Little Book of R for Time Series

“By Avril Coghlan, Parasite Genomics Group, Wellcome Trust Sanger Institute, Cambridge, U.K. Email: alc@sanger.ac.uk

This is a simple introduction to time series analysis using the R statistics software.

There is a pdf version of this booklet available at https://media.readthedocs.org/pdf/a-little-book-of-r-for-time-series/latest/a-little-book-of-r-for-time-series.pdf.

If you like this booklet, you may also like to check out my booklet on using R for biomedical statistics, http://a-little-book-of-r-for-biomedical-statistics.readthedocs.org/, and my booklet on using R for multivariate analysis, http://little-book-of-r-for-multivariate-analysis.readthedocs.org/…”

http://a-little-book-of-r-for-time-series.readthedocs.org/en/latest/index.html

Markov Chains – Explained

“Markov Chains is a probabilistic process, that relies on the current state to predict the next state. For Markov chains to be effective the current state has to be dependent on the previous state in some way; For instance, from experience we know that if it looks cloudy outside, the next state we expect is rain. We can also say that when the rain starts to subside into cloudiness, the next state will most likely be sunny. Not every process has the Markov Property, such as the Lottery, this weeks winning numbers have no dependence to the previous weeks winning numbers…”

http://techeffigy.wordpress.com/2014/06/30/markov-chains-explained/

How to gamble if you must—the mathematics of optimal stopping

“Every decision is risky business. Selecting the best time to stop and act is crucial. When Microsoft prepares to introduce Word 2020, it must decide when to quit debugging and launch the product. When a hurricane veers toward Florida, the governor must call when it’s time to stop watching and start evacuating. Bad timing can be ruinous. Napoleon learned that the hard way after invading Russia. We face smaller-consequence stopping decisions all the time, when hunting for a better parking space, responding to a job offer or scheduling retirement.

The basic framework of all these problems is the same: A decision maker observes a process evolving in time that involves some randomness. Based only on what is known, he or she must make a decision on how to maximize reward or minimize cost. In some cases, little is known about what’s coming. In other cases, information is abundant. In either scenario, no one predicts the future with full certainty. Fortunately, the powers of probability sometimes improve the odds of making a good choice.

While much of mathematics has roots that reach back millennia to Euclid and even earlier thinkers, the history of probability is far shorter. And its lineage is, well, a lot less refined. Girolamo Cardano’s famed 1564 manuscript De Ludo Aleae, one of the earliest writings on probability and not published until a century after he wrote it, primarily analyzed dice games. Although Galileo and other 17th-century scientists contributed to this enterprise, many credit the mathematical foundations of probability to an exchange of letters in 1654 between two famous French mathematicians, Blaise Pascal and Pierre de Fermat. They too were concerned with odds and dice throws—for example, whether it is wise to bet even money that a pair of sixes will occur in 24 rolls of two fair dice. Some insisted it was, but the true probability of a double six in 24 rolls is about 49.1 percent…”

http://www.americanscientist.org/issues/id.5783,y.2009,no.2,content.true,page.1,css.print/issue.aspx

The 10 Hardest Logic Puzzles Ever Created

“So you think you are clever, right? Then here is your chance to pit your brain against some of the world’s hardest logic puzzles ever created. After having created number puzzles like Calcudoku and Killer Sudoku for many years, I decided to try and find the most challenging ones out there. Every once in a while I added a new type of puzzle, until I ended up with a list of 10.

In the following list you will find both familiar puzzles and games such as Sudoku and Calcudoku as well as lesser known ones such as the Bongard Problem and Fill-a-Pix. Some of these puzzles can be solved right on this page while others can be downloaded or reached elsewhere. All of them, however, are promised to test your solving skills to the absolute limit and keep you busy for hours, if not days…”

http://www.conceptispuzzles.com/index.aspx?uri=info%2Farticle%2F424

Probablistic Programming & Bayesian Methods for Hackers

“The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a so-what feeling about Bayesian inference. In fact, this was the author’s own prior opinion…”

http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/

Probability Through Problems: a new approach to teaching probability

“Which team will win? – introducing tree diagrams and the method of collecting data which is then interpreted in terms of what we would expect if we could collect enough data
The dog ate my homework – building on this, expressing expected results in the form of proportions, and hence answering questions about how likely an event is
Who is cheating? – from expected results to probabilities in the form of fractions, and the multiplication rule (and onto conditional probability)
Prize Giving – from experiment to sampling with and without replacement…”

http://nrich.maths.org/newprobapproach