Get optimal parameters for GHMC

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Aim Plot optimal parameters for HMC model

Method Vary step size and angle

It is important to stress that the $M^2$ measurements are made by taking a regular autocorrelation. Taking into account the exponential trajectories is not necessary for the integrated autocorrelations. Otherwise the form would be $cos^2 \omega s$ and $\tau_{\text{int}} \to \infty\ \forall s$

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Two plots:

1. vary step size
2. vary angle

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got optimisation proceedure. Plotted $\tau$ with respect to cost for:

• $X^2$
• $M^2$

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• minimised HMC with respect to $\delta\tau$ and $n$
• minimised KMC with respect to $\vartheta$ and $\delta\tau$

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Discovered that the number of steps doesn't really have much of an impact on the the integrated autocorrelation in HMC

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Improved resolution

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Presentation feedback

Instead of solely using the integrated autocorrelation, should use a cost function which takes into account the acceptance probability.