DREAM1
Markov Chain Monte Carlo acceleration by Differential Evolution

DREAM1 is a C library which is an older implementation of the DREAM algorithm for accelerating Markov Chain Monte Carlo (MCMC) convergence using differential evolution, by Guannan Zhang.

Using the DREAM1 library to solve a problem requires:

• compiling a main program, for example, the DREAM1_test.C file;
• linking the main program with the DREAM1 and RNGLIB libraries;
• supplying two text files that define the input parameters and the prior probability density function, such as the examples given below.

A more recent version of the algorithm, with a simplified interface involving 5 user functions, is available as DREAM.

Web Link:

A version of the DREAM library is available in http://tasmanian.ornl.gov, the TASMANIAN library, available from Oak Ridge National Laboratory.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

DREAM1 is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

DREAM, a C program which implements the DREAM algorithm for accelerating Markov Chain Monte Carlo (MCMC) convergence using differential evolution, using five user functions to define the problem, by Guannan Zhang.

RANLIB, a C library which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.

RNGLIB, a C library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

Author:

Original FORTRAN90 version by Guannan Zhang; C version by John Burkardt.

Reference:

1. Pierre LEcuyer, Serge Cote,
   Implementing a Random Number Package with Splitting Facilities,
   ACM Transactions on Mathematical Software,
   Volume 17, Number 1, March 1991, pages 98-111.
2. Jasper Vrugt, CJF ter Braak, CGH Diks, Bruce Robinson, James Hyman, Dave Higdon,
   Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling,
   International Journal of Nonlinear Sciences and Numerical Simulation,
   Volume 10, Number 3, March 2009, pages 271-288.

Source Code:

• dream1.c, the source code.
• dream1.h, the include file.
• dream1.sh, BASH commands to compile the source code.

Examples and Tests:

• dream1_test.c, a sample calling program.
• dream1_test.sh, BASH commands to compile and run the sample program.
• dream1_test.txt, the output file.

Input files:

• input.txt, an input file, containing parameter values, read by INPUT_READ.
• prior.txt, an input file, defining the prior density functions for the parameters, read by PRIOR_READ.

Output files:

• chain000.txt, an output file, containing the sample values for chain 0, written by CHAIN_WRITE.
• chain001.txt, an output file, containing the sample values for chain 1, written by CHAIN_WRITE.
• chain002.txt, an output file, containing the sample values for chain 2, written by CHAIN_WRITE.
• chain003.txt, an output file, containing the sample values for chain 3, written by CHAIN_WRITE.
• chain004.txt, an output file, containing the sample values for chain 4, written by CHAIN_WRITE.
• chain005.txt, an output file, containing the sample values for chain 5, written by CHAIN_WRITE.
• chain006.txt, an output file, containing the sample values for chain 6, written by CHAIN_WRITE.
• chain007.txt, an output file, containing the sample values for chain 7, written by CHAIN_WRITE.
• chain008.txt, an output file, containing the sample values for chain 8, written by CHAIN_WRITE.
• chain009.txt, an output file, containing the sample values for chain 9, written by CHAIN_WRITE.
• gr.txt, an output file, the Gelman-Rubin statistic file, created by GR_WRITE.
• restart_write.txt, an output file, containing restart information, written by RESTART_WRITE.

List of Routines:

