## Day #20 : Independent Events – 365 DoA

Because we introduced the central limit theorem last post, it’s time to introduce another important concept. The idea of independent events, while this may seem intuitive, it is one of the assumptions we make in parametric statistics, another concept we will define, but for now let’s jump into independence.*

## Day #19 : The Central Limit theorem – 365 DoA

Well here we are again, if you recall from our last post, we talked Bonferroni Correction. You may also recall that when the post concluded, there was no real topic for today. Well after some ruminating, before we jump into more statistics, we should talk about the central limit theorem. So let’s do a quick dive into what that is and why you should know it!*

## Day #18 : The Bonferroni Correction – 365 DoA

By now we are masters of statistics… right? Okay, not really, but we are getting there. So far we’ve covered two types of errors, type 1 which you can read about here, and type 2 which you can read about here. Armed with this new knowledge we can break into a way to correct for type 1 errors that come about from multiple comparisons. Sound confusing? Well, not for long, let’s break it down and talk Bonferroni.*

## Day #17 : Type 2 errors – 365 DoA

Last post we did a quick bit on type 1 errors. As with anything, there is more than one way to make an error. Today we are talking type 2 errors! They are related in the sense and we’ll go over what that means and compare the two right… now!*

## Day #16 : Type 1 errors – 365 DoA

We did it, we cracked the coin conundrum! We managed the money mystery! We checked the change charade! We … well you get the idea. Last post we (finally) determined if our coin was bias or not. Don’t worry, I won’t spoil it for you if you haven’t read it yet. I actually enjoyed working through a completely made up problem, so if you haven’t read it, you really should. Today we’re going to talk dogs, you’ll see what I mean, so let’s dive in.*

## Day #15 : Significance, Part 3 – 365 DoA

It looks like we’ve arrived at part 3 of what is now officially a trilogy of posts on statistical significance. There is so much more to say I don’t want to quite call this the conclusion. Instead, let’s give a quick review of where we left off and we can get back to determining if an observed value is significant.*

## Day #14 : Significance, Part 2 – 365 DoA

Well here we are two weeks into 365DoA, I was excited until I realized that puts us at 3.8356% of the way done. So if you remember from last post we’ve started our significance talk, as in what does it mean to have a value that is significant, what does that mean exactly, and how to do we find out? Today is the day I finally break, we’re going to have to do some math. Despite my best efforts I don’t think we can finish the significance discussion without it and still manage to make sense. With that, let’s just dive in.*

## Day #13 : Significance, Part 1 – 365 DoA

If you’ve read my last post I hinted that today we would discuss filtering. Instead I think I want to take this a different direction. That isn’t to say we won’t go over filtering, we most definitely will. Today I want to cover something else though, significance. So you’ve recorded your signal, took an ensemble average, and now how do we tell if it actually means something, or if you are looking at an artificial or arbitrary separation in your data (IE two separate conditions lead to no difference in your data). Let’s look at significance.*

## Day #12 : Signal, cutting through the noise – 365 DoA

Noise, it can be troublesome. Whether you are studying and someone is being loud or you are trying to record something, noise is everywhere <stern look at people who talk during movies>. Interestingly enough the concept of noise in a signal recording sense isn’t all too different from dealing with talkative movie goers, so let’s talk noise!*

## Day #11 : Why even use the spectrogram? – 365 DoA

So you wanna use a spectrogram… but why? What does a spectrogram do that we can’t do using some other methods for signal processing? As it turns out, there is a lot of reasons you may want to use the spectrogram and today we are going to cover some of those reasons and number four may shock you! (okay not really, what do you think this is a clickbait website?)*

## Day #10 : Spectrogram vs. the banana of uncertainty – 365 DoA

Well ten days in and we’ve just introduced the idea of the spectrogram. While a lot of this information is just the broad strokes, I like to think that we’ve covered enough to give you a good idea about how to use these tools and what they are used for. However, we do need to discuss a limitation to the spectrogram, something called the banana of uncertainty, okay not quite the name, but you’ll see why I keep calling it that.*

