# Senior Year: Trying to walk without tripping

I saw my friend send a Snapchat story yesterday in San Francisco with a nice 48 degrees fahrenheit as the banner. I was lying in bed in Pennsylvania and it was currently 60 degrees. And to throw the punchline in...it's two days past Christmas. (Pls see previous post on the whole climate change thing).

But, this post is not about climate change. But wholly #\$@&%* it's December. I have one more semester of college left. Really! One more...which is like freakin' scary. And there's that whole real world thing I'm expected to do at some point, with all of the 'real world' stuff it has to offer. Gosh, I watched Shark Tank for about three hours yesterday and if 'real world' people are anything like Kevin I'm screwed.

I was talking to my friend in the car this week and we spoke about what it's like when someone pops the question to us: what are you doing with your lives? Coming from a generation where the life-span of our first after-college decision (i.e. graduate school, a job, etc.) is most likely less than five years, it becomes really hard to answer that question. If you've got a good answer, kudos to you. But for myself, I'm not sure what I want to do. I'd love to be able to travel in the future, do something with healthcare (though I still haven't figured out what)...maybe something in policy...maybe something in design. It would be great to be able to help people somehow throughout all of this...in some way shape or form. But then again I'm 21, why do I have to know all of this?

The reality is that I spend a lot of time thinking about what I'd like to do without taking a step-by-step approach on what's likely to get me there. Of course, there's a math-y way to model this problem.

In probability theory, there's an idea called a 'Hidden Markov Model', or HMM, that's commonly used to model and solve problems where you're given a set of outcomes and want to know what led to these outcomes. I'll show you a simple example of an HMM, and you'll see how it can be applied to the quarter-life crisis that seems to circulate each time I write a blog post.

The idea for a Hidden Markov Model is as follows. Imagine that we have a set of outcomes that depend upon things we do not know, things that are 'hidden' to us. For example, an outcome could be something as simple as getting a heads when you flip a coin, or as complex as whether you earned a job offer after an interview. An example of a 'hidden' dependency for a coin flip is whether the given coin is fair or biased. For your job interview tomorrow, a 'hidden' dependency might be whether you wear a blue suit vs. a black suit. To really make this a 'model', we're going to represent our outcome by a variable $o$, and our hidden dependency, or state by a variable $x$.

Say someone gives me a random coin, and I flip it, maybe 10 or so times. Each time I flip the coin, I get an outcome: heads or tails. My goal for this experiment is, given the outcome of the 10 flips, is it likely that my coin is biased, or not biased? Obviously if I get about 5 heads and 5 tails, it's likely that my coin is fair. If I were to receive 9 tails and 1 head, it seems pretty unlikely that I have a fair coin.

Now...let's take this one step farther (because my stat-freaks probably can tell a simple hypothesis test solves the above issue). Say I repeat the experiment above, where I flip a coin 10 times. Before I flip the coin, I'm either handed a fair coin or a biased coin to flip with. Occasionally, the type of coin is changed, but normally (maybe say 80% or so of the time), I'm given the same coin I just used. After I run the experiment, I have 10 outcomes of heads or tails, modeled by variables $o_1,o_2,...,o_{10}$. The goal is to now figure out the coins that were used during each trial, i.e. $x_1,x_2,...,x_{10}$. This is an example of an HMM: given a...

1. set of outcomes from an experiment $o_1,o_2,...$
2. set of possible states $x$
3. probability of getting each outcome based upon the state $P(o | x)$
4. the probability of transitioning between states $P(x_n|x_{n-1})$ (i.e. switching between a fair and biased coin)...

...what are the most likely set of states, $x_1,x_2,...$, that led to my experimental outcomes?

Soo...how does this apply to my life? Well, let's say I have a life goal...maybe it's to start a small business, or move to the west coast. There might be a set of a life decisions, or states, in front of me that affect the likelihood of achieving this outcome. If I think one state is more likely to lead to the outcome I want, I would then pick it. Once these paths get longer, and these choices get more complicated, having an HMM in my back pocket might be a helpful.

So the bright news is, if you were to magically have probabilities that become life outcomes, there are ways to find the most likely states in an HMM that lead to a set of outcomes you desire. The bad news...how do you assign probabilities to life events? Well...I'm not going to answer that. I'm still trying to figure it out for myself, and am going to be for a long time. But to end on a bright note...

...being in my 20s is a scary, but crazy exciting thing. I might be finishing college, but my whole career is ahead of me. And there's not too many opportunities where I can have no idea where I'll be five years from now, and that's perfectly fine. So instead of being overwhelmed, I'm going to try and stay excited. Excitement is a pretty beautiful feeling to have.

Happy Holidays!