• CHAIN_INIT starts Markov chains from a prior distribution.
• CHAIN_INIT_PRINT prints the initial values for Markov chains.
• CHAIN_OUTLIERS identifies and modifies outlier chains during burn-in.
• CHAIN_WRITE writes samples of each chain to separate files.
• CR_DIS_UPDATE updates the CR distance.
• CR_INDEX_CHOOSE chooses a CR index.
• CR_INIT initializes the crossover probability values.
• CR_PROB_UPDATE updates the CR probabilities.
• DIFF_COMPUTE computes the differential evolution.
• DREAM_ALGM gets a candidate parameter sample.
• FILENAME_INC increments a partially numeric file name.
• GR_COMPUTE computes the Gelman Rubin statistics R used to check convergence.
• GR_INIT initializes Gelman-Rubin variables.
• GR_WRITE writes Gelman-Rubin R statistics into a file.
• I4_BINOMIAL_SAMPLE generates a binomial random deviate.
• I4VEC_MULTINOMIAL_SAMPLE generates a multinomial random deviate.
• I4VEC_ZERO_NEW creates and zeroes an I4VEC.
• INPUT_PRINT prints the data from the input file.
• INPUT_READ reads the data from the input file.
• INPUT_SIZE reads the parameter size variable from the input file.
• JUMPRATE_CHOOSE chooses a jump rate from the jump rate table.
• JUMPRATE_TABLE_INIT initializes the jump rate table.
• JUMPRATE_TABLE_PRINT prints the jump rate table.
• MNOR_INIT initializes information for multivariate normal prior densities.
• MNOR_PROCESS sets data for the generation of multivariate normal deviates.
• MNOR_READ reads a file for multivariate normal prior densities.
• OB_READ reads observational data from a file.
• PRIOR_DENSITY evaluates the prior density function.
• PRIOR_PRINT prints information about the prior density.
• PRIOR_READ reads information about the prior density.
• PRIOR_SAMPLE samples from the prior distribution.
• R8_BETA_PDF evaluates the PDF of a beta distribution.
• R8_BETA_SAMPLE generates a beta random deviate.
• R8_CHI_PDF evaluates the PDF of a chi-squared distribution.
• R8_CHI_SAMPLE generates a Chi-Square random deviate.
• R8_EPSILON returns the R8 round off unit.
• R8_EXPONENTIAL_PDF evaluates the PDF of an exponential distribution.
• R8_EXPONENTIAL_SAMPLE samples the exponential PDF.
• R8_EXPONENTIAL_01_SAMPLE samples the standard exponential PDF.
• R8_GAMMA_LOG evaluates the logarithm of the gamma function.
• R8_GAMMA_PDF evaluates the PDF of a gamma distribution.
• R8_GAMMA_SAMPLE generates a Gamma random deviate.
• R8_GAMMA_01_SAMPLE samples the standard Gamma distribution.
• R8_INVCHI_PDF evaluates the PDF of an inverse chi-squared distribution.
• R8_INVGAM_PDF evaluates the PDF of an inverse gamma distribution.
• R8_MAX returns the maximum of two R8's.
• R8_MIN returns the minimum of two R8's.
• R8_MNOR_PDF evaluates the PDF of a multivariate normal distribution.
• R8_NORMAL_PDF evaluates the PDF of a normal distribution.
• R8_NORMAL_SAMPLE generates a normal random deviate.
• R8_NORMAL_01_SAMPLE samples the standard normal probability distribution.
• R8_ROUND_I4 rounds an R8, returning an I4.
• R8_SCINVCHI_PDF: PDF for a scaled inverse chi-squared distribution.
• R8_UNIFORM_PDF evaluates the PDF of a uniform distribution.
• R8_UNIFORM_SAMPLE generates a uniform random deviate.
• R8_UNIFORM_01_SAMPLE generates a uniform random deviate from [0,1].
• R8BLOCK_ZERO_NEW returns a new zeroed R8BLOCK.
• R8MAT_POFA factors a real symmetric positive definite matrix.
• R8MAT_ZERO_NEW returns a new zeroed R8MAT.
• R8VEC_COPY_NEW copies an R8VEC.
• R8VEC_HEAP_D reorders an R8VEC into a descending heap.
• R8VEC_MNOR_SAMPLE generates a multivariate normal deviate.
• R8VEC_SORT_HEAP_A ascending sorts an R8VEC using heap sort.
• R8VEC_SUM returns the sum of an R8VEC.
• R8VEC_ZERO_NEW creates and zeroes an R8VEC.
• RESTART_READ reads parameter sample data from a restart file.
• RESTART_WRITE writes a restart file.
• SAMPLE_CANDIDATE generates candidate parameter samples.
• SAMPLE_LIKELIHOOD computes the log likelihood function.
• SAMPLE_LIMITS enforces limits on a sample variable.
• STD_COMPUTE computes the current standard deviations, for each parameter.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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