Valida ion o he STable Au oCo ela ionIn eg al Es ima o (STACIE) Using TheAu oCo ela ion In eg al D ill (ACID) Tes Se model: lo en z(0.1)Gözdenu To aman,† Die e Fauconnie ,†‡ and Toon Ve s aelen✶¶† Soe e Labo a o y, Ghen Uni e si y, Technologiepa k-Zwijnaa de 46, 9052 Ghen , Belgium‡ Flande sMake@UGen , Co e Lab EEDT-MP, 3001 Leu en, Belgium¶ Cen e o Molecula Modeling (CMM), Ghen Uni e si y, Technologiepa k-Zwijnaa de 46, B-9052,Ghen , Belgium✶E-mail: [email p o ec ed]Ve sion 2025-06-25 (b 3 8a)Con en s1.Desc ip ion o Figu es and Tables ............................................................................ 22.Ke nel exp1p .................................................................................................. 33.Ke nel exp1w ................................................................................................. 51
1.Desc ip ion o Figu es and TablesThe ollowing sec ions con ain igu es and ables wi h he same ype o esul s in each sec ion, bu compu ed o di e en ke nels. All igu es and ables a e labeled wi h a le e and a e explained he e. Fo a ull discussion o he esul s, we e e o he STACIE pape : TODO ADD CITATION.(a)Illus a ion o inpu da a.•Le : an example inpu sequences ( i s 100 s eps).•Cen e : he sampling au oco ela ion unc ion (ACF) o he inpu da a (𝑁=1024, 𝑀=256, pu pleline) and he analy ical ACF (dashed line).•Righ : he sampling powe spec al densi y (PSD) o he inpu da a (𝑁=1024, 𝑀=256, u quoiseline) and he analy ical PSD (dashed line).(b)Scaling o unce ain y o he au oco ela ion in eg al wi h inpu da a.•The slope o he slan ed g ay lines indica es he ideal scaling o he unce ain y (p opo ional o1√𝑁𝑀). The spacing be ween he lines co esponds o a ac o o 2 in he unce ain y, he ideal casewhen changing 𝑁 by a ac o o 4.•A squa e ep esen s he s anda d de ia ions o e 64 epe i ions o STACIE’s es ima e o heau oco ela ion in eg al o a speci ic combina ion o 𝑁 and 𝑀.•The do ed lines ep esen he co esponding p edic ed unce ain ies.(c)Assessmen o he e o es ima e o he au oco ela ion in eg al.•The squa e blocks show he a io o he s anda d de ia ion o he STACIE es ima e and he RMS alue o he p edic ed unce ain y, o e 64 epe i ions. This alue is ideally 100%.•The do s show he a io o he mean e o and he RMS alue o he p edic ed unce ain y, o e 64 epe i ions. This alue is ideally 0%.(d)Scaling o he unce ain y o he exponen ial co ela ion ime wi h inpu da a.•This igu e ollows he same con en ion as in (b), bu shows esul s o he unce ain y o heexponen ial co ela ion ime.(e)Assessmen o he e o es ima e o he exponen ial co ela ion ime.•This igu e ollows he same con en ion as in (c), bu shows esul s o he unce ain y o heexponen ial co ela ion ime.( )Sensi i i y o he au oco ela ion in eg al o he cu o equency.•This plo shows how he au oco ela ion in eg al co ela es wi h he e ec i e numbe o poin s usedin he i ( op) and he cu o equency (bo om).•Resul s a e shown only o he 𝑀=64.•The colo code o di e en 𝑁 co esponds o he legends shown in igu es (b), (c), (d) and (e).(g)Sensi i i y o he exponen ial co ela ion ime o he cu o equency.•The same con en ions as in ( ) apply, bu his igu e shows esul s o he exponen ial co ela ion ime.(h)Numbe o success ul es cases (Failu es a e ypically due o no inding any cu o equency wi haccep able esul s.)(i)Sani y check coun s o he e ec i e numbe o poin s•Numbe o es cases o each combina ion o 𝑁 and 𝑀 whe e he e ec i e numbe o poin s used in he i is below 20𝑃=40.(j)Sani y check coun s o he eg ession cos z-sco e•Numbe o es cases o each combina ion o 𝑁 and 𝑀 whe e he z-sco e o he eg ession cos exceeds 2.(k)Sani y check coun s o he cu o c i e ion z-sco e•Numbe o es cases o each combina ion o 𝑁 and 𝑀 whe e he z-sco e o he cu o c i e ionexceeds 2.2
2.Ke nel exp1p(a) Illus a ion o inpu da a(b) Scaling o unce ain y o he au oco ela ionin eg al wi h inpu da a(c) Assessmen o he e o es ima e o heau oco ela ion in eg al(d) Scaling o unce ain y o he exponen ialco ela ion ime wi h inpu da a(e) Assessmen o he e o es ima e o heexponen ial co ela ion ime3
( ) Sensi i i y o he au oco ela ion in eg al o he cu o equency(g) Sensi i i y o he exponen ial co ela ion ime o he cu o equency(h) Numbe o success ul es cases𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=1024064646464𝑁=40966464646464𝑁=163846464646464𝑁=655366464646464(i) Sani y check coun s o he e ec i e numbe o poin s𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400000𝑁=409600000𝑁=1638400000𝑁=6553600000(j) Sani y check coun s o he eg ession cos z-sco e𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400011𝑁=409601000𝑁=1638400021𝑁=6553600003(k) Sani y check coun s o he cu o c i e ion z-sco e𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102401100𝑁=409610010𝑁=1638420100𝑁=65536100004
3.Ke nel exp1w(a) Illus a ion o inpu da a(b) Scaling o unce ain y o he au oco ela ionin eg al wi h inpu da a(c) Assessmen o he e o es ima e o heau oco ela ion in eg al(d) Scaling o unce ain y o he exponen ialco ela ion ime wi h inpu da a(e) Assessmen o he e o es ima e o heexponen ial co ela ion ime5
( ) Sensi i i y o he au oco ela ion in eg al o he cu o equency(g) Sensi i i y o he exponen ial co ela ion ime o he cu o equency(h) Numbe o success ul es cases𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400646464𝑁=4096064646464𝑁=163846464646464𝑁=655366464646464(i) Sani y check coun s o he e ec i e numbe o poin s𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400000𝑁=409600000𝑁=1638400000𝑁=6553600000(j) Sani y check coun s o he eg ession cos z-sco e𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400101𝑁=409600301𝑁=1638400011𝑁=6553600000(k) Sani y check coun s o he cu o c i e ion z-sco e𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400110𝑁=409600000𝑁=1638410001𝑁=65536031006
