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Fixes typos in chap. 5

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Dennis Mack 2015-09-25 19:16:30 +02:00
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commit b0bc969cbe
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05-Multivariate-Gaussians.ipynb
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@ -757,7 +757,7 @@
"\n",
"This is the first contour that has values in the off-diagonal elements of the covariance, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling us the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal.\n",
"\n",
"What does this mean in physical terms? Think of parallel parking a car. You can not pull up beside the spot and then move sideways into the space because cars cannot drive sideways. $x$ and $y$ are not independent. This is a consequence of the steering mechanism. When the steering wheel is turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk in a straight line or a zig zag. If $x$ changes, $y$ must also change in a defined way. \n",
"What does this mean in physical terms? Think of parallel parking a car. You can not pull up beside the spot and then move sideways into the space because cars cannot drive sideways. $x$ and $y$ are not independent. This is a consequence of the steering mechanism. When the steering wheel is turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, it cannot vary $x$ and $y$ independently, which means it cannot walk in a straight line or a zig zag. If $x$ changes, $y$ must also change in a defined way. \n",
"\n",
"When we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how the relative sizes of the variance in $x$ and $y$. For example, a very long and narrow ellipse tilted almost to the horizontal has a strong correlation between $x$ and $y$ (because the ellipse is narrow), and the variance of $x$ is much larger than that of $y$ (because the ellipse is much longer in $x$)."
]
@ -963,7 +963,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Recall that Bayesian statistics calls this the *evidence*. The ellipse points towards the radar. It is very long because the range measurement is inaccurate, and he aircraft could be within a considerable distance of the measured range. It is very narrow because the bearing estimate is very accurate and thus the aircraft must be very close to the bearing estimate.\n",
"Recall that Bayesian statistics calls this the *evidence*. The ellipse points towards the radar. It is very long because the range measurement is inaccurate, and the aircraft could be within a considerable distance of the measured range. It is very narrow because the bearing estimate is very accurate and thus the aircraft must be very close to the bearing estimate.\n",
"\n",
"We want to find the *posterior* - the mean and covariance of incorporating the evidence into the prior. As in every chapter so far we multiply them together. I have the equations for this and we could use those, but I will use FilterPy's `multivariate_multiply` method."
]