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Probability and Cumulative Dice Sums

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A Very Rough Guide to Getting Started in Data Science: Part II, The Big Picture

Data science to a beginner seems completely overwhelming. Not only are there huge numbers of programming languages, packages and algorithms, but even managing your data is an entire area itself. Some examples are the languages R, Python, Ruby, Perl, Julia, Mathematica, MATLAB/Octave; packages SAS, STATA, SPSS; algorithms linear regression, logistic regression, nested model, neural nets, support vector machines, linear discriminant analysis and deep learning.
For managing your data some people use Excel, or a relational database like MySQL or PostgreSQL. And where do things like big data, NoSQL and Hadoop fit in? And what's gradient descent and why is it important? But perhaps the most difficult part of all is that you actually need to know and understand statistics, too.

It does seem overwhelming, but there's a simple key idea - data science is using data to answer a question. Even if you're only sketching a graph using a stick and a sandbox, you're still doing data science. Your goal for data science should be to continually learn better, more powerful and more efficient ways to answer your questions. My general framework has been strongly influenced by George Pólya's wonderful book "How to Solve It". While it's directed at solving mathematical problems, his approach is helpful for solving problems in general.

"How to Solve It" suggests the following steps when solving a mathematical problem:
  1. First, you have to understand the problem.
  2. After understanding, then make a plan.
  3. Carry out the plan.
  4. Review/extend. Look back on your work. How could it be better?
Pólya goes into much greater detail for each step and provides some illustrative examples. It's not the final word on how to approach and solve mathematical problems, but it's very helpful and I highly recommend it. For data science, the analogous steps from my perspective would be:
  1. What questions do you want to answer?
  2. What data would be helpful to answer these questions? How and where do you get this data?
  3. Given the question you want to answer and the data you have, which approaches and models are likely to be useful? This can be very confusing. There are always tradeoffs - underfitting vs overfitting, bias vs variance, simplicity vs complexity, information about where something came from vs what's it doing. 
  4. Perform analysis/fit model.
  5. How do you know if your model and analysis are good or bad, and how confident should you be in your predictions and conclusions? A very critical, but commonly treated lightly or even skipped entirely.
  6. Given the results, what should you try next?
Let's follow Pólya and do an illustrative example next.

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