Dont use mathcal which mathjax default renders as squares on Colab+macOS

Explanation
https://math.meta.stackexchange.com/questions/35298/why-using-mathcal-command-produce-a-square

Issue tracker
googlecolab/colabtools#3192

Permanent fix (unlikely)
googlecolab/colabtools#2822

notebooks/T1 - DA & EnKF.ipynb

@@ -9,7 +9,7 @@
     "*Copyright (c) 2020, Patrick N. Raanes\n",
     "$\n",
     "% ######################################## Loading TeX (MathJax)... Please wait ########################################\n",
-    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathcal{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
+    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathscr{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
     "$"
    ]
   },

notebooks/T2 - Gaussian distribution.ipynb

@@ -38,7 +38,7 @@
     "# T2 - The Gaussian (Normal) distribution\n",
     "$\n",
     "% ######################################## Loading TeX (MathJax)... Please wait ########################################\n",
-    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathcal{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
+    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathscr{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
     "$\n",
     "Computers generally represent functions *numerically* by their values on a grid\n",
     "of points (nodes), an approach called ***discretisation***.\n",
@@ -64,14 +64,14 @@
    "metadata": {},
    "source": [
     "## The univariate (a.k.a. 1-dimensional, scalar) case\n",
-    "Consider the Gaussian random variable $x \\sim \\mathcal{N}(\\mu, \\sigma^2)$.  \n",
+    "Consider the Gaussian random variable $x \\sim \\NormDist(\\mu, \\sigma^2)$.  \n",
     "Its probability density function (**pdf**),\n",
     "$\n",
-    "p(x) = \\mathcal{N}(x \\mid \\mu, \\sigma^2)\n",
+    "p(x) = \\NormDist(x \\mid \\mu, \\sigma^2)\n",
     "$ for $x \\in (-\\infty, +\\infty)$,\n",
     "is given by\n",
     "$$\\begin{align}\n",
-    "\\mathcal{N}(x \\mid \\mu, \\sigma^2) = (2 \\pi \\sigma^2)^{-1/2} e^{-(x-\\mu)^2/2 \\sigma^2} \\,. \\tag{G1}\n",
+    "\\NormDist(x \\mid \\mu, \\sigma^2) = (2 \\pi \\sigma^2)^{-1/2} e^{-(x-\\mu)^2/2 \\sigma^2} \\,. \\tag{G1}\n",
     "\\end{align}$$\n",
     "\n",
     "Run the cell below to define a function to compute the pdf (G1) using the `scipy` library."
@@ -157,7 +157,7 @@
    "id": "94b6d541",
    "metadata": {},
    "source": [
-    "**Exc -- Derivatives:** Recall $p(x) = \\mathcal{N}(x \\mid \\mu, \\sigma^2)$ from eqn (G1).  \n",
+    "**Exc -- Derivatives:** Recall $p(x) = \\NormDist(x \\mid \\mu, \\sigma^2)$ from eqn (G1).  \n",
     "Use pen, paper, and calculus to answer the following questions,  \n",
     "which derive some helpful mnemonics about the distribution.\n",
     "\n",
@@ -201,7 +201,7 @@
    "metadata": {},
    "source": [
     "#### Exc (optional) -- Integrals\n",
-    "Recall $p(x) = \\mathcal{N}(x \\mid \\mu, \\sigma^2)$ from eqn (G1). Abbreviate it using $c = (2 \\pi \\sigma^2)^{-1/2}$.  \n",
+    "Recall $p(x) = \\NormDist(x \\mid \\mu, \\sigma^2)$ from eqn (G1). Abbreviate it using $c = (2 \\pi \\sigma^2)^{-1/2}$.  \n",
     "Use pen, paper, and calculus to show that\n",
     " - (i) the first parameter, $\\mu$, indicates its **mean**, i.e. that $$\\mu = \\Expect[x] \\,.$$\n",
     "   *Hint: you can rely on the result of (iii)*\n",

