# Models and the Scientific Method

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## The Scientific Method or the Data Science Life Cycle?

This section will describe the steps involved in the lifetime of a
project in data science.

The scientific method roughly follows a cycle of asking questions,
designing an experiment to model the world, and use the results of
this experiment to assess if the experiment answered the question at
hand. Results feed into more questions, or a refinement of the
approach when results are inconclusive.

![sm](imgs/scientific-method.png)

This description hides a much more complicated process that drives any
realistic scientific investigation. In particular, this glosses over:
* time spend understanding and investigating the domain or area in question,
* data may not be collected by experiment; existing data must be
  found,
* the experiment may involve complicated assumptions, as well as
  mathematical and statistical modeling,
* The results of the experiment may not clear-cut and may involve
  subtle statistical interpretation.
* Information gained at any step may result in stopping progress to
  further research and reformulate the question.
  
A diagram more realistically describing this process is more
complicated:

![dslc](imgs/dslc.png)

Any involved, real-world project is a complicated, iterative
process. As a Data Scientist, it's important to understand each
component well to maintain one's bearings, know how to correctly
interpret results, and quickly iterate through refinements of each
question being pursued. Navigating this diagram requires understanding
the logical and statistical arguments involved in each step, as well
as the software that executes these arguments.

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## Introduction to Models

A few important terms will be used in the text to describe how the
various steps in the diagrams above relate to one another:

* The *true or conceptual model* is the representation of a system in
  a domain that captures a question of interest.
* A *data generating process* is the physical process from which the
  true model creates the observed data. These processes involve
  complicated unknowns that cannot necessarily be observed or
  explicity modeled.
* A *probability model* is an idealized, simplified explanation of the
  data generating process. The model is probabilistic, as it must
  capture perceived randomness in the data generating process.
* An instance of *Observed data* is a real world manifestation of the
  data generating process, recorded as a dataset.
* A *(fit) statistical model* is the most likely explanation of what a
  probability model is in terms of the observed data.