## Day #9 : Reading a Spectrogram – 365 DoA

Last post we introduced a new tool in our arsenal of signal processing analysis, the spectrogram. Without knowing how to read it, it just looks sort of like a colored mess. Don’t get me wrong, it is an interesting looking colored mess, but a mess nonetheless. Well today we are going to talk about how to interpret the plot and why exactly we would ever use this seeming monstrosity.*

## Day #8 : The Spectrogram Function – 365 DoA

To (somewhat) continue with our signal processing theme that we have going on at the moment, over the next few days, let’s look at something called the spectrogram. It’s three dimensions of fun!*

## Day #7 : Small waves, or wavelets! – 365 DoA

*Waves!* We’re officially one week through 365 Days of Academia! Woo! 1 week down, 51(.142…) weeks left! Let’s wrap up this weeks theme (there wasn’t originally a theme, but it kind of ended up that way) by talking about other ways we can get to the frequency domain. Specifically, let’s stop the wave puns and let’s talk wavelets!*

## Day #6 : The fast and the Fourier – 365 DoA

Okay, if you’ve been keeping up with these posts, we know about Welch’s method, Thomson’s method, the things that make them different, and the things that make them similar. The thing that both of these transforms rely on is the Fourier transform. What is the Fourier transform? Well, something I probably should have covered first, but whatever this is my blog we do it in whatever order we feel like, so let’s dive in!*

## Day #5 : Whose window function is it anyway? – 365 DoA

One day someone looked at the windowed fourier transform and said, “Don’t be such a square!” and thus window functions were invented. If you believe that, then I have an island for sale, real cheap. But seriously, let’s do a dive into what a window function is and why the heck there are so many of them, because there ARE a LOT! So let’s get started!*

## Day #4 : Spectral leakage… embarrassing – 365 DoA

Leakage, it’s never a good thing. For today’s post we’re going to cover a very important topic. Spectral leakage, it’s a big reason why spectral density estimation is well, an estimation. The other reason it is an estimation is because the fourier transform is an approximation of the original signal, but the Fourier transform is a whole other post on its own. So let’s talk leakage!*

## Day #3 : Power Spectral Density Overview – 365 DoA

In our last post we introduced the two main characters in this story of spectrogram. On one end we have Welch’s method (pwelch) on the other end we have the Thomson multitaper method (pmtm). As promised here is a ~~awful~~ basic breakdown of why is more than one way to compute power spectral density (in fact there are several, far more than the two I’m talking about). So, let’s just dig right in!*

## Day #2 : Power Spectral Density (pmtm) – 365 Days of Academia

This is a (somewhat) continuation on what we were discussing in the previous post. We covered the pwelch MATLAB function, this time we will cover the PMTM function, this function uses the Thomson multitaper method to calculate power spectral density. We can do a deep dive into the differences between the two next time, but for now let’s talk about the command itself.*

## Day #1 : Power Spectral Density (pwelch) – 365 Days of Academia

Signal processing, it’s complex, there are a million ways to go about processing a signal, and like life, there is no best way to go about doing it. Trust me, it is as frustrating as it sounds. Today’s scratch pad note is on power spectral density or PSD for short. So let’s dive in.*

## Starting age of marijuana use may have long-term effects on brain development

The age at which an adolescent begins using marijuana may affect typical brain development, according to researchers at the Center for BrainHealth at The University of Texas at Dallas. In a paper recently published, scientists describe how marijuana use, and the age at which use is initiated, may adversely alter brain structures that underlie higher order thinking.

## Researchers find new clues in treating chronic pain

A chemical in the brain typically associated with cognition, movement and reward-motivation behavior — among others — may also play a role in promoting chronic pain, according to new research. The chemical, dopamine, sets the stage for many important brain functions, but the mechanisms that cause it to contribute to chronic pain are less well understood.

## Mind reading: Researchers observe moment a mind is changed

Researchers studying how the brain makes decisions have, for the first time, recorded the moment-by-moment fluctuations in brain signals that occur when a monkey making free choices has a change of mind. The findings result from experiments led by electrical engineering Professor Krishna Shenoy, whose Stanford lab focuses on movement control and neural prostheses – such as artificial arms – controlled by the user’s brain.