notebooks/T3 - Bayesian inference.ipynb

@@ -35,7 +35,7 @@
     "Now that we have reviewed some probability, we can look at statistical inference.\n",
     "$\n",
     "% ######################################## Loading TeX (MathJax)... Please wait ########################################\n",
-    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathcal{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
+    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathscr{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
     "$"
    ]
   },
@@ -48,7 +48,7 @@
     "studied the Gaussian probability density function (pdf), defined by:\n",
     "\n",
     "$$\\begin{align}\n",
-    "\\mathcal{N}(x \\mid \\mu, \\sigma^2) &= (2 \\pi \\sigma^2)^{-1/2} e^{-(x-\\mu)^2/2 \\sigma^2} \\,,\\tag{G1} \\\\\n",
+    "\\NormDist(x \\mid \\mu, \\sigma^2) &= (2 \\pi \\sigma^2)^{-1/2} e^{-(x-\\mu)^2/2 \\sigma^2} \\,,\\tag{G1} \\\\\n",
     "\\NormDist(\\x \\mid  \\mathbf{\\mu}, \\mathbf{\\Sigma})\n",
     "&=\n",
     "|2 \\pi \\mathbf{\\Sigma}|^{-1/2} \\, \\exp\\Big(-\\frac{1}{2}\\|\\x-\\mathbf{\\mu}\\|^2_\\mathbf{\\Sigma} \\Big) \\,, \\tag{GM}\n",
@@ -476,12 +476,12 @@
     "In response to this computational difficulty, we try to be smart and do something more analytical (\"pen-and-paper\"): we only compute the parameters (mean and (co)variance) of the posterior pdf.\n",
     "\n",
     "This is doable and quite simple in the Gaussian-Gaussian case, when $\\ObsMod$ is linear (i.e. just a number):  \n",
-    "- Given the prior of $p(x) = \\mathcal{N}(x \\mid x\\supf, P\\supf)$\n",
-    "- and a likelihood $p(y|x) = \\mathcal{N}(y \\mid \\ObsMod x,R)$,  \n",
+    "- Given the prior of $p(x) = \\NormDist(x \\mid x\\supf, P\\supf)$\n",
+    "- and a likelihood $p(y|x) = \\NormDist(y \\mid \\ObsMod x,R)$,  \n",
     "- $\\implies$ posterior\n",
     "$\n",
     "p(x|y)\n",
-    "= \\mathcal{N}(x \\mid x\\supa, P\\supa) \\,,\n",
+    "= \\NormDist(x \\mid x\\supa, P\\supa) \\,,\n",
     "$\n",
     "where, in the 1-dimensional/univariate/scalar (multivariate is discussed in [T5](T5%20-%20Multivariate%20Kalman%20filter.ipynb)) case:\n",
     "\n",
@@ -501,7 +501,7 @@
     "- (a) Actually derive the first term of the RHS, i.e. eqns. (5) and (6).  \n",
     "  *Hint: you can simplify the task by first \"hiding\" $\\ObsMod$ by astutely multiplying by $1$ somewhere.*\n",
     "- (b) *Optional*: Derive the full RHS (i.e. also the second term).\n",
-    "- (c) Derive $p(x|y) = \\mathcal{N}(x \\mid x\\supa, P\\supa)$ from eqns. (5) and (6)\n",
+    "- (c) Derive $p(x|y) = \\NormDist(x \\mid x\\supa, P\\supa)$ from eqns. (5) and (6)\n",
     "  using part (a), Bayes' rule (BR2), and the Gaussian pdf (G1)."
    ]
   },
@@ -522,11 +522,11 @@
    "source": [
     "**Exc -- Temperature example:**\n",
     "The statement $x = \\mu \\pm \\sigma$ is *sometimes* used\n",
-    "as a shorthand for $p(x) = \\mathcal{N}(x \\mid \\mu, \\sigma^2)$. Suppose\n",
+    "as a shorthand for $p(x) = \\NormDist(x \\mid \\mu, \\sigma^2)$. Suppose\n",
     "- you think the temperature $x = 20°C \\pm 2°C$,\n",
     "- a thermometer yields the observation $y = 18°C \\pm 2°C$.\n",
     "\n",
-    "Show that your posterior is $p(x|y) = \\mathcal{N}(x \\mid 19, 2)$"
+    "Show that your posterior is $p(x|y) = \\NormDist(x \\mid 19, 2)$"
    ]
   },
   {

