Has the NYC Taxi Medallion bubble burst?

There are 13,437 medallions, the license to operate a taxi in NYC. This artificially imposed limited supply has lead to an exponential rise in the price of medallions over the decades. The recent advent of UBER has increased the vehicle supply, reduced ride fares and more importantly, pricked the medallion price bubble. The price of the NYC taxi medallions is falling rapidly from a peak of $1 million in less than one year. The stock price of the Medallion Taxi Corp is plummeting. Reason TV has done a great job in covering this story.

Should the companies that invested in inflated taxi market, or the people who borrowed (multiple refinancing) again the medallion  be bailed out now?

Gambler’s Ruin


I discussed random variables,discrete probability distributions and expected values in my data analysis class this week. After the mundane definitions and examples, I threw at them, a variant of the gamblers ruin idea and asked them if they would be willing to bet their money on it. The idea goes like this:

I have a coin toss game where I give you 2 times your bet if you win and nothing if you lose. Assume we have a fair coin, would you play the game with me and bet your money? If you will, then what is your strategy, assuming you are in it to win…

It turns out that a few in the class wanted to play the game, but did not know the best strategy to win. These were risk takers and willing to bet their money with a 50-50 chance. Much of the class was conservative and didn’t want to play.

There were a handful who think gambling is bad!!.

There is a winning strategy in this game and if you have enough money to bet, there is a high chance that you will double your initial bet. I start with a bet of $x. If I win in the first toss, I will take my $2x and leave. If I lose in the first toss, I will double my bet to $2x and play again. If I win, I get $4x. Since my investment was $x + $2x, I make an additional $x. You can keep doing this till you win, but the first time you win, you should stop.

The game follows a geometric distribution, with a Pr(X = k) = (1-p)^{k-1}*p, probability of first win on the kth try. Since winning probability is 0.5 for a fair coin, the chance of winning it in the first try is 0.5; the chance of winning it in the second try is (0.5)(0.5), the chance of winning in the third try is (0.5)(0.5)(0.5) and so on…So, you will have a decent chance of winning (more than 90% chance) within the first 5 trails. Just stop playing it the first time you win..and take your money.

I know, it is easy to throw numbers and show that I can win… but will I bet my bucks on it? I can perhaps bet a $100 and win back my $100 plus an additional $100, because i can rise the bets up to a limit.. I am not willing to bet $1000 or more …

Here are some gambler’s ruin ideas.

UN Sustainable Development Science Symposium Talk

On Monday, September 21st, I spoke at the UN Sustainable Development Science Symposium held at CUNY Graduate Center. The circular science seminar series is organized in the context of the opening of the 70th General Assembly of United Nations. My talk was about Securing the Global Water Sustainability and Food Security. Here are some excerpts/key points from the talk:

Where will the food for the 9 billion people we expect on Earth by 2050 come from? The answer to this question depends on where the water and the energy for agriculture will come from. Establishing an economically, environmentally and physically feasible pathway to achieve water, energy and food security in the face of a changing climate is crucial to planetary well-being.

A central hypothesis of this work is that innovation towards agricultural sustainability in countries such as India and China, that have large populations relative to their water, energy and arable land endowment, and yet have opportunity for improvement in productivity metrics such as crop yield per unit water or energy use, can show us the way to achieve global water-food-energy sustainability.

These countries experience a monsoonal climate, which has a high frequency of climate extremes (more floods and droughts, and a short rainy season) relative to the developed countries in temperate climates. Strategies that are resilient to such extremes in monsoonal climates may be of global value in a warmer, more variable world. Much of the future population growth is expected to occur in Africa, S. America and S. Asia. Targeting these regions for higher productivity and resilience is consequently important from a national security perspective as well.

Learning from River’s History

Recently, I spoke to Lakis Polycarpou from Columbia University about my trip to
Bozeman, MT for an NSF project meeting on Paleo reconstruction of river discharges using tree rings for the Missouri River basin. Reconstruction of discharge from tree rings spanning past several centuries can provide a more complete picture of the range of variability (the deviation from average conditions) of the flows in the river at decadal to longer time scales. This proxy information (long history of flows) can be used to evaluate how good the current water policies are in the context of history. Here is the link to his article on our discussion.

treeflow.info is a very useful resource on tree rings, climate and water management.

For the more modeling-saavy, you can read my article on streamflow reconstruction using tree rings for the New York City reservoirs.






Source for the tree photograph: Dear friend Uday Maripalli’s Instagram.

China’s Water Sustainability in the 21st Century

China is facing a water resources crisis with growing concerns as to the reliable supply of water for agricultural, industrial and domestic needs. High rainfall variability (both within the year and across years) and increasing consumptive use across the country exacerbates the situation further and is a constraint on future development. During his visit to New York, Xi Chen worked on examining the overall water situation in China. Obtaining data for such an analysis, especially for all China is certainly a challenging task and Xi Chen has to be commended for his perseverance during this phase.

