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Bayes Error Rate For the general case of K different classes, the probability of classifing x instance correctly is: $$\label{eq1} \begin{split} P(correct) & = \sum_{i=1}^{K} p(x \in H_i, C_i) \\ & = \sum_{i=1}^{K} \int_{x \in H_i} p(x,C_i) \, dx\\ & = \sum_{i=1}^{K} \int_{x \in H_i} P(C_i|x)p(x)\,dx \\ \end{split}$$ ...

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Welcome to AI.SE @rudreshdwivedi! This is a great question, and I hope to see many more like it. Demster-Shafer Theory and Bayesian Networks were both techniques that rose to prominence within AI in the 1970's and 1980's, as AI started to seriously grapple with uncertainty in the world, and move beyond the sterilized environments that most early systems ...

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Your probability hasn't been normalized! In this case, you are computing the probability of being good, given that the other features have a fixed value. To obtain the correct probability, you need to normalize (divide) the value from your calculation by the probability that the features have taken on those fixed values. You can calculate this as follows: ...

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Position Detection In a traditional data acquisition and control scenario, with some assumptions, the relation between sensors signals $s_i$, emitters drive $\epsilon_j$, distances $x_{ij}$, and calibration factors is modelled as follows. $$\forall \, (i, j) \text{,} \quad \frac {s_i} {v_i} = \frac {\epsilon_j} {v_j \, x_{ij}^2}$$ The assumptions include ...

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Bernoulli naïve Bayes $P(x|c_k) = \prod^{n}_{i=1} p^{x_i}_{ki} (1-p_{ki})^{(1-x_i)}$ Let's examine the example of document classification. Let K different text classes and n different terms that our vocabulary contains. $x_i$ are boolean variables (0, 1) expressing if the $i^{th}$ term exists in document x. x is a vector of dimension n. $P(x|c_k)$ ...

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This is a bit of a puzzle but you can compute a reasonable narrow limit even without knowing whether or not $P(S,A) = P(S) P(A)$. Start with the contingency table relating $P(S, A)$, $P(S,\neg A)$, $P(\neg S, A)$, $P(\neg S,\neg A)$ to $P(S)$ and $P(A)$ : $$\begin{array}{cc|c} P( S,A)& P(\neg S,A) & P(A) \\ P(S,\neg A)& P(\neg S,\neg A) & P(... 1 Yes you can, provided you know about f and g. Expression X3 = f(X1, g(X1))can be written as X3 = h(X1) where h takes into account both f and g. After this finding the PDF is simple by differentiating the CDF:$$ F_{X3} (x3) = P(X3 \leq x3) = P(h(X1) \leq x3) = P(X1 \leq h^{-1}(x3)) \frac {d F_{X3} (x3)}{dx3} = \frac {d P(X1 \leq h^{-1}(...

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Model input: 1 mean scaled input for each emitter 1 distance value for each distance Multiple input You mentioned there is noise. If the noise is constant, ie you test it in place A and the values returned are always the same, then it means training in different places. If you place it in a place and the first reading is different from the second reading....

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