St George’s Church Lecture Theatre, University of Sheffield



point 1: \(x= 1\), \(y=3\) \[ 3 = m + c \]
point 2: \(x= 3\), \(y=1\) \[ 1 = 3m + c \]
point 3: \(x= 2\), \(y=2.5\)
\[2.5 = 2m + c\]
point 1: \(x= 1\), \(y=3\) \[ 3 = m + c + \epsilon_1 \]
point 2: \(x= 3\), \(y=1\) \[ 1 = 3m + c + \epsilon_2 \]
point 3: \(x= 2\), \(y=2.5\) \[ 2.5 = 2m + c + \epsilon_3 \]
Set the mean of Gaussian to be a function. \[ p\left(y_ix_i\right)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(\frac{\left(y_if\left(x_i\right)\right)^{2}}{2\sigma^2}\right). \]
This gives us a ‘noisy function’.
This is known as a stochastic process.







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ODE1 ARTIFICIAL EXAMPLE
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