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# System prepended metadata

title: 'Lecture 1:'

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# Lecture 1:
Model Fitting (p. 11)
    -    Discussion question: what is an analytical solution? Why do we care about analytical solutions? What are there are alternatives, and why might we consider the alternatives?
A Statistical Model for Regression (p. 13)
    -    This idea will come up again: convert one random variable into another. Combining our dataset with a normal variable gives us a new normal variable which we use as a model of the data generating process.
    -    Discussion question: what is the consequence of our choice for the random normal variable to be added to f(x)?
# Lecture 2:
Maximizing Likelihood is Equivalent to Maximizing Log-Likelihood (p. 11)
    -    These ideas will come up again: convex transformations don't change where the optima are. Log is a convex transformation that often simplifies our path to solutions.
    -    Possible image: visualization of surface plot w/ many local optima minima, all preserved by log transformation in second plot
    -    **Difficult concept: the difference between consistent and unbiased estimators**
        -    Is it possible for the difference to be explained the following way: consistent estimators are "eventually" close, and unbiased estimators are "overall" close
            -    Possible image: visualizing the difference between consistent & inconsistent, biased & unbiased, in a 2x2 matrix (i.e. consistent & unbiased, consistent & biased, inconsistent & unbiased, inconsistent & biased)
# Lecture 3:
Simulation: Bayesian Update for the Coin Flip (p. 23)
    -    Discussion question: does it matter in what order we collect our data when updating posteriors?
    -    Possible image: viewing the posterior updated sequentially as data collection increases (sorry for tiny font)
sequential update.png
    -    Could use this to reinforce what a consistent estimator looks like?