Category Archives: Logs

Hey everyone,

I’ve got some good news – I passed exam C/4! In retrospect, it felt like one of the most difficult exams I’ve ever taken, if not the hardest. I sacrificed three weeks of training and pretty much studied nonstop until I walked into the testing center for my sitting. The exam was a computerized test – the questions were drawn randomly with the passing score calibrated based on the difficulty of the questions. That means a test with easy questions will on average have a higher passmark than a test with hard questions. I must have gotten unlucky this time around because almost all of my questions were hard…there weren’t many questions I knew how to do right away, and I had to skip several when time ran out. I just felt relieved when I found out I had passed after submitting my answers.

I won’t get my score until mid-July, but my preliminary passing result has a 99.9975% chance of matching my final result. The one (or two) exams in the history of computerized actuarial exams whose preliminary results didn’t match the final results were due to human error in handling the scores. So, I’m confident that I passed…maybe barely. In my opinion didn’t study very well – I didn’t follow through with my plan to memorize every single definition and theorem from Loss Models. I did however, put in the recommended 300-400 hours, which is probably more than what most people did, but I think at my level, the efficiency of study was somewhat lacking. I ought to have improved over last time, but I didn’t get rid of the bad habit of holding off until the last two months to study…I kind of got away with it since I’m really familiar with the way standardized tests work. The raw probability of any one individual passing 4 exams in a row is only 2.6%…I ought to consider myself lucky for having a smooth path so far, but I aim to make my next pass based off hard work.

There might have been a slight improvement over the last sitting as I was seriously looking at the material at least two months ahead of time, compared to 6 weeks before the exam date last time and 4 weeks the time before that. Those are merely rough guesses, though, so for my next test, MFE/3F, which I’ll be taking in November, I’ve made it a point to start early (I started studying the day after I passed), to record each day what I’ve studied, and to use linear interpolation to predict when I’ll finish the material. I suppose in this sense I shouldn’t expect a miraculous improvement in studying…if I can just do one thing better than I did last time (like memorizing all of the definitions) for each of the next 6 exams, the cumulative effect of these small improvements should pay off over time.

I’m working on some interesting things – I’m currently designing some simulations on the dowry problem that I’ll write about next week. But for now I’m pretty tired. I finally got around to reading The Cyclist’s Training Bible and I’m almost a third of the way through it. There are a lot of things I learned from that book, and I’m looking forward to building a new training program in the coming months. It looks like I’m too out of shape to participate in the summer races, and I think I might have sacrificed too much of my fitness to target the late-season races…then again, I wouldn’t be able to race at all if I didn’t make the income to support it, so in the end I think it was worth it.

By the way, it looks like I finally broke my New Year’s resolution. I managed to update this blog 18 weeks in a row but I stopped because of the exam. Now I’m back.

Hey everyone,

So I’ve decided not to read any news on Sundays from now on. I think having a break once a week would be good for my stress, especially during these next three weeks as I really have to focus on studying. Statistically, I only have about a 45% chance of passing this sitting, and only about a 25%-35% on the upper examinations based on historical evidence. Realistically, I have to keep in mind that I might fail at one point, and even most good students fail somewhere along the way. Most of us are pretty open about when we fail an exam – and there’s no stigma against it, although it doesn’t feel good when it happens. I feel OK about this test, and my study progress is slightly better than that of MLC so we’ll see how it goes, though there is more information to learn this time around.

That being said, I don’t want to put all of my eggs in one basket, so I still make sure to spend time on other things that I find important. I went for a 3 hour ride Saturday morning around Clear Lake before visiting my parents. Chris Langley, a fellow racer on Bike Barn, decided to forgo racing at Coldspring because he was “out of shape,” and pulled for the last 20 minutes at 30mph while I barely managed to stay on his wheel, my heart pounding at 176 bpm. It’s nice that I’m still able to hold that heart rate, which is a sign that I haven’t lost too much fitness. I’m pretty bummed out about missing racing this weekend, or having to miss 2-3 months out of every year to study for these tests. The material itself is actually pretty interesting, but the pressure of exams can be mentally exhausting, and I think most statisticians would agree. In the end I think, it’ll be worth it.

