文件列表:

AutoRJ.f (12101, 2005-03-15)
toy.f (1595, 2005-03-15)
cptlp.f (4311, 2005-03-15)
dfnlp.f (2622, 2005-03-15)
gauss4.f (425, 2005-03-15)
Makefile (273, 2003-06-15)
rgamma.f (1316, 2005-03-15)
sd.c (2755, 2005-03-15)
sokal.f (6626, 2005-03-15)
algama.f (13410, 2005-03-15)

INSTALLATION The package distributed consists of: main source file AutoRJ.f auxiliary routines in fortran and C algama.f gauss4.f rgamma.f sd.c sokal.f makefile Makefile example model files toy.f dfnlp.f cptlp.f this file readme.txt It is provided as both a gzipped tarfile and as a zip archive. In the former, the files all have Unix-style newline characters, and in the latter Dos-style line endings. The makefiles should be appropriate for Unix and Dos respectively. For a free Unix-like shell that runs under Windows, try Cygwin (www.cygwin.com). The program has been run successfully: using f77 and cc under Solaris on Sun workstations using GNU compilers under Linux on Intel processors using GNU compilers and Cygwin under Windows on Intel PCs --------------------------------------------- USING AutoRJ AutoRJ is a Fortran program for Unix-like systems, implementing the methodology for automatic reversible jump MCMC sampling described in section 6 (pages 191-4) of Green (Highly Structured Stochastic Systems, chapter 6, pages 179-206, OUP, 2003). These notes assume familiarity with this chapter. In particular, possible users should carefully note the warnings in that chapter about the lack of sophistication of the approach to reversible jump embodied in this code. The reliability of results from this sampler depends on many factors, including the initial values and spread parameters provided by the user, and the degree of multimodality of the parameter (posterior) distribution within each submodel. The program is compiled with a user-provided Fortran or C function that defines the model in question; when run, it produces multiple output text files summarising the MCMC sample, for subsequent analysis and display (R or Splus are good choices for these tasks). Only very limited summary information is computed by this program itself. --------------------------------------------- WRITING the Model Function The model function has the structure, in Fortran: real function target(k,params) integer k real params(*) The function must be called 'target'. Both arguments k and params must be variables: k is an input parameter, which also controls the task performed by the function. k is read-only unless it takes the value 0 or a value between kmax+1 and 2*kmax on input; params is a real array, used for output for certain values of k, and input for others. The function has 5 distinct functions: 1. if k=0 on input, the function returns with k set to kmax, the number of sub-models being entertained (which are indexed 1,2,..., kmax). 2. if k lies between kmax+1 and 2*kmax on input, it is replaced by nk(k-kmax) on exit, where nk(j) is the dimension n_j of submodel j. 3. if k lies between 2*kmax+1 and 3*kmax, then on exit, params(j), j=1,2,...,nk(k-2*kmax) contains the initial values for the parameters in the corresponding submodel. 4. if k lies between 3*kmax+1 and 4*kmax, then on exit, params(j), j=1,2,...,nk(k-3*kmax) contains the spread parameters for the parameters in the corresponding submodel. 5. if k lies between 1 and kmax, then the function evaluates the logarithm of the target distribution, up to an additive constant, where k is given in the first argument k, and the vector \theta_k in the second argument params(), in consecutive entries starting at 1. The value of the log-target is returned through the value of the function target. In a Bayesian model determination problem, the log-target is the log-posterior, \log p(k,\theta_k|Y) in the notation of the HSSS book chapter. Typically, one provides simply \log p(k) + \log p(\theta_k|k) + \log p(Y|k,\theta_k), the sum of log model prior probability, log parameter prior density and log likelihood. By Bayes' theorem, this is equivalent. AutoRJ calls target once with k=0, and once for each value of k from 1 to kmax, for functions 2, 3 and 4 above. Of course, it calls target to perform function 5 many times in the simulation. Three examples are provided in the distribution - for