notebooks/T4 - Time series filtering.ipynb

@@ -36,7 +36,7 @@
     "let's get more familiar with time-dependent (temporal/sequential) problems.\n",
     "$\n",
     "% ######################################## Loading TeX (MathJax)... Please wait ########################################\n",
-    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathcal{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
+    "\\newcommand{\\Reals}{\\mathbb{R}} \\newcommand{\\Expect}[0]{\\mathbb{E}} \\newcommand{\\NormDist}{\\mathscr{N}} \\newcommand{\\DynMod}[0]{\\mathscr{M}} \\newcommand{\\ObsMod}[0]{\\mathscr{H}} \\newcommand{\\mat}[1]{{\\mathbf{{#1}}}} \\newcommand{\\bvec}[1]{{\\mathbf{#1}}} \\newcommand{\\trsign}{{\\mathsf{T}}} \\newcommand{\\tr}{^{\\trsign}} \\newcommand{\\ceq}[0]{\\mathrel{≔}} \\newcommand{\\xDim}[0]{D} \\newcommand{\\supa}[0]{^\\text{a}} \\newcommand{\\supf}[0]{^\\text{f}} \\newcommand{\\I}[0]{\\mat{I}} \\newcommand{\\K}[0]{\\mat{K}} \\newcommand{\\bP}[0]{\\mat{P}} \\newcommand{\\bH}[0]{\\mat{H}} \\newcommand{\\bF}[0]{\\mat{F}} \\newcommand{\\R}[0]{\\mat{R}} \\newcommand{\\Q}[0]{\\mat{Q}} \\newcommand{\\B}[0]{\\mat{B}} \\newcommand{\\C}[0]{\\mat{C}} \\newcommand{\\Ri}[0]{\\R^{-1}} \\newcommand{\\Bi}[0]{\\B^{-1}} \\newcommand{\\X}[0]{\\mat{X}} \\newcommand{\\A}[0]{\\mat{A}} \\newcommand{\\Y}[0]{\\mat{Y}} \\newcommand{\\E}[0]{\\mat{E}} \\newcommand{\\U}[0]{\\mat{U}} \\newcommand{\\V}[0]{\\mat{V}} \\newcommand{\\x}[0]{\\bvec{x}} \\newcommand{\\y}[0]{\\bvec{y}} \\newcommand{\\z}[0]{\\bvec{z}} \\newcommand{\\q}[0]{\\bvec{q}} \\newcommand{\\br}[0]{\\bvec{r}} \\newcommand{\\bb}[0]{\\bvec{b}} \\newcommand{\\bx}[0]{\\bvec{\\bar{x}}} \\newcommand{\\by}[0]{\\bvec{\\bar{y}}} \\newcommand{\\barB}[0]{\\mat{\\bar{B}}} \\newcommand{\\barP}[0]{\\mat{\\bar{P}}} \\newcommand{\\barC}[0]{\\mat{\\bar{C}}} \\newcommand{\\barK}[0]{\\mat{\\bar{K}}} \\newcommand{\\D}[0]{\\mat{D}} \\newcommand{\\Dobs}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\Dmod}[0]{\\mat{D}_{\\text{obs}}} \\newcommand{\\ones}[0]{\\bvec{1}} \\newcommand{\\AN}[0]{\\big( \\I_N - \\ones \\ones\\tr / N \\big)}\n",
     "$"
    ]
   },
@@ -208,7 +208,7 @@
     "Formulae (5) and (6) are called the **forecast step** of the KF.\n",
     "But when $y_1$ becomes available, according to eqn. (Obs),\n",
     "then we can update/condition our estimate of $x_1$, i.e. compute the posterior,\n",
-    "$p(x_1 | y_1) = \\mathcal{N}(x_1 \\mid x\\supa_1, P\\supa_1) \\,,$\n",
+    "$p(x_1 | y_1) = \\NormDist(x_1 \\mid x\\supa_1, P\\supa_1) \\,,$\n",
     "using the formulae we developed for Bayes' rule with\n",
     "[Gaussian distributions](T3%20-%20Bayesian%20inference.ipynb#Gaussian-Gaussian-Bayes'-rule-(1D)).\n",
     "\n",