I sacrificed some of my study time to finish up a Sociology book I’d been reading for the last couple of months. It was really fascinating, although a lot of it went over things that I already knew so it wasn’t the most efficient use of my time. It mainly focused on inequality with respect to wealth, rights, and gender, and discussed some of the theories by Marx, Durkheim, and Weber. I was somewhat disappointed as it didn’t focus much on human interaction on an individual or group basis. On the contrary, the style was more macro-oriented and dealt with human relations by class or nationality. Overall, I’d recommend it to most teenagers…I’d be disappointed if a high school graduate weren’t aware of the huge gap in living standards between Denmark and the DRC, for instance…or perhaps, the fact people in other countries have a greater life expectancy than those in the United States, even though they spend less on healthcare.

I’ve got a lot of interesting projects planned as soon as June starts. I’ll finally get around to reading the Cyclist’s Training Bible, and after that I’ll get started on Vonnegut’s Player Piano and Perry and Bratman’s Introduction to Philosophy. I also have some races planned this summer in Louisiana, where I went last year and had a lot of fun. I’m really looking forward to it.

Hey everyone,

Studying is going alright, but it looks like it’s taking over all my other activities so I won’t really have any creative projects to write about until the end of next month. I’ve managed to stay in shape so far, and by pure coincidence, I ran into one of my former UT teammates, Stephen, during a training ride at Memorial Park. He’s moved down here for the long term, which is pretty cool given that Ken and I are in the same general location. In the meantime, I’ve planned some projects in the back of my mind that I might want to start as soon as I finish my exam:

1. Monty Hall Simulation
2. N-Back
3. Project Euler
4. .GPX and .TCX data extraction

The first project, The Monty Hall Problem, involves a game-show situation in which a contestant chooses one of three objects, each hidden behind a curtain. Two of the objects are something undesirable, like a goat, and the other object is something desirable, like a fancy sports car. The hostess reveals one of the goats and asks the contestant if they wish to change their mind. It turns out the answer is the player should switch, which seems counterintuitive upon first exposure since most people would erroneously assume that there’s still 50/50 chance of getting a fancy sports car regardless of choice. The general proof of the problem involves Bayesian Statistics. I’d like to do a simple VBA simulation of this scenario to see how it works empirically, and perhaps in this way I can gain an intuitive understanding of how this new knowledge affects the conditional probability.

For the second project, I’d like to reconstruct a game called N-Back using VBA as a prototype, and then wxPython for the final version. N-Back is an iterative game in which the player must recognize patterns from say, 1,2,…,n iterations ago. It’s a game that tests the working memory of the player. I think this would be a very good exercise for GUI programming.

One of my friends recommended that I give Project Euler a try. It’s a website that has a bunch of problems that you can solve efficiently by constructing algorithms. I heard that attempting to recreate solutions in different programming languages is a good way learn new languages.

The fourth project involves the .GPX and .TCX data files that contain the training data I pull from my Garmin. It’s possible to convert them into tables that you can import in to R for statistical analysis. The plotting features of the free Garmin Training Center software are very limited, so I’d like to create a platform using R to make it easier to slice and compare two different data sets.

Other than that, I’ve been given some neat projects at work where I’ll be able to take a look at some huge data sets using SQL Server. I’ve also signed up for a meeting with the Houston-R users group on Wednesday, at which we’ll discuss the use of R in predictive modeling competitions.

