From 087f9560a03fd035b638d194512ef9aa4bc3414f Mon Sep 17 00:00:00 2001 From: James Schloss Date: Sat, 4 Dec 2021 14:19:07 +0100 Subject: [PATCH 1/2] changing the directory structure to be flat --- SUMMARY.md | 2 +- contents/metropolis/metropolis.md | 4 ++-- .../distributions.md | 0 .../res/double_die_frequencies.png | Bin .../res/normal_distribution.png | Bin 5 files changed, 3 insertions(+), 3 deletions(-) rename contents/{probability/distributions => probability_distributions}/distributions.md (100%) rename contents/{probability/distributions => probability_distributions}/res/double_die_frequencies.png (100%) rename contents/{probability/distributions => probability_distributions}/res/normal_distribution.png (100%) diff --git a/SUMMARY.md b/SUMMARY.md index 644fccc56..37e929218 100644 --- a/SUMMARY.md +++ b/SUMMARY.md @@ -20,7 +20,7 @@ * [Multiplication as a Convolution](contents/convolutions/multiplication/multiplication.md) * [Convolutions of Images (2D)](contents/convolutions/2d/2d.md) * [Convolutional Theorem](contents/convolutions/convolutional_theorem/convolutional_theorem.md) - * [Probability Distributions](contents/probability/distributions/distributions.md) + * [Probability Distributions](contents/probability_distributions/distributions.md) * [Tree Traversal](contents/tree_traversal/tree_traversal.md) * [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md) * [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md) diff --git a/contents/metropolis/metropolis.md b/contents/metropolis/metropolis.md index 88a33c296..62be78850 100644 --- a/contents/metropolis/metropolis.md +++ b/contents/metropolis/metropolis.md @@ -1,7 +1,7 @@ # The Metropolis Algorithm The [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) method uses random numbers to approximate the area of pretty much any shape we choose. -The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability/distributions/distributions.md): +The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability_distributions/distributions.md): $$ P(\mathbf{x}) = \frac{f(\mathbf{x})}{\displaystyle\int_D f(\mathbf{x})d\mathbf{x}}, @@ -42,7 +42,7 @@ $$ P(\mathbf{x}) = \frac{\displaystyle \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right]} {Q}, $$ -where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability/distributions/distributions.md), +where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability_distributions/distributions.md), $$ Q = \int_D \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right] d\mathbf{x}. diff --git a/contents/probability/distributions/distributions.md b/contents/probability_distributions/distributions.md similarity index 100% rename from contents/probability/distributions/distributions.md rename to contents/probability_distributions/distributions.md diff --git a/contents/probability/distributions/res/double_die_frequencies.png b/contents/probability_distributions/res/double_die_frequencies.png similarity index 100% rename from contents/probability/distributions/res/double_die_frequencies.png rename to contents/probability_distributions/res/double_die_frequencies.png diff --git a/contents/probability/distributions/res/normal_distribution.png b/contents/probability_distributions/res/normal_distribution.png similarity index 100% rename from contents/probability/distributions/res/normal_distribution.png rename to contents/probability_distributions/res/normal_distribution.png From 417a7e6e8b7d22342d8677919c4e2b9d6d0d128e Mon Sep 17 00:00:00 2001 From: James Schloss Date: Sun, 5 Dec 2021 14:42:36 +0100 Subject: [PATCH 2/2] changing probability chapter to use spaces instead of tabs --- SUMMARY.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/SUMMARY.md b/SUMMARY.md index 37e929218..8800c0142 100644 --- a/SUMMARY.md +++ b/SUMMARY.md @@ -20,7 +20,7 @@ * [Multiplication as a Convolution](contents/convolutions/multiplication/multiplication.md) * [Convolutions of Images (2D)](contents/convolutions/2d/2d.md) * [Convolutional Theorem](contents/convolutions/convolutional_theorem/convolutional_theorem.md) - * [Probability Distributions](contents/probability_distributions/distributions.md) + * [Probability Distributions](contents/probability_distributions/distributions.md) * [Tree Traversal](contents/tree_traversal/tree_traversal.md) * [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md) * [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md)