From c10fd9583e9e29ef0e4ff014c80cda03d2478f77 Mon Sep 17 00:00:00 2001
From: Adam Mantz <amantz@slac.stanford.edu>
Date: Mon, 29 Mar 2021 15:04:34 -0700
Subject: [PATCH 1/5] typos

---
 docs/notes/essential_probability.html | 6 +++---
 docs/notes/generative_models.html     | 4 ++--
 notes/essential_probability.ipynb     | 6 +++---
 notes/generative_models.ipynb         | 4 ++--
 4 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/docs/notes/essential_probability.html b/docs/notes/essential_probability.html
index 898f600..2ad506a 100644
--- a/docs/notes/essential_probability.html
+++ b/docs/notes/essential_probability.html
@@ -14424,7 +14424,7 @@ <h3 id="Bernoulli-distribution">Bernoulli distribution<a class="anchor-link" hre
 </div>
 <div class="jp-Cell-inputWrapper"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
-<h3 id="Binomial-distribution">Binomial distribution<a class="anchor-link" href="#Binomial-distribution">&#182;</a></h3><p>... whose PMF is $p(k|q,n) = {n \choose k} q^k (1-q)^{n-k}$ for $k$ successes. ${n \choose k}$ is the combinatoric "choose" function, $\frac{n!}{k!(n-k)!}$.</p>
+<h3 id="Binomial-distribution">Binomial distribution<a class="anchor-link" href="#Binomial-distribution">&#182;</a></h3><p>... whose PMF is $P(k|q,n) = {n \choose k} q^k (1-q)^{n-k}$ for $k$ successes. ${n \choose k}$ is the combinatoric "choose" function, $\frac{n!}{k!(n-k)!}$.</p>
 <p>The Binomial distribution is additive, in that the sum of two Binomial random variables with the same $q$, respectively with $n_1$ and $n_2$ trials, also follows the Binomial distribution, with parameters $q$ and $n_1+n_2$.</p>
 <p>This distribution might be useful for inferring the fraction of objects belonging to one of two classes ($q$), based on typing of an unbiased but finite number of them ($n$). (The multinomial generalization would work for more than two classes.)</p>
 <p>Or, consider the case that each Bernoulli trial is whether a photon hits our detector in a given, tiny time interval. For an integration whose total length is much longer than any such time interval we could plausibly distinguish, we might take the limit where $n$ becomes huge, thus reaching the...</p>
@@ -14434,7 +14434,7 @@ <h3 id="Binomial-distribution">Binomial distribution<a class="anchor-link" href=
 <div class="jp-Cell-inputWrapper"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
 <h3 id="Poisson-distribution">Poisson distribution<a class="anchor-link" href="#Poisson-distribution">&#182;</a></h3><p>... which describes the number of successes when the number of trials is in principle infinite, but $q$ is correspondingly vanishingly small. It has a single parameter, $\mu$, which corresponds to the product $qn$ when interpretted as a limit of the Binomial distribution. The PMF is</p>
-<p>$p(k|\mu) = \frac{\mu^k e^{-\mu}}{k!}$.</p>
+<p>$P(k|\mu) = \frac{\mu^k e^{-\mu}}{k!}$.</p>
 <p>Like the Binomial distribution, the Poisson distribution is additive. It also has the following (probably familiar) properties:</p>
 <ul>
 <li>Expectation value (mean) $\langle k\rangle = \mu$,</li>
@@ -14450,7 +14450,7 @@ <h3 id="Normal-or-Gaussian-distribution">Normal or Gaussian distribution<a class
 <p>$p(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp \left[ \frac{(x-\mu)^2}{\sigma^2} \right]$,</p>
 <p>and has mean $\mu$ and variance $\sigma^2$. With $\mu=0$ and $\sigma=1$, this is known as the standard normal distribution.</p>
 <p>Because physicists love Gauss more than normality, you can expect to see "Gaussian" more often in the (astro)physics literature. Statisticians normally say "normal".</p>
-<p>The limiting relationship between the Poisson and Normal distributions is one example of the <strong>central limit theorem</strong>, which says that, under quite general conditions, the average of a large number of random variables tends towards normal, even if the individual variables are not normally distributed. Whether and how well it applies, and just what "large number means", in any given situation is a practical question more than anything else, at least in this course. But the bottom line is that this distribution shows up quite often, and is normally a reasonable guess in those situations where we have to make a choice and have no better ideas.</p>
+<p>The limiting relationship between the Poisson and Normal distributions is one example of the <strong>central limit theorem</strong>, which says that, under quite general conditions, the average of a large number of random variables tends towards normal, even if the individual variables are not normally distributed. Whether and how well it applies, and just what "large number" means, in any given situation is a practical question more than anything else, at least in this course. But the bottom line is that this distribution shows up quite often, and is normally a reasonable guess in those situations where we have to make a choice and have no better ideas.</p>
 <p>Note that intentionally binning up data, when doing so throws out potentially useful information, in the hopes of satisfying the central limit theorem, is generally frowned upon in this class.</p>
 <p>Finally, the sum of squares of $\nu$ standard normal variables follows the...</p>
 
