Tag Archives: probability

Great Ideas.

Book review: ‘Ten Great Ideas about Chance’

If life is a game a chance, knowing how to weigh your odds makes all the difference.Great Ideas.

“Ten Great Ideas about Chance”
By Persi Diaconis, Brian Skyrms.
Princeton University Press, 272pp. | Buy on Amazon

Throughout the sixteenth and seventeenth centuries, gamblers and mathematicians set the stage for a new line of thinking that would shape nearly every field today, from economics and finance to physics and computer science: they transformed chance from something that happens to you into a well-ordered discipline, something you can calculate and quantify. This book traces ten great ideas that shaped the field, exploring the mathematical, historical, philosophical, even psychological aspects of probability and statistics.

Accessible, yet meticulous in its math, Persi Diaconis and Brian Skyrms‘ Ten Great Ideas about Chance is an instructive but fun lecture.

Roll the dice

The book was borne of an interdisciplinary course the two authors — one a mathematician and one a philosopher — taught at Stanford University. As such, it’s built on the assumption that you’ve had some prior experience with either statistics or probability. In case you haven’t, the authors included an Appendix with a brief rundown of the basic elements of probability.

Each of the ten great ideas discussed in the book gets its own chapter. The first will take you through a brief tour of the early days of probability theory, starting with the 1500s, and introduce the concept that chance is, in fact, something we can measure. Chapter 2 also deals with measurement, showcasing how probabilities can be measured in more complex situations that lack a finite collection of equally-probable outcomes.

The third great idea is that, as humans, we’re inherently bad at dealing with probabilistic concepts. One simple example that shows how much wording influences our perception is the operating room scenario: telling a patient that they have a 90% chance of surviving an operation, for example, is more likely to induce him to agree to the procedure than telling him he has a 10% chance of dying — despite that both statements mean the exact same thing.

The fourth and fifth chapter explores the connection between probability and frequency, followed by two chapters dedicated to Bayesian analysis. Chapter 7, titled “Unification”, binds all these together and cements the links between chance, probability, and frequency.

The following two chapters impart context to probability theory, showing how it relates to other disciplines. Chapter 8 deals with algorithmic randomness, the use of computers for random number generation, while chapter 9 looks at probability in the context of physics. The final chapter deals with Hume’s assertion that, in the authors’ words, “there is a problem of understanding and validating inductive reasoning.”

Should I read it?

Ten Great Ideas about Chance treats the topic from an unusual angle, and it will help any faculty members teaching probability by providing a fresh take. The book uses calculus quite freely, and a solid understanding of integral signs and limit arguments will come in very handy while navigating its pages.

But don’t get discouraged by the technical talk — the book packs this stuffy topic in a pleasant, easy to read format. As someone with only a summary education in the field, I can attest that even those of us who are newcomers to probability will find quite a lot of interesting information here, peppered with “aha” moments. Even if math wasn’t ever your cup of tea, Ten Great Ideas about Chance remains accessible — despite some chapters being quite challenging and likely to give non-specialists some hard times, most of the book (especially its earliest chapters) do a great job of conversing with a wide audience.

One feature I’ve especially appreciated is the inclusion of end-of-chapter summaries, as it really helped wrap my brain around some of the topics I’ve had difficulty with. Ten Great Ideas about Chance also features an annotated bibliography and appendices in many chapters, which treat topics the authors deemed too tangential or technical for the main body of the work.

All in all, it’s a great book for anyone who wants to understand some of the central tenets of probability, how they were discovered, and how they can be tamed in our day-to-day lives.

Probabilistic computing is a game changer

With the development of the internet, data availability is often times not a problem – it’s what you do with the data that actually matters. As a matter of fact, analyzing huge data sets and looking for patterns is a big part of what programmers do today. In what promises to be a huge game changer, computer scientists have developed so-called probabilistic programming languages, which let researchers mix and match different machine-learning techniques.

Image via Extreme Tech.

Using this newly developed technique of probabilistic computing, MIT researchers have demonstrated short programs (about 50 lines of code) which are competitive with conventional systems with thousands of lines of code. The development might be hugely important for facial recognition and reconstruction software, among many others.

“This is the first time that we’re introducing probabilistic programming in the vision area,” says Tejas Kulkarni, an MIT graduate student in brain and cognitive sciences and first author on the new paper. “The whole hope is to write very flexible models, both generative and discriminative models, as short probabilistic code, and then not do anything else. General-purpose inference schemes solve the problems.”

For many programmers, the probabilistic approach might seem like blasphemy – it’s so vague that it goes against some of the very cores of traditional programming. It’s basically straying away from mathematical thinking, and moving onto a more intuitive approach.

“When you think about probabilistic programs, you think very intuitively when you’re modeling,” Kulkarni says. “You don’t think mathematically. It’s a very different style of modeling.”

