Fixed numbers in MISE eval

tex/chapters/experiments.tex

@@ -27,7 +27,7 @@ Four estimates are computed with varying bandwidth using the KDE, BKDE, BoxKDE,
 All estimates are calculated at $30\times 30$ equally spaced points.
 %Evaluated at $50^2$ points the exact KDE is compared to the BKDE, BoxKDE, and extended box filter approximation, which are evaluated at a smaller grid with $30^2$ points.
 The graphs of the MISE between $f$ and the estimates as a function of $h\in[0.15, 1.0]$ are given in \figref{fig:errorBandwidth}.
-A minimum error is obtained with $h=0.35$, for larger values oversmoothing occurs and the modes gradually fuse together.
+A minimum error is obtained with $h=0.25$, for larger values oversmoothing occurs and the modes gradually fuse together.
 
 Both the BKDE and the ExBoxKDE resemble the error curve of the KDE quite well and stable.
 They are rather close to each other, with a tendency to diverge for larger $h$.
@@ -36,8 +36,8 @@ These jumps are caused by the rounding of the integer-valued box width given by
 
 As the extended box filter is able to approximate an exact $\sigma$, such discontinuities do not appear.
 Consequently, it reduces the overall error of the approximation, even though only marginal in this scenario.
-The global average MISE over all values of $h$ is $0.0049$ for the regular box filter and $0.0047$ in case of the extended version.
-Likewise, the maximum MISE is $0.0093$ and $0.0091$, respectively.
+The global average MISE over all values of $h$ is $0.0051$ for the regular box filter and $0.0049$ in case of the extended version.
+The global maximum MISE is $0.0011$ for both versions.
 The choice between the extended and regular box filter algorithm depends on how large the acceptable error should be, thus on the particular application.
 
 Other test cases of theoretical relevance are the MISE as a function of the grid size $G$ and the sample size $N$.

tex/chapters/introduction.tex

@@ -18,7 +18,7 @@ Additionally, in most practical scenarios the sample size, and hence the resolut
 
 It is obvious, that a computation of the full posterior could solve the above, but finding such an analytical solution is an intractable problem, which is the reason for applying a sample representation in the first place. 
 Another promising way is to recover the probability density function from the sample set itself, by using a non-parametric estimator like a kernel density estimation (KDE). 
-With this, the \qq{real} most probable state is given by the maxima of the density estimation and thus avoids the aforementioned drawbacks.
+With this, the \qq{real} most probable state is given by the maximum of the density estimation and thus avoids the aforementioned drawbacks.
 However, non-parametric estimators tend to consume a large amount of computation time, which renders them unpractical for real time scenarios.
 Nevertheless, the availability of a fast processing density estimate might improve the accuracy of today's sensor fusion systems without sacrificing their real time capability.
 

tex/chapters/realworld.tex

@@ -54,7 +54,7 @@ With new measurements coming from the hallway or other parts of the building, th
 
 Nevertheless, it can be seen that our approach is able to resolve multimodalities even under real world conditions. 
 It does not always provide the lowest error, since it depends more on an accurate sensor model than a weighted-average approach, but it is very suitable as a good indicator about the real performance of a sensor fusion system.
-In the here shown examples we only searched for a global maxima, even though the BoxKDE approach opens a wide range of other possibilities for finding a best estimate. 
+In the here shown examples we only searched for a global maximum, even though the BoxKDE approach opens a wide range of other possibilities for finding a best estimate. 
 
 %springt nicht so viel wie maximum
 %sehr ähnlich zu weighted-average. in 1000 mc runs ist sind average und std sehr ähnlich.