Fraud and Benford's Law

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From the course by University of Washington

Practical Predictive Analytics: Models and Methods

267 оценки

University of Washington

Practical Predictive Analytics: Models and Methods

267 оценки

Course 2 of 4 in the 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

From the lesson

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

Meet the Instructors

Bill Howe
Director of Research
Scalable Data Analytics

[MUSIC]

Okay.

So what's a second reason for this decline effect for the truth wearing off?

Well, another one is just people make mistakes and, in some cases,

there's instances of fraud.

And so there's some evidence here that these kinds of things are going up as

well, as measured.

One way to measure this is by the number of paper retractions.

And the number of retractions has gone up fairly significantly as Neorden

pointed out in 2011 in an article in Nature.

So from the period of time 2001 to 2011 there's been a 10 fold increase

in number of paper retractions but only a 1.44 fold increase in themselves.

Okay. And so

this plot is from two different depositories.

PubMed and Web of Science.

Neither one of which can include computer science papers, by the way.

But you can see that it's gone up pretty significantly.

So we're not gonna dive into too much detail into this phenomenon.

But I do want to give you one statistical Tool that is

sometimes used to detect fraud.

And that's Benford's Law.

So if you're not familiar with Benford's Law, it's a fun one to be familiar with.

So this law predicts the distribution

of the first digit of data.

And if you think about it without thinking too deeply,

you might intuitively think that this would be fairly uniform.

If you have random data, you might see an equal number of eights.

And an equal number of threes, an equal number of twos, and so on.

But it turns out, that the distribution is not random.

In some circumstances, in many circumstances.

It's not even, I should say, it is random.

It’s just not even, the distribution looks more like this.

You will get more ones in the first position than you will twos, and more twos

than threes and so on, until up to 30% of the numbers you measure are ones.

So this should, blow your mind a little bit, okay.

So some examples of this before we explain what's going on, taken from.

There’s a nice website testingbenfordslaw.com where they

pull real data in and show the plots.

This is the number of Twitter users by the numbers of followers they have.

Sorry not the number of Twitter users.

Twitter users by the number of followers they have.

Okay?

Alright, so the list of numbers is just the number of followers.

The number of Twitter users whose number of followers begins with

the digit one Is 32.62% if you can see that.

And the red dot is the prediction made by Benford's Law.

So, not too bad.

The number of instances that have the two as leading digit is 16.66% and

there's the red dot predicted by the original and so on.

So, not too, not too bad.

The distance of stars from Earth in light years follows a similar pattern.

This is remarkably close to Benford's law prediction.

Government spending in the UK, between the period of time May through September 2010.

Again, remarkable prediction.

Now, you might imagine there's some selection bias on this particular website.

And I can't guarantee that there's not.

But with some reading plus a little bit of trust that I hopefully have built up,

I hope you can then see that this is not fully explainable by this

website choosing particular data sets for which this is true.

Okay.

Google books the number of unique one grams and

we talked about one grams several, a couple weeks ago.

Terms essentially are what one grams are.

Okay, again, pretty good prediction.

[MUSIC]

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