Automatic burn-in through discordant network?

[krivit]

We already do this in tergm when running within-time-step MCMC.

We can keep track of the changes in Hamming distance between the initial network and the current MCMC state, a vector of +1s, 0s, and -1s. Initially, +1s will occur more frequently than -1s, as the network burns in. Eventually, once the network is sufficiently far away, they will balance out. At that point, we burn-in a bit longer to preserve the Markov property and conclude.

For valued ERGMs, we need some other notion of distance, perhaps sum of absolute differences.

Advantages:

1. A very simple approach.
2. Can be done entirely in C, so no need to go between R and C.
3. No need for time-series, Geweke, etc. diagnostics.
4. Pretty well tested in tergm.

Disadvantages:

1. May be unnecessarily conservative: typically we don't care if the network is burned-in but rather that the statistics are---and the latter have a much lower dimension than the former.
2. Requires storing the previous network.
3. Computational cost is incurred at every iteration from having to keep track.