the two examples on page 193 of the HSSS book chapter, and a simpler 'toy' example, a mixture of a univariate and a bivariate density. --------------------------------------------- COMPILING AutoRJ Edit the file Makefile to specify the name of the file containing model function (without the .f or .c extension) as variable TARGET. Then type 'make'. The compiled version will be named AutoRJ or AutoRJ.exe as appropriate. --------------------------------------------- RUNNING AutoRJ The run of the program is controlled by options, switches and parameter settings that have sensible default values, and can be set by command line arguments in Unix shell style. The options are as follows. In this list, N denotes a numerical value passed in as a parameter of the sampler, other options are logical settings that are by default off, turned on by specifying the option. Options -nN run sampler for N sweeps in within-model RWM phase, and 10*N sweeps in model-jumping phase -tN use t distributions with N degrees of freedom instead of normal distributions for proposing innovation variables u -p switch on random permutation option (matrix R) -seedN random number seed (default 0, meaning use clock time to initialise). In the log file for the run, the seed actually used is printed, and the run can be repeated with the same random numbers by specifying that value in this option on the subsequent run. -save save state (mu, B etc) after within-model RWM phase, so that subsequent runs can omit this phase and proceed directly to model jumping -sN thinning parameter for Sokal's estimate of autocorrelation time: default N=1, no thinning (N=0: suppress this computation) The only other command-line argument supported (and which is mandatory) is the name of a subdirectory of the current directory, which is used for all the output files created by the run, and for the save-state information, if the -save option is used. All the output files are given names of the form N_ext, where N is a unique integer assigned by the program to label successive runs (it chooses the smallest positive integer such that N_log does not already exist), and _ext signifies the type of output the file contains: _log records information about the run _model time-series of the model indicator k, thinned if the run is very long (to give a maximum of 10000 values) _parK for K=1,2,..., time-series of the sampled model-K parameters, thinned if the run is very long (to give a maximum of 5000 parameter sets over all sub-models) _acf autocorrelation function for the model indicator --------------------------------------------- EXAMPLE of compiling and running AutoRJ (a) ~/AutoRJDist $ cat Makefile FC = g77 CC = gcc FFLAGS = -O2 TARGET = dfnlp AutoRJ.exe: AutoRJ.o $(TARGET).o sd.o gauss4.o rgamma.o algama.o sokal.o $(FC) $(FFLAGS) -o AutoRJ.exe AutoRJ.o $(TARGET).o \ sd.o gauss4.o rgamma.o algama.o sokal.o sd.o: sd.c $(CC) -c -o sd.o -DRETS -DSUNF sd.c ~/AutoRJDist $ make g77 -O2 -c -o AutoRJ.o AutoRJ.f g77 -O2 -c -o dfnlp.o dfnlp.f gcc -c -o sd.o -DRETS -DSUNF sd.c g77 -O2 -c -o gauss4.o gauss4.f g77 -O2 -c -o rgamma.o rgamma.f g77 -O2 -c -o algama.o algama.f g77 -O2 -c -o sokal.o sokal.f g77 -O2 -o AutoRJ.exe AutoRJ.o dfnlp.o \ sd.o gauss4.o rgamma.o algama.o sokal.o (b) ~/AutoRJDist $ mkdir dfn (c) ~/AutoRJDist $ AutoRJ dfn -n10000 auto-rj nsweep = 10000 seed = 1055525484 normal proposals run: dfn/1 ... setting up, doing rwm for k = 1( 70) 2( 57) 3( 55) 4( 48) 5( 39) kmax = 5 nk: 1 2 2 3 4 ... auto-jumping: 9 8 7 6 5 4 3 2 1 0 model frequencies: 507 49152 10*** 44117 5160 percentage jumps accepted: 29.4 nkeep, nsokal, tau 32768 1 2.8256 (d) ~/AutoRJDist $ ls dfn 1_acf 1_par1 1_par2 1_par3 1_par4 1_par5 1_log 1_model This shows (a) compilation (b) creation of subdirectory for output files (c) run of AutoRJ, with output showing: number of sweeps random number seed to repeat type of proposal distribution index number of run RWM phase, with percentage acceptances in each submodel number of submodels dimensions of submodels countdown of main model-jumping run model frequencies percentage acceptance of model-jumping moves autocorrelation time statistics. (d) list of output files in subdirectory

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