Understanding Science and Models

Quote of the day

“To try to make a model of an atom by studying its spectrum is like trying to make a model of a grand piano by listening to the noise it makes when thrown downstairs.”

- Anonymous

Class Announcements

  • For Monday, please read Statistical Rethinking: Chapter 1: The Golem of Prague
  • Homework #1 posted (Due date: Monday, February 5, 1:00 pm)
    • Installing R and RStudio and working through a tutorial
    • Finishing lab worksheet that we will start on Thursday of next week

Scientific method

Science misconceptions

Statement: Scientists follow the same step-by-step scientific method.

“In fact, the Scientific Method represents how scientists usually write up the results of their studies (and how a few investigations are actually done), but it is a grossly oversimplified representation of how scientists generally build knowledge.”

- Understanding Science

Misconception #1: Rigid Workflow

University of California Museum of Paleontology’s Understanding Science (https://www.understandingscience.org)

Difference is between how how science is done versus how science is reported.

Misconception #1: Rigid Workflow

University of California Museum of Paleontology’s Understanding Science (https://www.understandingscience.org)

Misconception #1: Rigid Workflow

Asteroids and dinosaurs: Unexpected twists and an unfinished story
(PDF version)

University of California Museum of Paleontology’s Understanding Science (https://www.understandingscience.org)

Hypothesis vs Theory

Misconception #2: Hypothesis vs Theory

Statement: Well-supported hypotheses become theories, and well-supported theories become laws.

“…hypotheses, theories, and laws are rather like apples, oranges, and kumquats: one cannot grow into another, no matter how much fertilizer and water are offered.”

- Understanding Science

Misconception #2: Hypothesis vs Theory

“Hypotheses, theories, and laws are all scientific explanations that differ in breadth — not in level of support.”

- Understanding Science

Misconception #2: Hypothesis vs Theory

Hypothesis: Hypotheses are explanations that are limited in scope, applying to fairly narrow range of phenomena.

Theory: Theories are deep explanations that apply to a broad range of phenomena and that may integrate many hypotheses and laws.

Scientific evidence

Misconception #3: Scientific “proof”

Statement: The aim of scientific testing is to prove a hypothesis correct.

“Science is based on the principle that any idea, no matter how widely accepted today, could be overturned tomorrow if the evidence warranted it. Science accepts or rejects ideas based on the evidence; it does not prove or disprove them.”

- Understanding Science

Is math science?

Science

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POS vs POMM

Model vs Reality

“…all models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind…”

- George E. P. Box and Norman R. Draper

Model Representations

Multiple representations are important!!!

Models and Modeling

Discuss: What is a model?

Models and Modeling

Question: Is this a model?

Models and Modeling

Question: Is this a model?

Models and Modeling

Question: Is this a model?

Models and Modeling

Question: Is this a model?

https://www.xkcd.com/

Models and Modeling

Question: Is this a model?

Models and Modeling

Discuss: What are the components of a model?

  • Objects (nouns)
  • Processes or relationships (verbs)
  • Simplified, abstract/concrete (adjectives)
  • Function (use case) - Not strictly necessary for the definition of a model. This answers the “Why model?” question.

Definition: A model is a simplified, abstract (or concrete) representation of objects and their relationships and/or processes in the real world.

Bits-and-pieces

Question: What are the model components for this model?

  • Objects
  • Processes/Relationships
  • Functions

Models - General Definition

Definition: A model is a simplified, abstract (or concrete) representation of objects and their representations or processes in the real world.

The Importance of Good Data

Quote: “Meaningful data of sufficient quantity are the grist of scientific bread.”

  1. Is the study sound so that an inductive inference can be justified?
    • Experimental design should be able to address predictions from…
    • …one or a number of scientific hypotheses that have been well thought out.

The Importance of Good Data

Quote: “Meaningful data of sufficient quantity are the grist of scientific bread.”

  1. Are the data analysis methods sound? Relies on…
    • …adequate modeling and
    • objective approaches to model selection.

Information and Statistics

Quote: “If data are collected in an appropriate manner, then there is information in the sample data about the process or system under study.”

  • Mathematical model is required to obtain information from the data.
  • Inductive vs deductive reasoning
  • Inductive: “inference of a generalized conclusion from particular instances”
  • Statistics adds rigor to the inductive process.
  • The inference comes from a model that approximates the system or process of interest.

Models in Science

Quote: “Models must be derived to carefully represent each of the science hypotheses.”

\[ H_{1} \Leftrightarrow g_{1}, \ H_{2} \Leftrightarrow g_{2}, \ldots, H_{k} \Leftrightarrow g_{k}. \]

Scientific Question: What is the support or empirical evidence for the ith hypothesis (via its corresponding model), relative to others in the set.

Model Selection: What is the the evidence for each of the hypotheses (and their associated models), given the data.

Models are Approximations

“All models are wrong, but some are useful.”

- Box

Example: Population survival \[ n_{t+1} = s\cdot n_{t} \]

Assumptions:

  • Population survival rate \(s\) does not change over time.
  • Each individual most likely has a different survival rate (\(s\) represents the population average).
  • Biotic and abiotic factors that influence survival rate are being ignored.

Models are Approximations

Discuss: What about Hardy-Weinberg equilibrium? What are the assumptions and approximations that go into this model?

What is modeling?

Definition: Modeling is 1) the process of moving from observations of the real world to a model, 2) moving from one model representation to another model representation, or 3) comparing different models.

Why models and modeling are useful

Discuss: Why are models and modeling useful?

Answer: Models can be used for prediction, explanation and understanding.

Note: You are already constructing models and doing modeling!!!

In this course, we will work to become proficient in understanding, analyzing, and creating models - in particular mathematical models.

Process Of Science (POS)
Process Of Modeling (POM)

Why models and modeling are useful

  • models can make accurate predictions,
  • models can generate causal explanations.
  • simple, unrealistic models help scientists explore complex systems,
  • models can be used to explore unknown possibilities,
  • models can lead to the development of conceptual frameworks,
  • models help expose assumptions,
  • models help define expectations,
  • models help us to devise new tests.

Lab #1: What’s in the box?

Intro to Quantitative Biology, Spring 2024