Parallel Tempering
General Chain-Structured Models
There is an important probability distribution used in applications (Liu, 2008):
The simulating procedure is as follows:
Exact Method for Ising Model
For a one-dimensional Ising Model,
Parallel Tempering for Ising Model
Liu (2008) also introduced the parallel tempering strategy:
I wrote the following Julia program to implement this procedure and reproduce the simulation example of Liu (2008):
It is important to note that we should use logpdf
to avoid too big values, in which the rejection part doesn't work well. Refer to Ising-model.jl for complete source code.
Finally, I reproduce the Figure 10.1 as follows:
and the corresponding autocorrelation plots:
References
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