tweaks

docs/source/explainable_sir.ipynb

@@ -30,7 +30,7 @@
     "- [But for Analysis with Bayesian SIR Model with Policies](#but-for-analysis-with-bayesian-sir-model-with-policies)\n",
     "- [Causal Explanations using `SearchForExplanation`](#causal-explanations-using-searchforexplanation)\n",
     "- [Fine-grained Analysis of `overshoot` using Sample traces](#fine-grained-analysis-of-overshoot-using-sample-traces)\n",
-    "- [For Advanced Readers: Looking into Different Contexts](#ooking-into-different-contexts-for-curious-readers)"
+    "- [Looking into Different Contexts for Curious Readers](#ooking-into-different-contexts-for-curious-readers)"
    ]
   },
   {
@@ -746,7 +746,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We specifically compute the following four probabilities. In each of the computations, we condition on lockdown and masking actually being implemented in the factual world. Then we take an interventional setting and compute the probability that this setting has a causal power over the outcome. For instance, in 1., we assume lockdown (`ld`) and masking (`m`) have been implemented, and we ask about the joint prbability that both (a) removing both interventions, i.e. intervening for both  `ld`  and `m` to not happen - which we mark by the apostrophe - would lead to `oth` not happening, $\\mathit{oth}'_{\\mathit{ld}', m'}$, and (b) intervening for both to happend would lead to `oth`, $\\mathit{oth}_{\\mathit{ld}, m}$ (which, given the stochasticity between these interventions and the outcome, is non-trivial). Note that in computing these probabilities, we also marginalize over all the contexts that potentially can be kept fixed, i.e. all possible subsets of $W = \\{\\mathit{le}, \\mathit{me}\\}$\n",
+    "We specifically compute the following four probabilities. In each of the computations, we condition on lockdown and masking actually being implemented in the factual world. Then we take an interventional setting and compute the probability that this setting has a causal power over the outcome. For instance, in 1., we assume lockdown (`ld`) and masking (`m`) have been implemented, and we ask about the joint probability that both (a) removing both interventions, i.e. intervening for both  `ld`  and `m` to not happen - which we mark by the apostrophe - would lead to `oth` not happening, $\\mathit{oth}'_{\\mathit{ld}', m'}$, and (b) intervening for both to happend would lead to `oth`, $\\mathit{oth}_{\\mathit{ld}, m}$ (which, given the stochasticity between these interventions and the outcome, is non-trivial). Note that in computing these probabilities, we also marginalize over all the contexts that potentially can be kept fixed, i.e. all possible subsets of $W = \\{\\mathit{le}, \\mathit{me}\\}$\n",
     "\n",
     "1. $\\sum_{w \\subseteq W} P_w(w) \\cdot P(\\mathit{oth}^w_{\\mathit{ld}, m}, \\mathit{oth}'^w_{\\mathit{ld}', m'} | \\mathit{ld}, m)$\n",
     "\n",
@@ -1341,7 +1341,7 @@
     "1. Intervene on `lockdown=1` while keeping `mask_efficiency` fixed (or not).\n",
     "2. Intervene on `mask=1` while keeping `lockdown_efficiency` fixed (or not).\n",
     "\n",
-    "The key motivation for looking into this is the intuition that there is some part of the actual context in which removing lockdown would significantly lower the overshoot, whereas there is no corresponding part of the actual context in which removing masking would lead to lower overshoot - which is the core of the assymetricity between the two interventions in our example.\n",
+    "The key motivation for looking into this is the intuition that there is some part of the actual context in which removing lockdown would significantly lower the overshoot, whereas there is no corresponding part of the actual context in which removing masking would lead to lower overshoot - which is the core of the asymmetry between the two interventions in our example.\n",
     "\n",
     "We first intervene on `lockdown` being 1 and analyze how the distribution of `overshoot` changes as we keep the `mask_efficiency` fixed (or not)."
    ]
@@ -1452,8 +1452,6 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We use the notation $\\mathit{os}^m$ to describe the variable $\\mathit{os}$ when $m$ is kept fixed. \n",
-    "\n",
     "The above histogram plots the following distributions:\n",
     "1. `mask_efficiency fixed`: $P( \\mathit{os}^{\\mathit{me}}_{\\mathit{ld}'} | \\mathit{ld}, m)$\n",
     "2. `mask_efficiency not fixed`: $P( \\mathit{os}_{\\mathit{ld}'} | \\mathit{ld}, m)$\n",