diff --git a/docs/notes/generative_models.html b/docs/notes/generative_models.html
index cb04ad3..d515d37 100644
--- a/docs/notes/generative_models.html
+++ b/docs/notes/generative_models.html
@@ -14262,7 +14262,7 @@
 <h1 id="Notes:-Generative-Models">Notes: Generative Models<a class="anchor-link" href="#Notes:-Generative-Models">&#182;</a></h1><p>Containing:</p>
 <ul>
 <li>An introduction to probabilistic models, why we need them, and how to work with them</li>
-<li>Hopefully, some resolution of the frequently confusing key ideas from the overview: (i) data are random, and (2) data are constants</li>
+<li>Hopefully, some resolution of the frequently confusing key ideas from the overview: (1) data are random, and (2) data are constants</li>
 </ul>
 
 </div>
@@ -14462,7 +14462,7 @@ <h2 id="Interpreting-generative-models">Interpreting generative models<a class="
 <h4 id="Endnotes">Endnotes<a class="anchor-link" href="#Endnotes">&#182;</a></h4><ol>
 <li><p>If this bothers you, consider playing <a href="https://en.wikipedia.org/wiki/Frogger">Frogger</a> while blindfolded. The game is executing a fully deterministic program, so in reality there is no uncertainty about whether the frog will be smooshed if it hops into the road at a given time. The player is missing this key information, but can still, in principle, make predictions about how likely the frog is to be smooshed at any given time using probabilistic modeling. With repeated experimentation, they could even refine this model to make it more accurate. As far as the player is concerned, whether there is an obstacle in the road is <em>functionally</em> random, despite the underlying mechanics being non-random.</p>
 </li>
-<li><p>We'll follow the convention of using capital $P$ for the probability of a discrete outcome, e.g. $P(N)$ where $N$ is integer-values, or for a generic argument like "data". Probability <em>densities</em> over real-valued variables will get a lower-case $p$. The distinction between capital-$P$ Probability (aka "probability mass") and probability density doesn't matter too often, but occasionally can lead to confusion, so we'll try to keep them straight. (See <strong>probability notes</strong>.)</p>
+<li><p>We'll follow the convention of using capital $P$ for the probability of a discrete outcome, e.g. $P(N)$ where $N$ is integer-values, or for a generic argument like "data". Probability <em>densities</em> over real-valued variables will get a lower-case $p$. The distinction between capital-$P$ Probability (aka "probability mass") and probability density doesn't matter too often, but occasionally can lead to confusion, so we'll try to keep them straight. (See the <a href="essential_probability.html">probability notes</a>.)</p>
 </li>
 </ol>
 
