andrew/Implementations-of-Probability-Theory
1
0
Fork 0
mirror of https://github.com/asimonson1125/Implementations-of-Probability-Theory.git synced 2026-02-24 21:59:50 -06:00
Code Issues Packages Projects Releases Wiki Activity

ergodicity

Browse Source
This commit is contained in:
Andrew Simonson
2025-01-20 01:02:47 -05:00
parent 11c3888415
commit 70b340c76e
2 changed files with 5 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files

BIN
report/report.pdf
View File

Binary file not shown.

6
report/report.tex
View File

@@ -245,6 +245,10 @@ Nassim Taleb in \textit{Fooled By Randomness} describes this event with an analo
1/10,000 chance of harm? In this case, many less-than-rational actors use the game repeatedly to acquire wealth indefinitely, forgetting or even outright ignorant 1/10,000 chance of harm? In this case, many less-than-rational actors use the game repeatedly to acquire wealth indefinitely, forgetting or even outright ignorant
that eventually the unlikely, or, as the actor would see it, the unthinkable, happens and all of the gains are completely negated. that eventually the unlikely, or, as the actor would see it, the unthinkable, happens and all of the gains are completely negated.
Averaging a game of Russian Roulette leaves the average person \$833,333 richer, but this is where ergodicity comes into play. There is no 'average' person,
you can play and win many times but when you eventually bust you lose everything you put in. Removing the vocabulary from this concept, averaging many first
iterations will not necessarily predict the performance of an experiment with many iterations.
\subsubsection{Fooled By Randomness} \subsubsection{Fooled By Randomness}
While most statisticians are familiar with techniques to remove noise to get a clearer picture of long-term trends, many forget that noise over longer terms can While most statisticians are familiar with techniques to remove noise to get a clearer picture of long-term trends, many forget that noise over longer terms can
materialize as highly improbable events. For instance, it is improbable to flip a fair coin and have heads land face up 5 times in a row, but if the coin is flipped materialize as highly improbable events. For instance, it is improbable to flip a fair coin and have heads land face up 5 times in a row, but if the coin is flipped
@@ -734,7 +738,7 @@ calculated:
Two consecutive sunny days: Two consecutive sunny days:
\[(\frac{5}{6} * .95) * (.9 * .95) \approx 0.677 \] \[(\frac{5}{6} * .95) * (.9 * .95) \approx 0.677 \]
Cloudy, Sunny: Cloudy, Sunny:
\[(\frac{1}{6} * .6) * (.1 * .95) = 0.0095 \] \[(\frac{1}{6} * .6) * (.5 * .95) = 0.048 \]
\end{center} \end{center}
Hence, we can eliminate the \([\text{Cloudy, Sunny}]\) starting sequence from the most probable sequence of steps given the observations. Doing the same thing Hence, we can eliminate the \([\text{Cloudy, Sunny}]\) starting sequence from the most probable sequence of steps given the observations. Doing the same thing