By Michael Halls Moore
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Additional resources for Advanced Algorithmic Trading
It won’t land on its side), the flips will appear randomly and will be completely independent of each other. The fairness of the coin will also be stationary, that is it won’t alter over time. We will denote the fairness by the parameter θ. We will be considering stationary processes in depth in the section on Time Series Analysis later in the book. 2. Prior Beliefs - To carry out a Bayesian analysis, we must quantify our prior beliefs about the fairness of the coin. This comes down to specifying a probability distribution on our beliefs of this fairness.
The trace plot is extremely useful for assessing convergence of an MCMC algorithm and whether we need to exclude a period of initial samples (known as the burn in). 2. In addition we can see that the MCMC sampling procedure has "converged to the distribution" since the sampling series looks stationary. 6 Bibliographic Note The algorithm described in this chapter is due to Metropolis. An improvement by Hastings led to the Metropolis-Hastings algorithm. The Gibbs sampler is due to Geman and Geman.
Well, these two concepts neatly correspond to the mean and the variance of the beta distribution. Hence, if we can find a relationship between these two values and the α and β parameters, we can more easily specify our beliefs. 15) 31 Hence, all we need to do is re-arrange these formulae to provide α and β in terms of µ and σ. 289, since this is the standard deviation of a uniform density (which itself implies no prior belief on any particular fairness of the coin). Let’s carry out an example now.