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6 changes: 3 additions & 3 deletions S31_vacuum_state.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -269,7 +269,7 @@
"```\n",
"Therefore, we represent the state space by an *undirected* graph.\n",
"Taken together, the collection of states along with connectivity information is referred to as the **state space**,\n",
"which in this case can be represented by the connectivity graph shown in Figure [4](#fig:House-ss)."
"which in this case can be represented by the connectivity graph shown in Figure [2](#fig:House-ss)."
]
},
{
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"This means that we view probabilities as describing our *knowledge* about events, rather than tallying up the frequencies by which they occur.\n",
"For example, think of the weather forecaster talking about the probability of rain tomorrow: this represents a belief about a future state, rather than statistics about previous rainy days.\n",
"Probabilities viewed this way can be used to describe knowledge about the state of the world, and how actions affect the state of an agent and the world.\n",
"This view is named after the Reverend Thomas Bayes, shown in Figure [4](#fig:Bayesian), who (among others) laid the mathematical groundwork for updating beliefs in light of new evidence.\n",
"This view is named after the Reverend Thomas Bayes, shown in Figure [3](#fig:Bayesian), who (among others) laid the mathematical groundwork for updating beliefs in light of new evidence.\n",
"\n",
"<figure id=\"fig:Frequentist\">\n",
"<img src=\"https://github.com/gtbook/robotics/blob/main/Figures3/N3-Frequentist.png?raw=1\" style=\"width:9cm\" alt=\"\" />\n",
"<figcaption>The caricature of the frequentist view involves counting many heads and tails.</figcaption>\n",
"</figure>\n",
"\n",
"This is to be contrasted with a **frequentist view**, where probabilities are based on the frequencies of events in a series of repeated trials.\n",
"Figure [5](#fig:Frequentist) highlights this perspective, where probabilities emerge as ratios derived from repeated experiments.\n",
"Figure [4](#fig:Frequentist) highlights this perspective, where probabilities emerge as ratios derived from repeated experiments.\n",
"A Bayesian, instead, might qualify knowledge about an event that has not even happened yet, let alone multiple times.\n",
"Of course, in most cases this belief is based on experience, i.e., lots of repeated events in the past, and so it can be seen that perhaps these views are not so different after all.\n",
"\n",
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