We're a little crazy, about science!

Archive for September, 2019

Day 42: Conditional Probability

Conditional probability pdf plot

How does this not exist on the internet?! This is directly from my book, so it looks a little… well loved.

Up to now we’ve been dealing with single variable pdf and the corresponding CDF. We said that these probabilities relied on the fact that our variable of interest was independent. However, what if we knew some property that impacted our probability? Today we are talking conditional probability and that is the question we will be answering. It’s going to be a long, long post so plan accordingly.*

(more…)


Day 41: Connecting the Concepts

catinthebag

Maybe we shouldn’t phrase it this way, since there is still quite a few days left of 365DoA, but you made it to the end! No, not THE end, but if you’ve been following along the past few posts we’ve introduced several seemingly disparate concepts and said, “don’t worry they are related,” without telling you how. Well today, like a magician showing you how to pull a rabbit from a hat, let’s connect the dots and explain why we introduced all those concepts!*

(more…)


Day 40: The Normal Approximation (Poisson)

Poisson vs Gaussian

Poisson’s return!

You have all been really patient with seeing how we tie these last few posts together and frankly I think that we are on track to do that in the next post. Today however we have one more thing to introduce then we can bring it all together, that would be yet another normal (again we usually refer to this as the gaussian) distribution. If you recall I hinted at this a few days ago in the Poisson pdf post.  Let’s look at what this means and why we would want to use this.*

(more…)


Day 39: The Normal Approximation (De Moivre-Laplace)

Binomial_distribution plot

The binomial distribution, don’t worry we’ll get into it.

Well we haven’t covered the binomial distribution, but it should be vaguely familiar if you’ve been keeping up, specifically if you’ve already read about the gaussian pdf. Today we are going to talk about what the binomial distribution is and how it relates to the normal distribution. So let’s get into it and see how it relates to some of the topics we’ve been covering!*

(more…)


Day 38: The Poisson Distribution

poisson

The Poisson distribution changes shape as λ changes

Well in an effort to catch up to what we’re currently learning in my class today we should hammer out the Poisson distribution so we can get to combining some ideas. The interesting thing about this distribution as you can see from above, is that as we adjust λ the shape of the distribution changes. Let’s get started.*

(more…)


Day 37: Bayes’ Theorem

bayes light

We’re talking Bayes for days.

Okay, it looks like we have our topics for the next few posts and today we need to introduce something called Bayes’ rule (or theorem) if we are going to get into some of the things I want to talk about. We also need to talk about the Poisson distribution eventually, but we’ll get to that in time. For now, let’s talk Bayes!*

(more…)


Day 36: The uniform pdf

Uniform distribution

The uniform distribution, a very simple looking distribution indeed.

Today we are going to take it a bit easy, after all we still have 329 days of blog posts and not every one has to be a novel. That is why today we are introducing something called the uniform distribution. Ever wonder what would happen if nothing really mattered? Well you’re in for a treat! Let’s get started.*

(more…)


Day 35: Example of the Gaussian pdf

Normal distribution with marbles

The gaussian (or normal) distribution demonstrated by plinko.

Well what a fun day it is! Today we are going to dive into some examples (or maybe just an example) of the gaussian (also known as the normal) distribution. Last post we looked at the laplace distribution and discovered there aren’t a whole lot of uses for it because it is technically a special case of the exponential distribution. This isn’t the case with the gaussian, there are lots of really interesting things we can model using the distribution that are applicable to everyday life, so let’s get started!*

(more…)


Day 34: Example of the Laplace pdf

laplace pdf and CDF

The Laplace pdf (left) and the associated Laplace CDF (right). Remember the CDF is just the area under the curve of the pdf.

Last post, we finally got to use the exponential pdf and discovered the math wasn’t completely useless (okay, hopefully by now you know that). However, in the spirit of finding a use for the equations we are covering, let’s look at how we use the laplace pdf. It’s going to be a blast, so let’s get started!

(more…)


Day 33: Example of the Exponential pdf

exponential probabilty density function example post

For those who need a refresher, this is a plot of the exponential pdf we are working with today.

Over the past couple of days, I’ve been talking about several different types of pdf and the associated C.D.F. Hopefully, we have a clear understanding of each of those concepts, for those of you scratching your head, I would recommend you start here at this other post. Otherwise, let’s (finally) look at a real life example using the exponential pdf!*

(more…)


Day 32: The Laplace pdf

laplace plot

The laplace p.d.f with a θ = 0.

Well here we are again… maybe unless you’re new, in which case welcome. If you are just joining us we are talking p.d.f. no not the file format, the probability density function version. If you’re new, you may want to start back here(ish) If not, then let’s talk the strangely similar laplace distribution.*

(more…)


Day 31: The Exponential pdf

Exponential_probability_density

Today we are talking this guy! The exponential p.d.f and its C.D.F.

Well, it has been a week, don’t even get me started. But if you’re here you don’t want to hear me complain about my week, that isn’t why we come together! Well today let’s do a bit of a dive into the exponential p.d.f. I hope you’ve brushed up, because this is going to get interesting.*

(more…)


Day 30: Confidence Interval

Confidence intervals

Yep, we’re talking confidence!

