	bins = 6
	xc = xcorr(noisy,noisy); mid = Int(length(xc)/2+0.5)
end; md"Data xcorr"

# ╔═╡ 0f4161b4-9099-11eb-0b23-5f155bdc1cb6
nulldist = let
	boots = 1000
	B = fill(NaN, (boots, length(-bins:bins)))
	for bx = 1:boots
		newseq = sample(noisy, length(noisy), replace=false)
		B[bx,:] = xcorr(newseq, newseq)[mid-bins:mid+bins]
	end
	B
end; md"Generate shuffled sequence"
		

# ╔═╡ 87621054-9098-11eb-02d8-cf064f1fe551
begin
	plot(-6:6,xc[mid-bins:mid+bins], marker=:circle, title="Noisy 1-0-0 Sequence")
	plot!(-6:6,nulldist',color=:grey, alpha=0.5, legend=:false)
end

# ╔═╡ 135e0552-909b-11eb-246b-f143c2db75bb
@bind A Slider(0:0.05:1)

# ╔═╡ Cell order:
# ╠═b63ef62c-9097-11eb-0d6a-b9c24d0b13f4
# ╠═bd82f474-9097-11eb-0d2f-3fbe5cdcbf76
# ╠═1301ad3c-9098-11eb-377b-655794eedeb7
# ╟─843f6622-909a-11eb-1a0f-195649300b81
# ╟─c4af9504-9097-11eb-2661-397f406c4ad7
# ╟─c6a4901e-9097-11eb-0e9c-c92acb4bf00c
# ╟─0f4161b4-9099-11eb-0b23-5f155bdc1cb6
# ╠═87621054-9098-11eb-02d8-cf064f1fe551
# ╠═135e0552-909b-11eb-246b-f143c2db75bb