Some textual corrections

example/MicrostructureNoise.ipynb

@@ -6,6 +6,8 @@
    "source": [
     "# MicrostructureNoise\n",
     "\n",
+    "## Introduction\n",
+    "\n",
     "(Available as Jupyter notebook at https://github.com/mschauer/MicrostructureNoise.jl/blob/master/example/MicrostructureNoise.ipynb)\n",
     "\n",
     "`MicrostructureNoise` is a Julia package for Bayesian volatility estimation in presence of market microstructure noise implementing the methodology described in our new preprint: \n",
@@ -15,7 +17,7 @@
     "This blogpost gives a short introduction.\n",
     "\n",
     "\n",
-    "## Description\n",
+    "### Description\n",
     "\n",
     "MicrostructureNoise estimates the volatility function $s$ of the stochastic differential equation\n",
     "\n",
@@ -34,7 +36,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Setup\n",
+    "### Setup\n",
     "\n",
     "Install `MicrostructureNoise` via the package manager. \n",
     "```\n",
@@ -59,7 +61,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Real data example\n",
+    "## Real data example\n",
     "\n",
     "As a first example, we apply our methodology to infer volatility of the high frequency foreign exchange rate data made available by Pepperstone Limited, the London based forex broker (https://pepperstone.com/uk/client-resources/historical-tick-data). Specifically, we use the EUR/USD tick data (bid prices) for 2 March 2015. We retrieve, log-transform and subsample the data and express time in milliseconds."
    ]
@@ -1082,7 +1084,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# How good does it work: Test with the Heston model"
+    "## How good does it work: Test with the Heston model"
    ]
   },
   {
@@ -1110,14 +1112,14 @@
     "collapsed": true
    },
    "source": [
-    "## Generate data from the Heston model\n",
+    "### Generate data from the Heston model\n",
     "\n",
     "To define the model in Julia and to simulate the trajectory use the package `Bridge`.\n",
     "Install it via the package manager. \n",
     "```\n",
     "Pkg.add(\"Bridge\")\n",
     "```\n",
-    "Usually we would not with $S$ directly, but with its logarithm $X_t=\\log S_t$. Here we simulate $S$ directly for simplicity."
+    "Usually we would not work with $S$ directly, but with its logarithm $X_t=\\log S_t$. Here we simulate $S$ directly for simplicity."
    ]
   },
   {
@@ -1237,7 +1239,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Generate a sample path with the Euler scheme from correlated Brownian motions, $\\log$-transform and subsample the data. Also we now the true volatility of of the transformed process by Itô's formula."
+    "Generate a sample path with the Euler scheme from correlated Brownian motions, $\\log$-transform and subsample the data. Also we now the true volatility of the transformed process by Itô's formula."
    ]
   },
   {
@@ -1267,7 +1269,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Perform inference using `MicrostructureNoise`.\n",
+    "### Perform inference using `MicrostructureNoise`.\n",
     "\n",
     "This proceeds along the same lines as before."
    ]
@@ -1588,10 +1590,10 @@
     "The greyish band mostly covers the red curve, the true volatility.\n",
     "\n",
     "This is nice: Without even using the knowledge of the model, completely ignoring the drift, \n",
-    "we still get a nice estimate and reasonable uncertainty quantification of the underlying volatility, and that using from indirect and \n",
-    "erroneous observations.\n",
+    "we still get a nice estimate and reasonable uncertainty quantification of the underlying volatility, and that having only indirect and \n",
+    "erroneous observations at our hands.\n",
     "\n",
-    "A histogram confirms that also the estimate of the observations noise is good."
+    "A histogram confirms that also the estimate of the observations noise is close to the true value."
    ]
   },
   {
@@ -1855,8 +1857,17 @@
     "\n",
     "* Shota Gugushvili, Frank van der Meulen, Moritz Schauer, and Peter Spreij: Nonparametric Bayesian volatility estimation. [arxiv:1801.09956](https://arxiv.org/abs/1801.09956), 2018.\n",
     "\n",
-    "* Shota Gugushvili, Frank van der Meulen, Moritz Schauer, and Peter Spreij: Nonparametric Bayesian volatility learning under microstructure noise. In preparation."
+    "* Shota Gugushvili, Frank van der Meulen, Moritz Schauer, and Peter Spreij: Nonparametric Bayesian volatility learning under microstructure noise. [arxiv:1805.05606](https://arxiv.org/abs/1805.05606), 2018."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {