Two-state telegraph process as a doubly stochastic Poisson model of neuronal burst spiking. A, Neuronal spiking is modeled as a doubly stochastic Poisson process with the underlying firing rate following a random two-level telegraph process. H and L denote the high and low firing states, with respective firing rates r_H and r_L, transition rates leaving the states μ_H and μ_L, τ_H and τ_L are the mean dwell time in each state. B, Three sample trials of model-simulated telegraph processes with the corresponding generated spike trains. The model parameters used here are in a biophysically plausible range: r_L = 5 sp/s, r_H = 100 sp/s, τ_L = 350 ms, τ_H = 65 ms. Colored bursts typically occur in the high firing state. C, Any homogeneous Poisson process with constant firing rate has FF equal to 1, whereas the example doubly stochastic Poisson process, defined in B, has FF equal to 6.15. D, The model in general can generate different levels of burstiness at fixed mean firing rate r_mean by tuning the four parameters. The intermittent bursting regime is characterized by low r_L, high r_H, and low <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL. Less burstiness can be achieved by raising the low firing rate r_L, or by increasing the ratio <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL.