Sometimes, especially when reading news articles, I get the feeling people consider probabilities and odds to be the same thing. For example, here is a Business Insider headline claiming that Nate Silver is predicting “92% odds” of Obama victory. I think what they really mean is that Mr. Silver is predicting a 92% probability of Obama victory. There is a big difference between these two statements! Mathematically, the odds of an event are defined as the probability of the event happening divided by the probability that the event doesn’t happen. So, while a probability can take on any value from 0 to 1 (or, in percentage terms, 0%-100%, the odds can range anywhere from zero to infinity. In fact, when the odds of an event are 1, the probability is only 50%. In the example from above, if the odds of Obama victory were really 92% (=0.92), then the probability of victory would be only 0.48, or 48%. Here are some plots showing the relationship between probability and odds:

Finally, here is another blog post from “Simply Statistics” that illustrates the importance of variance in comparing statistical estimates. The main idea is that if the variance of your estimate is small (ie, that the estimate is very precise), then it could be numerically close to some other comparison value but still be considered “significantly different”.



One of my classmates in my statistics class at Georgetown asked me how I went from doing tropical biology to becoming a software tester. I decided to share my response here because it might be interesting to others who are contemplating a radical change in career direction.

I was convinced throughout college that I wanted to be a tropical field biologist. I studied abroad at a field station in Monteverde, Costa Rica, and after graduation spent almost a year doing research in the Philippines on seed dispersal of a particular understory tree. I even got a publication out of the latter in a German ecology journal. So, I was all set to go for a PhD in bio, but while I was in Manila and Bataan I took some time to reflect on where things were going and I realized I didn’t want to do fieldwork for the rest of my life. It is an amazing experience and I’m glad I had the chance to try it out, but as a career it is a very isolated and difficult lifestyle. You have to spend a lot of time in very remote, uncomfortable, and occasionally dangerous situations to collect data. Experiments often fail, and you have to wait a whole year until you can try again (due to the seasonality of flowering, fruiting, migrating animals, etc). Almost no one pays attention to biology research unless it has a medical application, and most tropical biologists spend their lives documenting the ongoing destruction of species and ecosystems they care for very much but feel powerless to protect. What this means is that in order to follow this path, one must be extremely passionate and dedicated to their discipline. I actually had the good fortune to study under such a person in the Philippines- a man named Leonard Co who in my opinion was a modern-day Linnaeus. Sadly, he was shot about a year ago while doing fieldwork. He was a cheerful, multilingual, botanical genius whose whole life was dedicated to scientific discovery and conservation.

Yet as much as I admired him, I realized I did not want to follow in his footsteps, because I couldn’t imagine myself specializing and focusing so intensely on a single subject. I like learning about a wide variety of things, and since the financial crisis was going on at the same time, I started reading a lot about economics, which I didn’t know much about previously. Furthermore, I had never lived in a big city prior to Manila, and even though I always thought of myself as a rural person, I learned to love the excitement and mental stimulation of the urban environment. By the time I came back to the US, I was totally confused about what I wanted to do career-wise, so I just decided to keep an open mind when I got a job offer to do software testing in Charlottesville. I have enjoyed this work for the past 3 years and am grateful to the folks who decided to take a chance on hiring someone based more on his sense of curiosity than his programming experience. Since I still enjoy learning about both biology and economics (and especially how they sometimes intertwine), I decided to go ahead and try for a masters through night classes in something that seems to be useful in both fields, which is how I ended up studying math and statistics. My career philosophy now is more about just making the most of whatever opportunities come around and trying to always be learning something new rather than having a master plan to save the world. I do hope to someday use my technical skills to help conservation efforts in places like the Philippines and other parts of the tropics, but I imagine it will be more in my personal time than as a career. Indeed, I have continued to visit tropical countries and am always inspired by the beauty of the landscapes and the generosity of the people in places like Colombia, Ecuador, Brazil, and Malaysia. I also feel fortunate to have maintained a connection to environmental issues through my work in that most of my projects have been supporting government (EPA) air quality and energy efficiency programs.

My Dad sent me a link the other day about entitlements, and how some of the most popular google searches in recent months have been people looking for ways to sign up for government benefits like unemployment, disability, etc. Also there was something about how a large fraction of Americans now depend on the government for at least part of their income. I don’t have a full understanding of these complex issues but here are some ideas about it floating in my head.

I agree that the entitlement system is unsustainable in the long-term. I’m reading a book right now called The Forgotten Man about the Great Depression that strongly argues against the New Deal, which was basically the start of the system we have today. The author argues that FDR’s heavy-handed, government oriented approach, which was partially inspired by observations of socialist policies in England, and to a lesser extent those of soviet Russia, stifled private sector innovation. She instead thinks Wendell Wilkie would have done a better job as president. On the other hand, according to this article, the historical origin of the entitlements was not out of the beneficence of the elite but rather a concession to avert European-style class warfare which could have led to an even more radical outcome (revolution), like it did in Russia and China.
“The Gilded Age plutocrats who first acceded to a social welfare system and state regulations did not do so from the goodness of their hearts. They did so because the alternatives seemed so much more terrifying.”
So as far as I can tell we are stuck between a rock and a hard place. Keeping entitlements undermines the strength of the national economy due to excessive tax burden on workers and investors, but eliminating them could lead to violent unrest among those who cannot make ends meet. I have no idea what the right solution is, but it seems likely it would have to involve some way of improving peoples’ training and education levels so that they can have the skills that are needed to survive. Here’s one social-entrepreneurial example along those lines that I admire: . Another interesting, related question is, to what extent does technological change affect unemployment?


This weekend I went on an awesome bike ride in Washington, DC through Rock Creek Park and back down to Georgetown via the Capital Crescent Trail. If you’d like to try it, here are some notes I sent to my friend about the ride:

  • I had no trouble parking on Water Street near Jack’s Boathouse even though there were a ton of other people out shopping in Georgetown.If coming across the Key Bridge turn on M Street going east then right on Wisconsin Ave.
  • From there I rode down the street to the Rock Creek trail which basically runs parallel to Rock Creek Parkway. It was narrow and crowded with pedestrians at first but after ~2 miles there wasn’t any problem.
  • Beach Drive through the park is closed on Sundays to cars, so it’s ideal for biking. I followed it all the way to Maryland.
  • Beach Dr turns into Jones Mill Rd. after crossing East West Hwy. I followed it to the intersection with Jones Bridge Rd. and turned left (South/West) onto Georgetown Branch Trail/ Capital Crescent Trail. Up to this point, the trail was paved and relatively flat with a slight uphill trend.
  • The first couple of miles on the Georgetown Branch trial were gravel but posed no threat to my very narrow road bike tires
  • After going through a giant tunnel, it empties out right in the middle of Bethesda row. You have to go across a tricky intersection but then the trail starts up again with pavement and is basically downhill the whole rest of the way.
  • You can then follow the Capital Crescent all the way back to Georgetown. It runs parallel to the C&O for the last several miles.
  • I think the total distance is a little less than 20 miles and it took me about 1.5 hours.
  • You could also do the loop in reverse, in which case it would be a long gradual uphill for the first half and then a slightly hilly flat/downhill the second half.

Many people are interested in trying out Google’s new social network Google+, but trying to re-add hundreds of friends is tedious. Facebook deliberately prevents users from exporting the email addresses of their friends directly. However, there is an indirect, legal way to extract all of your contacts from Facebook in a format suitable to be imported into any other social network or email system such as Gmail or Microsoft Outlook.