diff --git a/notes/essential_probability.ipynb b/notes/essential_probability.ipynb
index cb51ce5..f5eeafe 100644
--- a/notes/essential_probability.ipynb
+++ b/notes/essential_probability.ipynb
@@ -269,7 +269,7 @@
    "source": [
     "### Binomial distribution\n",
     "\n",
-    "... whose PMF is $p(k|q,n) = {n \\choose k} q^k (1-q)^{n-k}$ for $k$ successes. ${n \\choose k}$ is the combinatoric \"choose\" function, $\\frac{n!}{k!(n-k)!}$.\n",
+    "... whose PMF is $P(k|q,n) = {n \\choose k} q^k (1-q)^{n-k}$ for $k$ successes. ${n \\choose k}$ is the combinatoric \"choose\" function, $\\frac{n!}{k!(n-k)!}$.\n",
     "\n",
     "The Binomial distribution is additive, in that the sum of two Binomial random variables with the same $q$, respectively with $n_1$ and $n_2$ trials, also follows the Binomial distribution, with parameters $q$ and $n_1+n_2$.\n",
     "\n",
@@ -286,7 +286,7 @@
     "\n",
     "... which describes the number of successes when the number of trials is in principle infinite, but $q$ is correspondingly vanishingly small. It has a single parameter, $\\mu$, which corresponds to the product $qn$ when interpretted as a limit of the Binomial distribution. The PMF is\n",
     "\n",
-    "$p(k|\\mu) = \\frac{\\mu^k e^{-\\mu}}{k!}$.\n",
+    "$P(k|\\mu) = \\frac{\\mu^k e^{-\\mu}}{k!}$.\n",
     "\n",
     "Like the Binomial distribution, the Poisson distribution is additive. It also has the following (probably familiar) properties:\n",
     "* Expectation value (mean) $\\langle k\\rangle = \\mu$,\n",
@@ -309,7 +309,7 @@
     "\n",
     "Because physicists love Gauss more than normality, you can expect to see \"Gaussian\" more often in the (astro)physics literature. Statisticians normally say \"normal\".\n",
     "\n",
-    "The limiting relationship between the Poisson and Normal distributions is one example of the **central limit theorem**, which says that, under quite general conditions, the average of a large number of random variables tends towards normal, even if the individual variables are not normally distributed. Whether and how well it applies, and just what \"large number means\", in any given situation is a practical question more than anything else, at least in this course. But the bottom line is that this distribution shows up quite often, and is normally a reasonable guess in those situations where we have to make a choice and have no better ideas.\n",
+    "The limiting relationship between the Poisson and Normal distributions is one example of the **central limit theorem**, which says that, under quite general conditions, the average of a large number of random variables tends towards normal, even if the individual variables are not normally distributed. Whether and how well it applies, and just what \"large number\" means, in any given situation is a practical question more than anything else, at least in this course. But the bottom line is that this distribution shows up quite often, and is normally a reasonable guess in those situations where we have to make a choice and have no better ideas.\n",
     "\n",
     "Note that intentionally binning up data, when doing so throws out potentially useful information, in the hopes of satisfying the central limit theorem, is generally frowned upon in this class.\n",
     "\n",
diff --git a/notes/generative_models.ipynb b/notes/generative_models.ipynb
index 7ee0fbf..344d40e 100644
--- a/notes/generative_models.ipynb
+++ b/notes/generative_models.ipynb
@@ -8,7 +8,7 @@
     "\n",
     "Containing:\n",
     "* An introduction to probabilistic models, why we need them, and how to work with them\n",
-    "* Hopefully, some resolution of the frequently confusing key ideas from the overview: (i) data are random, and (2) data are constants"
+    "* Hopefully, some resolution of the frequently confusing key ideas from the overview: (1) data are random, and (2) data are constants"
    ]
   },
   {
@@ -261,7 +261,7 @@
     "\n",
     "1. If this bothers you, consider playing [Frogger](https://en.wikipedia.org/wiki/Frogger) while blindfolded. The game is executing a fully deterministic program, so in reality there is no uncertainty about whether the frog will be smooshed if it hops into the road at a given time. The player is missing this key information, but can still, in principle, make predictions about how likely the frog is to be smooshed at any given time using probabilistic modeling. With repeated experimentation, they could even refine this model to make it more accurate. As far as the player is concerned, whether there is an obstacle in the road is _functionally_ random, despite the underlying mechanics being non-random.\n",
     "\n",
-    "2. We'll follow the convention of using capital $P$ for the probability of a discrete outcome, e.g. $P(N)$ where $N$ is integer-values, or for a generic argument like \"data\". Probability _densities_ over real-valued variables will get a lower-case $p$. The distinction between capital-$P$ Probability (aka \"probability mass\") and probability density doesn't matter too often, but occasionally can lead to confusion, so we'll try to keep them straight. (See **probability notes**.)"
+    "2. We'll follow the convention of using capital $P$ for the probability of a discrete outcome, e.g. $P(N)$ where $N$ is integer-values, or for a generic argument like \"data\". Probability _densities_ over real-valued variables will get a lower-case $p$. The distinction between capital-$P$ Probability (aka \"probability mass\") and probability density doesn't matter too often, but occasionally can lead to confusion, so we'll try to keep them straight. (See the [probability notes](essential_probability.ipynb).)"
    ]
   }
  ],

