# Can I Get A Squee For Math?

So today has been an absolute blast, and it’s all because of math.

Seriously.

I know, I know, you’re probably rolling your eyes and thinking Gillis has finally lost his gourd. But no, that is not the case. Well, it might be the case, but that’s a story for another time.

So why was today all-that-and-a-bag-of-chips thank you very much mathematics? Well, for at least 2 reasons:

• Today my friend Kim defended her Ph.D. dissertation. Her talk was fantastic and I couldn’t help but smile as I watched her explain some rather complicated and complex mathematics in a way that was understandable – even to those who had no mathematics training. This was due to Kim’s obvious mastery of the subject, and the obvious passion she has for it. She is exceptionally talented and has the very desirable and sought after ability to translate high-brow math-speak to something that everyone can grasp.
• I also spent the afternoon playing around with some mathematics1 for a paper that I’m coauthoring with my friend Almost Doctor Lorna. You see, she has spent the last little while working on a rather incredible simulation study built on a statistical model that is intended to understand disease spread in animal populations. Her work is pretty phenomenal, and I can’t wait until the day she too gets to defend. Anyway, she noticed some interesting results and we are now trying to determine the mathematical justification for what she saw. That, or identify that it might just be coincidence – that is, no pattern actually exists; we just think it’s there.

Anyway, I’m currently trying to show the following (generally speaking – or possibly on average):

$\ln\displaystyle{\prod_{t}}\displaystyle{\prod_{i}}p(x|\bar\theta)\displaystyle{\prod_{j}}(1-p(x|\bar\theta))>\ln\displaystyle{\prod_{t}}\frac{1}{m}\displaystyle{\sum_{l=1}^{m}}\displaystyle{\prod_{i}}p(x|\theta^{(l)})\displaystyle{\prod_{j}}(1-p(x|\theta^{(l)})),$

where

$p(x|\mathbf{\theta})=1-\exp\left\{-f(\mathbf{\theta}, x)\right\},$

and

$\bar\theta=\displaystyle{\sum_{l=1}^{m}}\frac{\theta^{(l)}}{m},$

but I’m stuck. This could be a side effect of being tired. Or perhaps I’ve been staring at this problem too long and the answer is actually obvious. Or it could be that my brain may or may not be enjoying the soothing aromas and flavours of a scotch-y beverage2. It really is a mystery.

1 Squee!

2 If you know me, you’ll know the answer to this riddle3.

3 It’s so not a riddle. Ha!

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# Dividing By Zero Is Like A Punch In The Face…

…because they both hurt your brain.

So apparently time flies when you’re sitting at work running statistical simulations. :)

In case you were wondering, I just so happened to look at the clock and realized the hour. Given that I’ve been on campus since 9am, and up and working since 6am, I think I should probably go home. And I will. As soon as this current simulation finishes running.

Why on earth are you still on campus?

I had a meeting with my Undergraduate Research Assistant Justin today. We’ve been working on a simulation study that is testing a hopefully improved method for estimating the abundance of animal populations given only harvest data. Justin had very observantly noticed that our simulations were sometimes breaking down. That is, the model was ending without completing the task of analyzing the data.

Weird, right?

Anyway, because of that I’ve been on campus playing. Seriously. I’ve spent the last 3 or so hours working through the model that simulates a population of animals in the wild. So far, I’ve found a few interesting things. The most significant issue was that there existed a significant probability that our model would produce a population that was negative. As in, less than zero animals. Clearly that can’t be – except maybe in Bizarro World1.

I also noticed that some of the code was permitting division by zero. GASP! How did I miss that before? Of course, our model was adjusting for these instances by thankfully ignoring them. Regardless, as a big-ole math and stats nerd, I couldn’t let that go uncorrected. Dividing by zero is asking for trouble. Serious, serious trouble. The worst kind of trouble.

Not sure what dividing by zero will do? Consider these images.

Moral of the story: dividing by zero is dangerous, and not just mathematically speaking.