  1. Set up a free Yahoo Mail account.
  2. Select the “Contacts” tab and click “Import Contacts”
  3. Select “Facebook” and sign in with Facebook credentials.
  4. Yahoo imports the email addresses of all your Facebook friends automatically.
  5. Again on the “Contacts” tab, select “Actions” and click “Export All”
  6. Select “Export All” as Yahoo CSV (comma separated values list).
  7. Save this backup file to your local computer. You can open it in Excel or any text editor.
  8. Now sign into Google+. If you don’t have Google+ yet, sign up for a free Gmail account and skip to step 12.
  9. In Google+, select “Circles” and then “Find and Invite”.
  10. Select Yahoo and sign in with your Yahoo credentials.
  11. Google+ automatically imports all of your friends. If they are already on Google+ you can now add them to a circle. If they are not on Google+, you can send them an email invitation.
  12. If you don’t have Google+ you can also just import your friends into Gmail contacts and they will then appear in Google+ if/when you do sign up. To do this, log into Gmail and select Contacts, then Import Contacts. Gmail will ask you where your CSV file is stored (from step 7). Once it has uploaded, all of your Facebook friends’ email addresses will be in your Gmail contacts.
  13. Note that you can also use the Yahoo contact exporter to transfer Facebook friends’ emails into Microsoft Outlook or any other email/ address book (you might have to export as Vcard or some other format if the CSV option doesn’t work).

And that’s it! I look forward to seeing all of you on Google+.

Yesterday was my birthday, and it was a fantastic, joyful day that filled me with delight. It wasn’t because I got a bunch of presents or cake or anything like that (although last weekend I did have a great time celebrating in such fashion with my family in North Carolina too). In fact, I spent most of the day in the office working. The reason I am so happy is that so many of my friends and family sent me birthday greetings from all over the world! I know it seems like a small thing just to post on someone’s facebook wall or send them a text message, but those small gestures mean a lot to me.  I want to say THANK YOU to all of you near and far for being my friends. Whether I met you only for a weekend while traveling or have known you since I was a little child, your kindness, inspiration, and the new perspectives you have given me are what make me glad to be alive. If a good friend is more valuable than gold, then today I feel like the richest man in the world.

[En Espanol] Ayer fue mi cumpleanos, y fue un dia fantastico con mucho felicidades, que me lleno con gusto. No fue porque yo recibi muchos regalos, ni pastel, ni algo asi (aunque la fin de semana pasada me diverti mucho celebrando con ellas cosas con mi familia en Carolina del Norte). En serio, yo pasaba la mayoria del dia trabajando en la oficina. El razon que estoy tan feliz es porque tantos amigos y familia me mandaron saludos desde muchos paises y lugares diversos del mundo! Se que parece una cosa de poca importancia poner algo en el “muro” del facebook o mandar un mensaje por text, pero esas cosas pequenitas significan mucho a mi. Quiero decir GRACIAS a todos Uds. cerca y lejos por ser mis amigos. Si te conoci solo por una fin de semana cuando viajando, o si te he conocido desde cuando eramos ninos, tu amabilidad, inspiracion, y las vistas nuevas Uds. me han ofrecidos son los que me dan feliz vivir. Si un amigo verdadero o amiga verdadera vale mas que oro, entonces hoy me siento como el hombre mas rico del mundo.

[Em Portugues] Ontem foi o meu aniversario, e foi um dia fantastico com muitos felicidades que me cheio com gosto. Nao foi porque eu recebi muitos regalos, nem bolo, nem algo assim (ainda que a fim de semana passada me divirti muito celebrando de tal forma com minha familha em Carolina do Norte). Em realidade, eu passava a maioria do dia trabalhando no escritorio. O razao que estou tao feliz e porque tantos amigos e familha me mandaram saudacoes desde muitos paizes e lugares diversos do mundo! Sei que parece uma coisa de pequena importancia colocar algo no “muro” do facebook ou mandar um mensagem de text, mas essas coisas pequenas significam muito pra mi. Quero dizer OBRIGADO a todos voces perto e longe por ser meus amigos. Se eu te conheci so por uma fim de semana quando viajando, ou se eu te tenho conhecido desde quando eramos criancas, teu amabilidade, inspiracao, e as vistas novas voces me tem ofrecidos sao os que me dar feliz viver. Se um amigo verdadeiro ou amiga verdadeira vale mais que ouro, entao hoje me sinto como o homem mais rico do mundo.