In this project, we modeled the differences in water demand and supply and their spatio-temporal distribution to quantify the dimensions of the water risk. The work provides a detailed quantitative assessment of water risk as measured by the cumulated deficits for China. Considering daily precipitation and temperature variability over fifty years and the current water demands, risk measures are developed to inform county level water deficits that account for both within year and across year variations in climate. We choose political rather than watershed boundaries since economic activity and water use are organized by county and the political process is best informed through that unit. The risk measures highlight North China Plain counties as highly water stressed. These regions now have depleted groundwater aquifers.


Water requirements for industrial use and energy and mineral processing and production will continue to increase in China, as will the need for high quality domestic water use as living standards and economic factors continue to improve. Given this, we also provided some recommendations for future water sustainability in China. The full article can be found here.

Predicting Rainfall in China’s Huai River Basin

Here’s a shout out to Xi Chen, a visiting scholar from Hohai University for publishing his first journal article. His research on forecasting summer rainfall in China’s Huai River Basin using large scale climate information is now published in Hydrology and Earth System Sciences (HESS)journal. HESS is an open access journal that is operated by the European Geophysical Union. Xi Chen led the project from data collection and quality control to model development and validations. During his visit, he worked on several projects on climate forecasts, water sustainability, and hydrologic extremes in droughts and floods. This is the first of a series of publications he is working on. The full article can be found here. A brief description about the project and its importance:

Huai River Basin is densely inhabited and serves as one of the main cropping area in China. The region has 36 reservoirs designed for supplying water for various needs and for controlling floods. One of the main issues in managing water in this basin is periodic droughts and floods caused by high variations in rainfall. In this work, we developed a statistical model that will forecast the amount of total summer rainfall before the season begins; i.e. the probable rainfall for the months of June, July and August every year will be predicted at the beginning of May. This one month lead time will enable water managers to make decisions on whether to release more water during the season (if there is a forecast of good rainfall) or to store more water in the dams (if there is a forecast of drought). Farmers can use this forecast information and the lead time to make choices on what type of crop to grow and secure the sources of irrigation.

Since we are interested in predicting the rainfall and river flows in 14 different locations in the basin, we develop a multivariate regression model that relates the rainfall and flows with identified pre-season climate predictors (like El-Nino Southern Oscillations). Knowledge on the evolving conditions in the tropical Pacific Ocean (climate predictor) will inform the atmospheric moisture tracks and ultimately the amount of rainfall. This is a high dimensional problem that required accurate representation of uncertainties and simultaneous predictions at multiple locations. Given these challenges, we used a Hierarchical Bayesian Model to explicitly quantify the parameter uncertainty through each estimation stage using appropriate conditional and prior distributions. It allows for grouping of information across the different locations. The covariance structure will provide the ability to properly represent the cross site correlation.

We are now using these forecasts along with changing demand through adaptive human behavior to specify dynamic rules for operating multiple reservoir systems in the basin. This will allow for better management of deficits from the reservoirs.

Engineering New York City

Next week is the start of a busy Fall semester.

I am teaching “Civil Engineering Data Analysis” again where I cover applied probability and statistics for engineering students. It is an introductory class that provides fundamentals in exploratory data analysis and descriptive statistics, probability distributions and their applications in civil engineering problems, statistical inference and hypothesis tests, and finally introduces regression and non-parametric models.

The student groups will develop statistical models for analyzing the reliability and resilience of New York City engineering systems. This is my take on finding Engineering in New York City:

“From now through your senior years, you will learn a variety of concepts in Civil Engineering that will enable you to solve societal problems by efficient application of the underlying scientific principles. New York City adds a special flavor to your ongoing pursuit of mastery in engineering discipline. It is among a few on the planet where you will witness a collage of interlinked systems working coherently for a smoothly functioning city providing a fascinating urban experience. Perceive the marvels in your city, for nowhere in the world will you notice an entire civil engineering manual in practice.

Some of you may end up as structural engineers where you learn the theory of structuresstrength and properties of materials, building designs and loadings. You will be reinforcedwith the concepts of pre-stressed concrete and steel designs. Remember to stop, think and appreciate the massive building construction projects that you come across daily. You may be designing them in the near future.

Do not curse the subway workers for delays on your way back home during the wee hours. Perhaps they, like you, are finishing up their homework on surveying and site investigation. They are conceivably the best experts on geology, soil and rock mechanics and tunneling.

Occasionally, embrace the complexity of the city’s road and highway networks whether you are simply walking down the block or commuting from suburbs via tunnels and bridges. One of these days, you will be asked to come up with a “lowest toll charge for optimal traffic flow inbound and outbound of the Lincoln tunnel” or infrastructure upgrade for the growing populous. Oh, did I forget how busy you will get, changing signals with your computer models when you have to evacuate people during hurricanes.