Hey everyone,

A few short updates:

Training

Last week I decided to take it easy, so on each of the training rides I deliberately kept my heart rate at or below 140 bpm. For weights, I deloaded my squats from 215 pounds to 140 pounds, which feels really light. I didn’t drastically cut back on the other exercises since I don’t have fatigue in my upper body. On Saturday, I met up with my friend Mark Knight from the Rice collegiate team, and we rode around the South Loop for about two hours, with him pulling the entire time at around 160 bpm. I was able to keep my HR at around 135 by drafting. I asked him how long he could sustain that heart rate, and in reply he told me “pretty much all day.” I can hold 160 for about 55 minutes (1×20 min & 1×25 min)…I think 1 consecutive hour is well within reach, so I’ll make that my next goal. In the meantime, I’ve decided to take it easy for another week. Then, I’ll start building with short 160 bpm efforts, gradually increasing the duration until I can sustain it for an hour.

Studying

I’ve picked up the pace of studying, but I still feel behind. The difficult thing about studying as an adult is that I don’t have the luxury of asking a professor for help, so I’m mostly doing it on my own. The notation can be intimidating at times, but the most important thing is to understand the purpose of the theory and how it applies to actuarial practice. For instance, last week I was reviewing Credibility Theory, which attempts to construct a flexible model for the pricing of insurance policies in a world where the underlying variables of risk constantly change. Charging too low of a price leaves the company vulnerable to heavy losses whereas charging too high of a price leaves the company vulnerable to competitors that charge more attractive rates. However, once you find the market rate, you have to develop a model that takes into consideration the fact that risks evolve over time.  Credibility Theory allows us to compare the predictive power of a theoretical model against empirical data, which we’ve observed in the form of claims, losses, or payments. If the characteristics of the observed data differ substantially from those of the theoretical model, more weight is given to our prior experience than to the model itself.

Academic actuaries strive to create mathematical justification for current actuarial practices. The following example provides a glimpse of how actuaries link Credibility Theory to Bayesian Statistics. We can represent a sequence of independently distributed losses 1,…,n as a vector:

$latex displaystyle mbox{bfseries{X}} = (X_1,ldots,X_n)^T $

Where each X_j has the probability density function:

$latex displaystyle f_{X_j|Theta}(x_j), quad j = 1,ldots,n,n+1 $

The parameter Θ represents the unknown risk parameter, which allows for some level of uncertainty and heterogeneity amongst individual policyholders. The following equation represents the joint density function of the X_js, given our risk parameter, Θ:

$latex displaystyle f_{mathbf{X},Theta}(mathbf{x},theta)=f(x_1,ldots,x_n| theta)left [prod^n_{j=1}f_{X_j|Theta}(x_j|theta)right]pi(theta)$

We can then integrate to obtain the marginal density function of x:

$latex displaystyle f_{mathbf{X}}(mathbf{x})=intleft[prod^n_{j=1}f_{X_j|Theta}(x_j|theta)right]pi(theta),mathrm{d}theta $

Where π(θ) represents the density function of our risk parameter Θ. We now want to predict our next loss, X_{n_1}, based on our past experience, X. We can now do so using the above formula to construct the conditional density of X_{n_1}, given X:

$latex displaystyle f_{X_{n+1}|mathbf{X}}(x_{n+1}|mathbf{x})=frac{1}{f_{mathbf{X}}(mathbf{x})}intleft[prod^{n+1}_{j=1}f_{X_j|Theta}(x_j|theta)right]pi(theta),mathrm{d}theta $

Using the definition of the posterior distribution from Bayesian Statistics, we define the posterior density function of Θ as:

$latex displaystyle pi_{Theta|mathbf{X}}(theta|mathbf{x})=frac{f_{mathbf{X},Theta}(mathbf{x},theta)}{f_mathbf{X}(mathbf{x})}=frac{1}{f_mathbf{X}(mathbf{x})}left[prod^n_{j=1}f_{X_j|Theta}(x_j|theta)right]pi(theta) $

Rearrangement of this definition yields:

$latex displaystyle left[prod^n_{j=1}f_{X_j|Theta}(x_j|theta)right]pi(theta)=pi_{Theta|mathbf{X}}(theta|mathbf{x})f_{mathbf{X}}(mathbf{x}) $

We can now substitute the right side of this equation into the numerator of the conditional density function of X_{n_1}, which yields:

$latex displaystyle f_{X_{n+1}|mathbf{X}}(x_{n+1}|mathbf{x})=int f_{X_{n+1}|Theta}(x_{n+1}|theta)pi_{Theta|mathbf{X}}(theta|mathbf{x}),mathrm{d}theta $

The conditional density function of X_{n_1} now has the form of the density function of the predictive distribution from Bayesian Statistics. Thus, we have established (a small part of) Credibility Theory as a form of Bayesian Statistics.

Hey everyone,

I think it’s safe to say that I’m a little burned out – both physically and mentally. I had a really good ride two weekends ago back in Clear Lake, and that’s the last time I managed to put in some sustained efforts at 170 bpm. However, ever since Lago Vista, I’ve been waking up sore almost every single day but I managed to keep putting in 10% increases in wattage each week, but the fatigue has finally caught up with me and I just couldn’t put in any power during any of my training rides last week. I don’t have any races planned until the summer, so I’ve decided to lower the intensity over the next two week while maintaining the same number of hours so I don’t lose too much fitness.

I think that’s one of the really hard parts about training – you can’t monotonically increase resistance day after day and expect yourself to improve without interruption, so you have to know when to reduce your efforts and let your body heal. The drawback to doing that though, is that when you start increasing your efforts again you’ll have lost a little bit of fitness. That’s why I’m scared of falling back – I keep thinking to myself, “I’ve gotten this far, but if I take a break I’ll lose fitness and I would have lost all the gains I’ve made, and all this work would have been for nothing.” I learned the lessons from that kind of thinking the hard way when I tore three of my tendons three years ago. That injury set me back for half a year, which was one of the most frustrating moments I’ve ever had as I was also dealing with hand problems at that time. Since then, I’ve learned to take it easy when I get fatigued, and I’ve been injury free for the last two and a half years.

From experience, I’ve noticed that it takes me about 4-6 weeks after a 2 week break (from doing absolutely nothing) to be back to where I was before, and over the next 4 weeks I’ll be doing things that I wasn’t able to do previously. That takes a lot of patience, but sometimes when I see my friends getting great results, it’s really tempting to increase my workouts beyond what my body can handle. So, sometimes it’s hard to convince myself to take a break, even when I’m fatigued.

With respect to my studies, I’ve been burned out since the first semester of my junior year of college, though there have been some periods, maybe 1-2 months at a time where I’d really be able to focus on learning. I feel like I’ve been close several times, but I still haven’t put in a sustained effort for 6 months or more since then. One of the things that’s different about adulthood is that you don’t have 4-5 months off like you do in college to rest and take your mind off things. On the other hand, in college, there are a lot more instances where the stress is really intense, whereas with work it’s spread out more evenly throughout the year, except you don’t get as much time off to relax. In my opinion, this is why it’s more important in your adult years to manage your time wisely – it’s really easy to get burned out if you don’t regulate your efforts carefully. In college, there are times when you can really push yourself, sleeping only 4 hours a night the month before finals because you know you’ll have a long time to rest afterwards once you’re done. It’s a lot trickier to effectively time your efforts as an adult, as once you’re done with a big project, you’ll have to go back to work the next day. I haven’t taken more than 4 consecutive days off work since November 2010…which seems like a big difference compared to the 100-day break I had in between semesters. It was especially though during my internship, but by now I’ve gotten used to it. I think if I took more than 2 weeks off, I’d start getting bored.

Anyway, I don’t really have anything new planned besides studying like crazy until the end of next month. I’ll try to keep the physical activity up, but last fall, I had to take 2-3 weeks off training before my exam to prepare. After that, I plan on starting up my Algebra studies again and hopefully sticking with it until I finish the course. Sometimes, I wonder if I’m wasting my time with basic material, but I don’t feel secure without a firm grasp of the fundamentals. I suppose that’s what my actuarial exams are for…as they cover concepts based on material from branches of mathematics that I haven’t seen before. In that way, I’ll at least have something new to learn while reviewing things from the past.