# partemp - Parallel tempering optimizer¶

 parallel_tempering Perform a MCMC walk using multiple temperatures in parallel.

Parallel tempering for continuous function optimization and uncertainty analysis.

The program performs Markov chain Monte Carlo exploration of a probability density function using a combination of random and differential evolution updates.

bumps.partemp.parallel_tempering(nllf, p, bounds, T=None, steps=1000, CR=0.9, burn=1000, monitor=<function every_ten>, logfile=None)[source]

Perform a MCMC walk using multiple temperatures in parallel.

nllf : function(vector) -> float
Negative log likelihood function to be minimized. $$\chi^2/2$$ is a good choice for curve fitting with no prior restraints on the possible input parameters.
p : vector
Initial value
bounds : vector, vector
Box constraints on the parameter values. No support for indefinite or semi-definite programming at present
T : vector | 0 < T[0] < T[1] < …
Temperature vector. Something like logspace(-1,1,10) will give you 10 logarithmically spaced temperatures between 0.1 and 10. The maximum temperature T[-1] determines the size of the barriers that can be easily jumped. Note that the number of temperature values limits the amount of parallelism available in the algorithm, so it may gather statistics more quickly, though it will not necessarily converge any faster.
steps = 1000 : int
Length of the accumulation vector. The returned history will store this many values for each temperature. These values can be used in a weighted histogram to determine parameter uncertainty.
burn = 1000 : int | [0,inf)
Number of iterations to perform in addition to steps. Only the last steps points will be preserved for each temperature. Since the value should be in the same order as steps to be sure that the full history is acquired.
CR = 0.9 : float | [0,1]
Cross-over ratio. This is the differential evolution crossover ratio to use when computing step size and direction. Use a small value to step through the dimensions one at a time, or a large value to step through all at once.
monitor = every_ten : function(int step, vector x, float fx) -> None
Function to called at every iteration with the step number the best point and the best value.
logfile = None : string
Name of the file which will log the history of every accepted step. Note that this includes all of the burn steps, so it can get very large.
history : History
Structure containing best, best_point and buffer. best is the best nllf value seen and best_point is the parameter vector which yielded best. The list buffer contains lists of tuples (step, temperature, nllf, x) for each temperature.