From ef26ae79c68f59a76c86b985df46c181b05ab534 Mon Sep 17 00:00:00 2001
From: Adam Mantz <amantz@slac.stanford.edu>
Date: Sun, 4 Apr 2021 17:46:58 -0700
Subject: [PATCH 2/5] mortifying typo in the expression for the Gaussian PDF

---
 docs/notes/essential_probability.html | 2 +-
 notes/essential_probability.ipynb     | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/notes/essential_probability.html b/docs/notes/essential_probability.html
index 2ad506a..8e2dbdc 100644
--- a/docs/notes/essential_probability.html
+++ b/docs/notes/essential_probability.html
@@ -14447,7 +14447,7 @@ <h3 id="Poisson-distribution">Poisson distribution<a class="anchor-link" href="#
 <div class="jp-Cell-inputWrapper"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
 <h3 id="Normal-or-Gaussian-distribution">Normal or Gaussian distribution<a class="anchor-link" href="#Normal-or-Gaussian-distribution">&#182;</a></h3><p>... which is, more generally, defined over the real line as</p>
-<p>$p(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp \left[ \frac{(x-\mu)^2}{\sigma^2} \right]$,</p>
+<p>$p(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp \left[ -\frac{(x-\mu)^2}{2\sigma^2} \right]$,</p>
 <p>and has mean $\mu$ and variance $\sigma^2$. With $\mu=0$ and $\sigma=1$, this is known as the standard normal distribution.</p>
 <p>Because physicists love Gauss more than normality, you can expect to see "Gaussian" more often in the (astro)physics literature. Statisticians normally say "normal".</p>
 <p>The limiting relationship between the Poisson and Normal distributions is one example of the <strong>central limit theorem</strong>, which says that, under quite general conditions, the average of a large number of random variables tends towards normal, even if the individual variables are not normally distributed. Whether and how well it applies, and just what "large number" means, in any given situation is a practical question more than anything else, at least in this course. But the bottom line is that this distribution shows up quite often, and is normally a reasonable guess in those situations where we have to make a choice and have no better ideas.</p>
diff --git a/notes/essential_probability.ipynb b/notes/essential_probability.ipynb
index f5eeafe..3c3bc2f 100644
--- a/notes/essential_probability.ipynb
+++ b/notes/essential_probability.ipynb
@@ -303,7 +303,7 @@
     "\n",
     "... which is, more generally, defined over the real line as\n",
     "\n",
-    "$p(x|\\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp \\left[ \\frac{(x-\\mu)^2}{\\sigma^2} \\right]$,\n",
+    "$p(x|\\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp \\left[ -\\frac{(x-\\mu)^2}{2\\sigma^2} \\right]$,\n",
     "\n",
     "and has mean $\\mu$ and variance $\\sigma^2$. With $\\mu=0$ and $\\sigma=1$, this is known as the standard normal distribution.\n",
     "\n",

From d93edd2d1ee2d11327790c231059f80fb97e9785 Mon Sep 17 00:00:00 2001
From: Adam Mantz <amantz@slac.stanford.edu>
Date: Mon, 12 Apr 2021 14:32:55 -0700
Subject: [PATCH 3/5] add link to MC Packages from frontpage