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Just like the name says, probabilistic programming is… probabilistic; well, sort of. The difference maker is something called the inference algorithm – an algorithm that continuously readjusts probabilities on the basis of new pieces of data. It constantly changes, but it’s probabilistic, not deterministic – hence the not-so-mathematical thinking.

Among the tasks they tackled was reconstructing a 3D image of a face using only 2D images. This new work is basically a new take on inverse graphics, which is one of the oldest issues associated with machine learning. For their experiments, they created a probabilistic programming language they call Picture, which is an extension of Julia, another language developed at MIT.

“Picture provides a general framework that aims to solve nearly all tasks in computer vision,” says Jianxiong Xiao, an assistant professor of computer science at Princeton University, who was not involved in the work. “It goes beyond image classification—the most popular task in computer vision—and tries to answer one of the most fundamental questions in computer vision: What is the right representation of visual scenes? It is the beginning of modern revisit for inverse-graphics reasoning.”

Kulkarni says, Picture is designed so that its inference algorithms can themselves benefit from machine learning, modifying themselves as they go to emphasize strategies that seem to lead to good results.

“Using learning to improve inference will be task-specific, but probabilistic programming may alleviate re-writing code across different problems,” he says. “The code can be generic if the learning machinery is powerful enough to learn different strategies for different tasks.”

 

Lady Luck

Dwelling inside the gambler’s mind

Lady Luck

Lady Luck

There’s a lot more to gambling than just luck, and whilst it’s impossible to predict an outcome or utilise a system effectively, the human brain and our emotions have a lot to do with the decisions we make during the gambling process.

Expectation

spinning wheels

spinning wheels and that feeling of hope

Say you slide a coin into a one armed bandit, pull the lever and watch the reels spin. Whilst there’s no way you can predict which of the fruits are going to eventually present themselves once the reels have stopped, we still have that feeling of hope. These kind of machines are programmed to return only about 90% of wagered money, so the chances are high that you lost your money – but what makes us return for more?

The answer lies with neurology
. The human brain is invaded by dopamine neurons – these are used to predict future rewards. These neurons struggle to decipher the patterns or determine a solid outcome when you are gambling. Because they can’t get to grips with the machine’s patterns or algorithms produced by a microchip, our dopamine neurons, instead of surrendering, become obsessed. Because the release of dopamine is a ‘feel good’ chemical like serotonin, whenever we pull the lever and win, we experience a rush of pleasure. The end result of our neurons continuously trying to figure a pattern out is that the machine transfixes us and we continue to play.

Chemicals

Technically All You Enjoy

Serotonin and dopamine are both chemicals linked with feeling good, so when these are stimulated through winning and the thrill of the next win, they can influence the decisions you make. Whilst the pragmatic side of you may know you will lose, the feelings induced by winning may over power any pragmatism.
Alcohol also affects the way you gamble. If you mix alcohol with dopamine and serotonin you are creating a mix almost impossible to surrender to should you start winning at the casino. Alcohol creates confidence and gives you a false sense of security about future wins.

Addiction

Some people are more susceptible to feeling a dopamine rush than others, and as games of chance are designed to take advantage of this cellular pathway inside the brain, some people are more likely to become addicted to gambling than others. Gamblers who experience massive rushes of pleasure from a win are blinded by the fact they are losing money searching for that next win. Casinos have figured out a way to make us almost want to lose money.

Psychological Trickery

casino chips

Although it’s the gambler that usually cheats the casino, these establishments use a few psychological tricks on the brains of its visitors.

A casino’s flashing lights and the sounds of clinking money express winning and the joy felt by winning – it’s contagious. Because we possess the need to feel socially normal, experiencing the thrill of winning and being admired by those around you is extremely powerful.

Chips are used instead of real money – this alters the gamblers’ sense of money. Throwing down three £50 chips whilst in the act of an exciting gambling moment becomes just like using three $10 chips.
Casinos always offer complimentary alcoholic drinks and food to keep players gambling, and as I previously mentioned, alcohol can impair judgement as to the chances of winning. The money a casino makes from the gamblers’ loss massively outweighs the cost of the food and drink.

Cheating

cheating at cards

Cards the classic cheaters hit

I think it’s safe to say everyone has considered or thought about cheating, especially after hearing about people who’ve cheated millions from a casino. Unfortunately this is nothing but a romantic image only seen in the movies. Although cheating has serious consequences in real life, this doesn’t seem to prevent the interest in gambling cheats.

Past posting is a method used by players after a bet has been made. In roulette, for example, the player will attract the attention of the dealer so they can either switch the winning chips for a higher denomination chip or push their chips to the winning number.

Collusion is a very popular form of cheating, one in which needs two or more people. You often see this used in the movies but it can be picked up on by the casinos. In poker, the two partners signal to each, expressing to each other the values of their cards. A player may have a friend strategically placed as to spy on the other players and then signal their cards.

So the next time you are in the casino or playing online at Gaming Club online casino and find yourself faced with that tricky decision whether to stop or not, take a minute and ask yourself what your brain is really trying to tell you.