Day 30 already! Where does the time go? It feels like we just started this whole project and it probably wouldn’t be a good idea to look at the remaining time to completion, so let’s not and just enjoy the nice round 30. We will get back to our p.d.f another day, but today is going to be short. That’s what I usually say before typing out 10 pages worth of information so to avoid that, let’s touch on something important, but something I can do briefly. Today we’re talking about confidence intervals*

(more…)


Day 29: Probability density functions, Part 3

gaussian CDF vs pdf

Don’t be scared, we’re going to tackle this guy today!

Well, apparently you guys really appreciated my probability density function posts. It’s good to see people interested in something a little less well-known (at least to me). So for those of you just joining us, you’ll want to start at part 1 here. For those of you who are keeping up with the posts, let’s review and then look at specific functions. Namely let’s start by going back to our gaussian distribution function and talk about what’s going on with that whole mess. It will be fun, so let’s do it!*

(more…)


Day 28: Cumulative Distribution Functions

Exponential_distribution_cdf

An example C.D.F. of an exponential distribution

Today we were going to do another deep dive into the p.d.f and C.D.F. relationship. Specifically today we were going to talk about specific p.d.f. functions and why we use them, however… I am not doing so hot today, so instead we are going to back track just a bit and talk about what how a C.D.F. differs from our p.d.f. even though we kind of covered it, it would be nice to be clear and I can do this in a (fairly) short post for the day. So that said, let’s get started and we will pick up our p.d.f. discussion next time (maybe).*

(more…)


Day 27: Probability density functions, Part 2

PDF_CDF

Today we are looking at our p.d.f. (yes this image has p.d.f. written as PDF, please don’t be confused!) and our C.D.F.’s let’s do this!

Oh hi didn’t see you there. Today is part 2 of the probability density functions notes (posts?), whatever we are calling these. You can read part 1 here as you should probably be familiar with the (super confusing) notation we use to describe our p.d.f. and our C.D.F. now that we’ve given that lovely disclaimer, let’s look once again at probability density functions!*

(more…)


Day 26: Probability density functions, Part 1

statisics jokes

Dashing dreams one comic at a time, via Saturday Morning Breakfast Cereal 

We are well on our way to wrapping up week 4, what a ride it’s been! It’s been a long day for me, so today might be short. However, I really, really, really want to break into probability density functions. This topic is going to be a bit more advanced than some of the things we’ve covered (IE more writing) so it will most definitely be broken up. Let’s look at why and discover the wonderful weirdness of probability density functions!*

(more…)


Day 25: The p-value

P-value joke showing a very confident man with this is what p less than .05 feels like printed on top of the image
P-value joke showing a very confident man with this is what p less than .05 feels like printed on top of the image

It’s true!

Now it seems like we are getting somewhere. Last post we covered z-score and you can read that if you haven’t already, it might be good to familiarize yourself with it since today we are going to talk p-value and the difference between z-score and p-value. That said, let’s dive in and look at the value in the p-value.*

(more…)


Day 24: The z-score

Statistics cartoon

Statistics cartoon

So if you recall from last post… well I’m not linking to it. It was hellishly personal and frankly I’m still attempting to recover from it. We’re going to take it light this time and we can do a deep dive into something in another post. For that reason, let’s talk about z-score and what exactly it is, I mean we used it in this post and never defined it formally, so let’s do that. Let’s talk z-score!*

(more…)


Day 23: I was lucky…

IMG_20130704_221101_377 (2)

This was home, for a while anyway.

Okay, so not every post has to be strictly academic. If my twitter feed is any indication yesterday was world suicide prevention day. So with a heavy heart I have not one, but two very personal stories regarding suicide. Obviously this is a content warning for those wanting to go further, we will be dealing with suicide, death, and suicidal ideation.

(more…)


Day 22: Parametric vs. NonParametric Statistics

How Mean Meme

Technically we could call this parametric statistics part 2. However, since we are covering nonparametric statistics and more importantly the difference between parametric and nonparametric statistics, it would seem that this title makes more sense. As usual with a continuation, you probably want to start at the beginning where we define parametric statistics. Ready to get started?*

(more…)


Day 21: Defining Parametric Statistics

normal-distribution

It’s halloween time, we are talking about normally distributed data, so this fits, and I don’t want to hear otherwise!

Well my lovely readers, we’ve made it to the three week mark, 5.7% of the way through! Okay maybe that doesn’t seem like a big deal written like that, but hey it’s progress. So last post we had our independence day, or rather defined what it meant to have independent events vs. dependent events. We also said it was an important assumption in parametric statistics that our events are independent, but then we realized we never defined what parametric statistics even is, oops. So let’s stop dragging our feet and talk parametric statistics!*

(more…)


Day 20: Independent Events

correlation

By: xkcd

 

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.*

(more…)


Day 19: The Central Limit theorem

 

 

CLT

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!*

(more…)