It wasn’t a swift detour, but we got somewhere. We know that state-space models maximize a log-likelihood function, and

import statsmodels.api as sm model_ll = sm.tsa.UnobservedComponents(y, level=True) model_fit = model_ll.fit() σ_sq_hat = model_fit.params[0] print(np.round(σ_sq_hat,5))

Wi-Fi: Wi-Fi itself works, but it is not shown in the system settings. “Wi-Fi Unavailable” is displayed, and the list of networks is empty. (At the same time, the command ifconfig shows a normally working wlan0 adapter in the running status and an IP address.)

Ubuntu 20.10 Groovy Gorilla has official support for the Raspberry Pi 4, and as announced, the Raspberry Pi is now a “first-class citizen” for this version. Let’s try to figure out what came of this and how “first class” corresponds to reality.

http://molos.bodasturias.com/qxz/Video-Sasi-Kumar-Mukund-Harri-Heliovaara-v-en-gb-1vrl-24.php

http://startup.munich.es/dyn/video-mountfield-v-ac-sparta-praha-v-cs-cs-1onj-25.php

http://main.ruicasa.com/tgq/v-ideos-severstal-cherepovets-v-kunlun-red-star-v-ru-ru-1fnc-1.php

http://startup.munich.es/dyn/video-mountfield-v-ac-sparta-praha-v-cs-cs-1zhv-17.php

http://main.ruicasa.com/tgq/video-severstal-cherepovets-v-kunlun-red-star-v-ru-ru-1njb-5.php

http://elta.actiup.com/mto/v-ideos-guingamp-v-amiens-v-fr-fr-1slg-12.php

http://molos.bodasturias.com/qxz/Video-Sasi-Kumar-Mukund-Harri-Heliovaara-v-en-gb-1wgu30122020-21.php

http://molos.bodasturias.com/qxz/v-ideos-Dimitar-Kuzmanov-Mirza-Basic-v-en-gb-1muw-.php

http://elta.actiup.com/mto/Video-guingamp-v-amiens-v-fr-fr-1qcm-6.php

http://elta.actiup.com/mto/videos-guingamp-v-amiens-v-fr-fr-1min-21.php

http://molos.bodasturias.com/qxz/Video-Dimitar-Kuzmanov-Mirza-Basic-v-en-gb-1jrk-25.php

http://main.ruicasa.com/tgq/video-iokerit-v-khk-sochi-v-ru-ru-1ctr-26.php

http://elta.actiup.com/mto/video-guingamp-v-amiens-v-fr-fr-1hkv-8.php

http://molos.bodasturias.com/qxz/v-ideos-Dimitar-Kuzmanov-Mirza-Basic-v-en-gb-1lrs-25.php

http://main.ruicasa.com/tgq/v-ideos-iokerit-v-khk-sochi-v-ru-ru-1uie-19.php

http://elta.actiup.com/mto/video-Ajaccio-Pau-FC-v-en-gb-1shw-.php

http://startup.munich.es/dyn/video-Mountfield-HK-Sparta-Prague-v-en-gb-xpt-.php

http://www.ectp.org/kzz/videos-Yertis-Pavlodar-Kazzinc-Torpedo-v-en-gb-ehh30122020-.php

http://molos.bodasturias.com/qxz/video-Umut-Akkoyun-Pavel-Kotov-v-en-gb-1mnd30122020-.php

http://old.cocir.org/media/qas/videos-sparta-warriors-v-gruner-v-no-no-1cmo-15.php

internet were controlled by a few small companies. The future of the internet may very well be owned by its users and controlled by nobody. In other words, we’re moving from centralized ownership to decentralized ownership. This transition is fascinating to me.

First, we need to configure Wi-Fi, for which we edit the 50-cloud-init.yaml file using the sudo nano/etc/netplan/50-cloud-init.yaml command. Add access point parameters to it:

As simple as that, we have our model fitting the data. We can see our two parameters sigma2.irregular (ε_t) and the level component μ_1. We also get several statistical tests that we will learn about in the future.

I first decided to go through all the steps from scratch, choose the console version Ubuntu Server 64-bit 20.04.1 LTS (because this version has a “RECOMMENDED” status), and install the missing components myself. After download and boot, we get into the standard Ubuntu console.

network: ethernets: eth0: dhcp4: true optional: true version: 2 wifis: wlan0: optional: true access-points: 'MYWIFIPOINT': password: '12345678' dhcp4: true

The installation process is not much different from the standard Raspbian installation. We need to download the system image, write it to a micro SD card, and start the device. The images themselves can be downloaded from ubuntu.com/download/raspberry-pi:

In this estimation, we will not be focusing so much on our Bayesian workflow and using all the good practices that we learned in the last post. But don’t worry, we will get back to it in the future. The reason behind it is our intention of showing that the MLE and the MAP are indeed the same thing, if we use flat priors. We will be using very vague priors (not actually flat, to help our sampler slightly).

For small sample sizes, our estimator is unlikely to perfectly represent the data. Using this normalization term is a way of reducing the bias on our estimator. Let’s implement the latter.

Unobserved Components Results ================================================================================== Dep. Variable: y No. Observations: 192 Model: deterministic constant Log Likelihood 63.314 Date: Wed, 25 Nov 2020 AIC -124.628 Time: 16:24:36 BIC -121.375 Sample: 0 HQIC -123.310 - 192 Covariance Type: opg ==================================================================================== coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------------ sigma2.irregular 0.0294 0.003 8.987 0.000 0.023 0.036 =================================================================================== Ljung-Box (Q): 637.74 Jarque-Bera (JB): 0.73 Prob(Q): 0.00 Prob(JB): 0.69 Heteroskedasticity (H): 2.06 Skew: 0.09 Prob(H) (two-sided): 0.00 Kurtosis: 2.76 =================================================================================== Warnings: [1] Covariance matrix calculated using the outer product of gradients (complex-step).

Almost there. Just a small note on the σ (hat) value. Let’s run the same model with a library that has everything set up for us. We will go through that code, but I need you to see something.

And here we have our parameters. For now, focus only on the columns mean and sd from the table above. As you can see, we have posterior distributions for our parameters μ_1 and σ_ε², not only a point estimate. Let’s compare our results with the ones that we got from our implementation using statsmodel.

After rebooting, we can check for an internet connection with ping 8.8.8.8 command, and if everything works, we can install Ubuntu desktop. Run the commands sudo apt-get update, sudo apt-get upgrade, and finally sudo apt-get install ubuntu-desktop. The process takes about 30 minutes, after which we can reboot the system and get a full U.