Benford's Law Explained Visually

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En provenance du cours de University of Washington

Practical Predictive Analytics: Models and Methods

287 notes

University of Washington

Practical Predictive Analytics: Models and Methods

287 notes

Cours 2 sur 4 dans Specialization Data Science at Scale

Statistical experiment design and analytics are at the heart of data science. In this course you will design statistical experiments and analyze the results using modern methods. You will also explore the common pitfalls in interpreting statistical arguments, especially those associated with big data. Collectively, this course will help you internalize a core set of practical and effective machine learning methods and concepts, and apply them to solve some real world problems. Learning Goals: After completing this course, you will be able to: 1. Design effective experiments and analyze the results 2. Use resampling methods to make clear and bulletproof statistical arguments without invoking esoteric notation 3. Explain and apply a core set of classification methods of increasing complexity (rules, trees, random forests), and associated optimization methods (gradient descent and variants) 4. Explain and apply a set of unsupervised learning concepts and methods 5. Describe the common idioms of large-scale graph analytics, including structural query, traversals and recursive queries, PageRank, and community detection

À partir de la leçon

Practical Statistical Inference

Learn the basics of statistical inference, comparing classical methods with resampling methods that allow you to use a simple program to make a rigorous statistical argument. Motivate your study with current topics at the foundations of science: publication bias and reproducibility.

Outliers and Rank Transformation3:24

Example: Chi-Squared Test3:39

Bad Science Revisited: Publication Bias4:47

Effect Size4:26

Meta-analysis5:05

Fraud and Benford's Law4:09

Intuition for Benford's Law2:50

Benford's Law Explained Visually3:50

Rencontrer les enseignants

Bill Howe
Director of Research
Scalable Data Analytics

[MUSIC]

So what does that probability look like?

Well, this figure's a little bit misleading because the X-axis

is on the log scale.

But, if you just look at the heights, what's going on here,

is on the Y axis is the probability of drawing a particular digit.

The blue line is associated with the digit one.

The green line is digit two and so on.

This was generated by a simulation,

where I really did select random numbers from a distribution.

And then I really didn't order them in the manner described in the previous slide.

And put one in and then measured the probability of drawing it,

a value with the number one, or where the vertices is one.

And so if you think about this, the numbers,

what's happened here, this is where one and this is ten and this is 100 and so on.

Well, as soon as I put a one in,

the chance of drawing a card with the one on the front is 100%.

When I put a two in it's now 50%.

When I put a three in it's now 33% and so on.

But then as soon as I get to ten, it goes back up to a higher percentage.

Again. And it stays there, ten, 11, 12, 13,

14 and so on.

And then as soon as it gets to 20, it drops down a little bit.

And so that's why it's climbing here, is through the tens.

And then it starts dropping again.

Again, sharply.

Okay. And so

the point here is that under this model, values where the first integer is

one always are in the hat already by the time you get to the twos.

And the twos are always there before you get to the threes.

And the threes are always there before you get to the fours and so on.

And so you end up with these height, these peaks are led by the ones.

And the area under this curve, although remember this is a log plot so

the area's no quite right, represents the probability of drawing this.

So the probability does actually get higher.

Okay.

And there's a few different other models you can find if you read up on this, and

I encourage you to.

There's other ways to sort of think about the probability here.

And there is actually closed form expression for Benford's Law as well.

One of the limitations here, it's not always true, and one of the key, or

the key situation in which it's applicable,

is the dataset has to span many, many orders of magnitude.

All right, it can't be valued between, I mean, think about it.

If you have values between 50 and 90, and you select those randomly, well,

you're not gonna get any numbers with the is one.

And similarly if you do from one to 100, well,

you have this effect a little bit but not universally.

So you wanna span a lot of orders of magnitude.

And so this is sort of illustrated by this plot here is that the red areas are,

represent the probability of selecting something where the first digit is one.

And the blue areas are where the first digit is eight, okay?

And so as long as you span enough orders of magnitude,

you get much more area where the first digit is one, okay?

But if you take a narrow case, well, and

then the probability is more defined by the distribution itself.

And there's not enough chance for

this area under the curve under the digits one, two, to get big.

So fine, I just want to introduce you to that law.

Mention that it can be used to detect fraud and

then connect the fraud, plus change the mistakes

back to this original context we're in of trying

to understand the weakness of statistical results.

[MUSIC]

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