---
 html/index.ipynb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/html/index.ipynb b/html/index.ipynb
index ff63c6f..4b067cc 100644
--- a/html/index.ipynb
+++ b/html/index.ipynb
@@ -52,7 +52,7 @@
     "* [Bayesianism and Other \"isms\"](notes/statistical_isms.ipynb)\n",
     "* [Monte Carlo Sampling](notes/montecarlo.ipynb)\n",
     "* [MCMC Diagnostics](notes/mcmc_diagnostics.ipynb)\n",
-    "* [More Sampling Methods](notes/more_samplers.ipynb)\n",
+    "* [More Sampling Methods](notes/more_samplers.ipynb) (and [MC Packages](notes/MC_packages.ipynb))\n",
     "* [Hierarchical Models](notes/hierarchical.ipynb)\n",
     "* [Model Evaluation and Comparison](notes/model_evaluation.ipynb)\n",
     "* [Missing Data and Selection Effects](notes/missingdata.ipynb)\n",

From db294986437a28d3ff8d26bd6ec07147fad97590 Mon Sep 17 00:00:00 2001
From: Adam Mantz <amantz@slac.stanford.edu>
Date: Tue, 13 Apr 2021 09:46:30 -0700
Subject: [PATCH 4/5] typos

---
 tutorials/gaussians.ipynb                   | 2 +-
 tutorials/probability_transformations.ipynb | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/tutorials/gaussians.ipynb b/tutorials/gaussians.ipynb
index 39a9b3c..b453515 100644
--- a/tutorials/gaussians.ipynb
+++ b/tutorials/gaussians.ipynb
@@ -300,7 +300,7 @@
    "source": [
     "Now, compute the parameters of the posterior for $\\beta$ based on $\\mu_\\beta$ and $\\Sigma_\\beta$ (parameters that appear in the sampling distribution) and the parameters of the conjugate prior. Set the prior parameters to be equivalent to the uniform distribution for the check below (you can put in something different to see how it looks later).\n",
     "\n",
-    "Transform `post_mean` to a shape (3,) numpy array for convenience (as opposed to, say, a 3x1 matrix)."
+    "Transform `post_mean` to a shape (2,) numpy array for convenience (as opposed to, say, a 2x1 matrix)."
    ]
   },
   {
diff --git a/tutorials/probability_transformations.ipynb b/tutorials/probability_transformations.ipynb
index 64a758e..2a1f2cb 100644
--- a/tutorials/probability_transformations.ipynb
+++ b/tutorials/probability_transformations.ipynb
@@ -33,7 +33,7 @@
    "source": [
     "## 1. Solve it\n",
     "\n",
-    "Given the PDF of $\\theta$ and the function $b(\\theta)$, what is the PDF of $b$, $p(b)$? Fill in an equation below, and also define it as a function. (As simple as it is, you might want to explciitly write down $p(\\theta)$ first.)"
+    "Given the PDF of $\\theta$ and the function $b(\\theta)$, what is the PDF of $b$, $p(b)$? Fill in an equation below, and also define it as a function. (As simple as it is, you might want to explicitly write down $p(\\theta)$ first.)"
    ]
   },
   {

From c2c93daa5aa1238b1aac0006f5e8b7aa2f5ff528 Mon Sep 17 00:00:00 2001
From: Adam Mantz <amantz@slac.stanford.edu>
Date: Wed, 14 Apr 2021 15:38:19 -0700
Subject: [PATCH 5/5] typo

---
 notes/mcmc_diagnostics.ipynb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/notes/mcmc_diagnostics.ipynb b/notes/mcmc_diagnostics.ipynb
index beb19dd..cc5758c 100644
--- a/notes/mcmc_diagnostics.ipynb
+++ b/notes/mcmc_diagnostics.ipynb
@@ -51,7 +51,7 @@
     "\n",
     "Convergence does **not** mean\n",
     "* that parameters are \"well constrained\" by the data. If you're not satisfied with the constraints you're getting, that's a function of the data and the model, not necessarily a failing of the MCMC sampler.\n",
-    "* that the autocorrelation length is small. A chain can be converged _and_ still highly correlated (though this is not desirable.\n",
+    "* that the autocorrelation length is small. A chain can be converged _and_ still highly correlated (though this is not desirable).\n",
     "* that there are not occasional excursions beyond a locus in parameter space. If the PDF has tails, the chain will need to occasionally find its way to them; otherwise it isn't doing its job."
    ]
   },