steps (coda)

for some unnormalized target failure density, which is our target (and nominal trajectory \(p\qty(\tau)\)):

\begin{equation} \bar{p} \qty(\tau \mid \tau \not \in \psi) = \mathbb{1}\qty {\tau \not \in \psi} p\qty(\tau) \end{equation}

sample \(\tau \sim q\qty(\cdot)\)

where \(q\) is the proposal distribution where you start generating your samples; you want this to be as close as you can to the target failure distribution.

reject if \(cq\qty(\tau) r > \bar{p}\qty(\tau)\)

first, choose a normalizing constant \(c\) which makes

Let \(X \sim \mathcal{N}\).

“How much more likely is \(x=10\) than \(x=5\)?”

We note that \(P(x=value) = 0\) for any value if \(X\) is continuous. However, we can still get an answer:

\begin{equation} \frac{\dd{X} P(x=10)}{\dd{X} P(x=5)} \end{equation}

these two things cancel out. Therefore, you can just divide the PDF:

\begin{equation} \frac{f(x=10)}{f(x=5)} \end{equation}

Problems with Relavitivism:

1. missing disagreement problem
2. arbitrariness: anything could be right and wrong
3. social infallibility; if people all agree on something, it becomes right

Mind-to-World Desire of Fit

When you have a desire, you change the world so that you fulfill it. “truth-apt”

“when you are hungry, you want food”

Mind-to-World Desire of Fit

Your belief changes as a function of the world. “truth-apt”

“reasoning/cognition and truth”

Simple Subjectivism

“murder is wrong” <=> “I disapprove of mrder.”

background info

Recall asymtotic analysis. We remember that:

constant time < logarithmic time < linear time < polynomial time < exponential time

The question? What happens if dynamic programming is too slow/not good enough for the problem? What if dynamic programming is not needed; instead, why don’t we just settle for a pretty good solution?

Take, for instance, Nueva Courses. The optimal solution is “most students get their highest possible preferences.” However, this is impractical and pretty much impossible. Instead, what if we endeavor to figure a schedule that generally maximize happiness?

replication is the exact copying of cell information