MIXTURE
Dirichlet Mixture Simulation

MIXTURE is a FORTRAN90 program which simulates a process governed by a Dirichlet Mixture probability density function (PDF).

Each realization of the process involves choosing one of a specified set of Dirichlet PDF's, with given weight, and then sampling that PDF.

The current code is pretty rough, and simply does a simulation. An improved version would involve using the simulation to test procedures for estimating the number of Dirichlet densities in the mixture, and their parameters, using a Bayesian approach.

Licensing:

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

Languages:

MIXTURE is available in a FORTRAN90 version.

Related Data and Programs:

ASA266, a FORTRAN90 library which evaluates various properties of a Dirichlet distribution.

References:

• Carl Branden, John Tooze,
  Introduction to Protein Structure,
  Second Edition,
  Garland Publishing, 1999,
  ISBN: 0815323050,
  LC: QP551.B7635.
• Luc Devroye,
  Non-Uniform Random Variate Generation,
  Springer, 1986,
  ISBN: 0387963057,
  LC: QA274.D48.
• William Kennedy, James Gentle,
  Statistical Computing,
  Marcel Dekker, 1980,
  ISBN: 0824768981,
  LC: QA276.4.K46.
• Kimmen Sjoelander, Kevin Karplus, Michael Brown, Richard Hughey, Anders Krogh, Siara Mian, David Haussler,
  Dirichlet Mixtures: a method for improved detection of weak but significant protein sequence homology,
  Computer Applications in the Biosciences,
  Volume 12, Number 4, pages 327-345, 1996.

Source Code:

• mixture.f90, the source code;

Examples and Tests:

• mixture.txt, a mixture definition file;
• mixture.txt, the output file.

List of Routines:

• MAIN is the main program for the mixture simulation.
• AMINO_PRINT prints the amino acid parameters.
• BINOMIAL_SAMPLE samples the Binomial PDF.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_NEXT "reads" space-separated characters from a string, one at a time.
• CH_TO_AMINO_NAME converts a character to an amino acid name.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• COMP_PARAM_PRINT prints the parameters for the mixture components.
• COMP_STATS_PRINT prints the mean and variance for the mixture components.
• DISCRETE_CDF_INV inverts the Discrete CDF.
• DISCRETE_SAMPLE samples the Discrete PDF.
• FAVOR_RATIO_COMPUTE computes the ratio by which a component density favors an amino acid.
• FAVOR_RATIO_PRINT prints the favor ratios.
• GAMMA_LOG calculates the natural logarithm of GAMMA ( X ) for positive X.
• I4_NEXT "reads" integers from a string, one at a time.
• MIXTURE_PRINT prints the Dirichlet mixture parameters.
• MIXTURE_READ reads the Dirichlet mixture parameters from a file.
• MULTINOMIAL_PDF computes a Multinomial PDF.
• MULTINOMIAL_SAMPLE samples the Multinomial PDF.
• OBSERVE repeatedly observes the process and updates the parameter estimates.
• R4_NEXT "reads" real numbers from a string, one at a time.
• R4_RANDOM returns a random real in a given range.
• R4ROW_MEAN returns the means of rows of a real array.
• RR4OW_VARIANCE returns the variances of the rows of a real array.
• S_BEGIN is TRUE if one string matches the beginning of the other.
• S_EQI is a case insensitive comparison of two strings for equality.
• S_TO_I4 reads an integer value from a string.
• S_TO_R4 reads a real number from a string.
• SAMPLE_ANALYZE analyzes the samples from the Dirichlet mixture PDF.
• SAMPLE_PROJECT computes the projection of a sample onto the mixture components.
• SAMPLE_PROJECT computes the projection of a sample onto the mixture components.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WEIGHT_INIT initializes the estimated weights.
• WEIGHT_UPDATE updates the estimated weights.

You can go up one level to the FORTRAN90 source codes.