The likelihood measures the goodness of fit of a model to a sample of data, for given values of the unknown parameters.
It is formed from the Joint probability distribution of the sample, but viewed and used as a function of the parameters only, treating the random variables as fixed at the observed values (like in Bayes?).
See also Learning
In their book Art & Fear: Observations On the Perils (and Rewards) of Artmaking, David Bayles and Ted Orland say that by their observation the elements that prove to allow a creative person to work are essentially idiosyncratic.
For example, they say, Hemingway discovered that in order to be productive, he needed to stand up while typing.
And, they continue, this discovery of Hemingway's is useless to nearly everyone else: other artists find what they need to be productive is something different.
Most productivity suggestions are naturally from people who found something that worked for them, and so recommend that's what you should do: "The Standing Up Method for Productive Writing".
So in lieu of a working general theory, the solution is to be experimental on a personal level: find a way to measure your productivity, even if subjectively, vary your working conditions in systematic way, and see what makes a difference for you.
– www.greaterwrong.com/posts/NyFtHycJvkyNjXNsP/chaotic-inversion?commentId=oGXDkvKc2XDJKJEQ6
A typical city grows in two dimensions, and would happily grow in three and four and five if it was possible.
That doesn't mean it should.
A basic problem of city planning is making sure everything is within reasonable reach of every highway, bus route and subway station, while not spending too much.
What's a city planner's wet dream? That this would be straightforward, easy. That you could predict the load on a given section of subway, now and in the future.
Suppose you didn't have any cities. You're a king in a country of farmers. What even is a city, they ask you.
Suppose you then build a stretch of rail across your kingdom. With no particular location to connect to, you can choose the flattest parts of land, to make your rail as cheap and straight as possible. It's still expensive, but it lets farmers from one end trade with farmers from the other end.
You build your castle and other stuff along this rail. Eventually there are marketplaces, industries, services, hotels, and apartment buildings. The rail is starting to pay for itself. Ford is marketing a new thing called 'automobile', but you feel no need to import any. There's still plenty of empty spots along your rail, and all buildings are within walking distance of the rail. Even bicycles don't interest anyone: the train is fastest.
Commute is sometimes long. But there is now so much dense cityscape along your rail, that you can afford to build a vacuum-tube train. Now commute is short, always short. The use of the vactrain is 100%: it's perfectly placed, so its potential is reached.
#statistics, Identifying power law data
Under at least one definition, a fat-tail distribution is one whose tail is fatter than that of the exponential distribution.
Examples
All exist in Stan.
Pareto and Zipf are both simple power laws with a negative exponent, scaled so that their cumulative distributions equal 1. The difference is that Zipf is discrete.
The "80-20 law", according to which 20% of all people receive 80% of all income, and 20% of the most affluent 20% receive 80% of that 80%, and so on, holds precisely when the Pareto index is α = log4(5) = log(5)/log(4), approximately 1.161.
80-20 also implies 64/4 and approx. 50/1 (51.2/0.8)
Cauchy has no well-defined mean.