1 Bizarro World – best explained by watching this clip.

# Inversion Excursion

Holy crapshite – how is Sunday almost over?

My goal today was to check off a bunch of things on my to do list, but sadly I don’t think I’ve completed nearly as much as I would have liked to. Ultimately I wanted to start Monday with fewer things on my list so that the week would be a bit easier. Additionally, I had a brainstorm the other day and I’m very antsy to get started on a new simulation study. Seriously, every time I think of this particular idea I have a bit of a nerd-gasm.

Sadly, my list is still going to be mammoth come Monday morning. To be perfectly honest, I don’t think my list really had a chance of being reduced this weekend. Not when you consider that I had to run 9+ km yesterday in order to stay on track with marathon training (a total of 54.07 km for the week – w00t). And of course, one also needs to have some sort of social life such as going to dinner with Jamie, having breakfast with Manon, heading to Solutions with Jasper and Liz, and scratching one lazy cat’s belly.

It’s a rough job, but someone has to do it.

A quick note: the shopping excursion to Solutions in Cambridge – a paradise for those that want to organize anything and everything in their life – with Jasper and Liz was very much impromptu (although Jasper did catch it on film – of course – embedded below for your viewing pleasure). It came about after learning that Jasper had just purchased an inversion table. Clearly, once I learned of this table I had to try it. Jasper being Jasper (read awesome) invited me over for a spin. For those not in the know, an inversion table allows the user to strap themselves in by the ankles and hang upside down. The theory being that it helps to decompress the spine and relax the muscles around the spine. I won’t lie, it was a lot of fun.

Anyway, since I returned home from my shopping excursion and inversion, I’ve managed to read a Ph.D. proposal (including drafting what I hope are several solid questions that will at once put the student at ease but also challenge their understanding of the subject), organize my files, set up a draft template slide presentation for a 3-day course that I’m giving at the Public Health Agency of Canada in February (with the help of Mr. Rick), posted on my other blog, and am now trying to determine if I should

1. work on notes for my 2nd year class,
2. finish an analysis for a colleague,
3. work on an analysis for a paper,
4. edit one of two papers that I had hoped to edit this weekend,
5. read a 2nd Ph.D. proposal,
6. set up an assignment for my 2nd year class,
7. mark an assignment for my 2nd year class,
8. scour the interwebs for a rich data set for use with the Public Health Agency training, or
9. scratch Elliot’s belly.
Decisions, decisions.
Why do I know that Elliot is going to win out?

# Wee Researchers

And just like that another week has flown by. I’m completely exhausted, but in a good way. Between training, running back and forth to various meetings, teaching, preparing presentations, early mornings, late nights, and all the other fun, this week was a blast.

However, given the craziness of the week I think I forgot to mention something amazing!

That is, earlier this week I learned that I was given funding to hire an undergraduate research assistant (URA) this summer.

Yay – Minions!

*Ahem* I mean:

Yay – Wee Researchers!

I’m actually really stoked about this because I have so many projects that I’m trying to complete. I plan to have the URA extend some of the research that I’m currently doing which includes:

• a simulation study of metrics used in population level risk assessment,
• an investigation of the spatiotemporal distribution of a particular fish population,
• an investigation of the spatiotemporal distribution of larval fish,
• a review of an existing database used to house much of the data I work with,
• a simulation study of genetic data, and
• a risk assessment of harvest on wild populations of fish.

Of course, these aren’t my only projects. I’m also finalizing two papers related to scenario analyses, finishing edits on a third, updating some analyses for a fourth, waiting for edits from a co-author on a fifth, and have several students co-authoring 5 others. Crazy!

It should be noted that the URA will only work on one or two of these projects. But hopefully between the two of us we’ll be able to finish as much of this work as possible before the end of the summer. Additionally, I am also hoping to hire at least 2 other undergrads (I just have to find some funding). And, if things go extremely well, I’m going to try to garner some Mitacs funding for an MSc or PhD student. Wish me luck.

But all of this nerdery can wait because it’s Friday – Elliot is curled up next to me, and I have a scotch in hand. Life is good.