Your soaring water and sewer bills are invisibly gravitating oceans of clean water from Catskill Mountains to your house and disposing your sewage to the oceans. While you are grumbling about the raising bills, look for opportunities to repair and retrofit the crumbling water infrastructure in the City and the Country.

If you don’t like water supply, stretch yourself towards the waterfront to power the “city that never sleeps”. While you are at the harbor front, try your luck as an impressive maritime engineer over a hot summer break.

Brag about the Wall Street while you are a New Yorker, for one day, you may also become the director of innovative financial insurance company that hedges the risk to the civil infrastructures.

Recognizing the inherent uncertainties in engineering systems, let us develop “statistical thinking” that will give us valuable tools to understand and incorporate the variability into final decision making process.

Throughout this semester, we will work on analyzing and designing New York City’s engineering systems. So, groom your calculus; assimilate your Math skills; fortify your Csc 102 and finally assemble your logical deductive reasoning for an amazing semester long statistical engineering experience.”

Gripe on Units and Conversions

I went to DUANEreade to get an instant photograph. I wanted a 4 cm by 3 cm photo. The photographer, who is also the store manager was not thrilled at this prospect since his camera did not carry 4 by 3 option. However, since it had 43mm by 33mm option, I asked him to use that. The picture is taken, the prints are out and he used the standard paper trimmer to give me 25mm by 25mm photo. I don’t possess a sharp measuring eye, but this clearly did not look like what I asked for. I requested him to check the size once again since this was clearly looking anomalous. He gave me a startled look and said it was accordingly to what I asked for. He even browsed through his smart phone for 5 minutes to convince me that 4cm by 3cm = 40mm by 30mm. Unfortunately, his validation should have been using the ruler or the measuring scale on his paper trimmer and not the phone.

I am not giving up.. I went to the stationary section, grabbed a ruler and proved to him that he gave me a 25mm by 25mm photo. He clearly did not like this verification and hesitantly agreed to take another photo. So, the photo is take again, printed out (only this time, he used the option of 43 by 33 on his computer) and trimmed. All the while he alluded to his 30 years photography experience where he never encountered a customer who asked for a passport sized photo that is 40 by 30 and that the standard size he is used to is the 25 by 25. I thanked him, paid at the checkout and left. I am never going back to DUANEreade again for an instant photograph even for a standard size of 25 by 25.


This is an old post when I first got my iPhone. I still like my 5s but may be it is time to upgrade to the 6 series.

January 17, 2014:

For some time now, as I am about to get off the bus every day in Weehawken, I am counting the number of people who are busy with their smart phones. The bus carries about 50 passengers and almost always 40 of them are either on “game center”“networking” (Facebook blah blah) or music (mostly iTunes). I was among the few who are left out of the action, perhaps because of my adamancy on pretending to be a medieval person.

Not anymore, as I recently switched to the most elegant smart phone in the market, the one and only iPhone 5s. Indeed, we have made amazing technological progress since the medieval age and the recent smart phone revolution personifies this brilliance. This is not meant to be a review for iPhone 5s as I am still naïve to smart phones, but soon I may have to participate in the eternal debates of iPhone technology vs Android technology. I just hope that it won’t end up like emacs Vs vim. I created a chronology of my exposure to phones that dates back to the antique ringer phone. Have you given a thought about how may phones you had?


Yellen is the Road to Weimar

I wrote about Janet Yellen and her thoughts on gold when she was appointed as the Fed Chairman. She will have to come out with QE infinity to hold the slipping stock market. Here are my thoughts on her (I wrote this blog on December 4, 2013).

“She’s a very bright lady,” Greenspan said of Yellen on CNBC. “I think she will surprise everybody, I mean in a positive way.”

The only person who should be happy about Janet Yellen’s nomination as Federal Reserve Chairman is Uncle Ben himself. Just like how Greenspan got out of dodge before the housing bubble burst, Ben Bernanke is getting off the hook before the next economic collapse. During his term, Bernanke managed to double the stock market with his QE 1 – QE 4 and Operation Twist. He can now leave without tapering and claim credit for putting the economy back on track in five years. However, for this fake growth (bubble) to sustain, Janet Yellen has to take QE4 to QE infinity and destroy the purchasing power of the dollar. Yellen is oblivious to inflation and doesn’t believe in sound money or austerity.

“Nobody has a good model of what the fundamental value of gold is or should be”, stated Janet Yellen in her hearing before the Senate. If one cares about the value of gold (the Fed Chairman should be the first person to care), we do not need “models”. We need to open up our eyes to the fundamental theory of money and realize that it is the very inflation of the fiat money supply that causes the price of gold to rise. With such crazy inflation all around the world now, Weimar Republic and Zimbabwe will only become median statistics in history. We are going to witness, in our lifetimes, the tail of this distribution. Get some gold and crash proof yourself.