[Sa Tagalog] Kahapon ay ang aking kaarawan, at ito ay isang mabuting, masayang araw na napuno ako sa tuwa. Ito ay hindi dahil ibigay ng mga regalo o cake o anumang bagay tulad na (bagaman katapusan ng linggo ko ay may isang mahusay na oras pakikisalu-salo sa tulad ng paraan kasama ang aking pamilya sa North Carolina pa rin). Sa katunayan, nagtrabaho lang ako sa opisina. Ang dahilan ako kaya masaya ay na kaya marami sa aking mga kaibigan at pamilya na ipinadala sa akin na pagbati ng kaarawan mula sa buong mundo! Alam ko ito tila tulad ng isang maliit na bagay lang sa post sa facebook wall ng isang tao o ipadala ang isang text na mensahe, ngunit ang mga maliliit na gestures ibig sabihin ng marami sa akin. Gusto kong sabihin SALAMAT sa lahat ng kayo malapit at malayo para sa pagiging mga kaibigan ko. Kung makilala kita lamang para sa isang katapusan ng linggo habang naglalakbay o may kilala kita mula sa kailan ako ay isang maliit na bata, ang inyong kabaitan, inspirasyon, at ang mga bagong perspectives sa iyo ay may ibinigay sa akin ay kung ano gumawa ako masaya mabuhay. Kung ang isang mabuting kaibigan ay mas mahalaga kaysa sa ginto, tapos ngayon pakiramdam ko ang pinakamayamang tao sa mundo.

I recently had a conversation with two friends from work about personal finance and investing. Having read many articles about the precarious state of most American families’ finances, I am trying to discipline myself to spend less than I earn and plan for the future. Here’s my basic strategy:

  1. Build up “emergency savings” cash in a regular savings account, enough to pay all bills for 3-6 months. Bankrate is a good tool to compare offerings by online banks.
  2. Pay off debt, especially student loans since they are the only ones that can’t be discharged by personal bankruptcy.
  3. Put some of each paycheck into a roth IRA (can fund it up to $5000 per year of earned income)
  4. Within the roth IRA, buy index funds once every 2-3 months (and almost never sell, to avoid commission fees) to maintain asset allocation based roughly on the following formula:
  • 30% domestic (US) stocks, such as SPY
  • 15% real estate investment trusts, such as VNQ
  • 15% international developed market stocks (Europe, Japan), such as VEA
  • 12.5% government bonds, such as TLT
  • 12.5% inflation protected government bonds, such as TIP
  • 10% emerging market stocks (Brazil, China, etc), such as VWO
  • 5% commodities/ individual stocks, such as POT

Any dividends/interest/tax refund/etc gets reinvested in roth as well. I use Scottrade as broker but there are a bunch of other cheap ones too.

The reason I prefer index funds over individual stocks is because the risk is associated with the whole economy, rather than an individual company, and I don’t have the skill to predict which company will go up or down in the future (on the other hand, because the variation in returns is smaller, the potential for large gains is also less). Mutual funds have the same features of diversification, but the reason I don’t like them is because they often have high “management fees”. In the 401(k) you have almost no choice but to put up with such fees, which is why I like the roth IRA better. Here are some more articles that explain the pros and cons of index funds:

Vanguard is a company that is well-known for its low-fee funds (example: VWO tracks emerging market equities)

Another example of an exchange-traded index fund (ETF) that tracks the S&P 500 index is SPY.

I also like the “motley fool” site for general personal finance advice.

Finally, here are a couple of counter-perspectives: