KKRR-ShPrP(120–232) event histogram and initial and optimal HMM models.

<p>(<b>a</b>) <b>(Left)</b> The KKRR-ShPrP(120–232) event histogram (blue) is divided into three regimes/states a high-state (black), mid-state (green) and low-state (red). The location of the peak and width of the distribution for each state in our initial model represents our best guess of the location and size of a given regime. <b>(Right)</b> The model parameters: <i>π</i> (i.e. the initial condition or probability that an event begins in a given state), <i>q</i> (the location of the peak of the Gaussian distribution, in terms of I/I0, for a given state), <i>b</i> (the standard deviation on the Gaussian of each state, which defines a state’s noise properties), and <i>A</i> (the state-to-state transition probability matrix). In our initial model we assume ignorance of the probabilities and therefore assume <i>π</i> to be uniformly distributed (i.e. an event is assumed equally likely to begin in any of the three states). Similarly with the transition probability matrix <i>A</i>, we assume all transitions to be equally likely (e.g. if in the low-state there is an equal probability for remaining in the low-state as there is for transitioning into the mid-state or the high-state). (<b>b</b>) <b>(Left)</b> After 40 iterations of the EM algorithm the optimal three-state model that best describes the data (i.e. the maximum likelihood model estimate) is converged upon. The low-state, far from encompassing all of the low current (as was presumed in our initial model) is very narrow and well defined, while the mid and high states both broaden out (the peak of the mid-state also shifts to a deeper conductance level relative to the initial model). <b>(Right)</b> The corresponding optimal model parameters.