Example #1
0
def fit_beta(nsteps):
    """Fit a beta distribution by MCMC."""
    num_dimensions = 1
    # Create the dummy model
    b = BetaFit(0.5, 0.5)

    # Create the options
    opts = MCMCOpts()
    opts.model = b
    opts.estimate_params = b.parameters
    opts.initial_values = [1.001]
    opts.nsteps = nsteps
    opts.anneal_length = nsteps/10
    opts.T_init = 100
    opts.use_hessian = False
    opts.seed = 1
    opts.norm_step_size = 0.01
    opts.likelihood_fn = b.likelihood
    opts.step_fn = step

    # Create the MCMC object
    mcmc = MCMC(opts)
    mcmc.initialize()
    mcmc.estimate()
    mcmc.prune(nsteps/10, 1)

    plt.ion()
    for i in range(mcmc.num_estimate):
        plt.figure()
        (heights, points, lines) = plt.hist(mcmc.positions[:,i], bins=100,
                                        normed=True)
        plt.plot(points, beta.pdf(points, b.a, b.b), 'r')
    return mcmc
Example #2
0
    def __init__(self, opts, num_chains, max_temp, min_temp=1, swap_period=20):
        self.options = opts
        self.max_temp = max_temp
        self.min_temp = min_temp
        self.swap_period = swap_period

        self.iter = 0
        """Current step iteration (runs to ``nsteps``)."""
        self.chains = []
        """The set of chains in the temperature series."""

        # Calculate the temperature series
        temps = np.logspace(np.log10(min_temp), np.log10(max_temp),
                                           num_chains)
        # Initialize each of the chains
        for i, temp in enumerate(temps):
            chain = MCMC(opts)
            chain.options.T_init = temp
            chain.initialize()
            chain.iter = chain.start_iter
            self.chains.append(chain)

        # Initialize arrays for storing swap info
        num_swaps = self.options.nsteps / swap_period
        self.swap_proposals = np.zeros((num_swaps, 2))
        """Each swap proposal is stored as [i, j] row in this array."""
        self.pi_xi = np.zeros(num_swaps)
        """The posterior of chain i at the position of i."""
        self.pi_xj = np.zeros(num_swaps)
        """The posterior of chain i at the position of j."""
        self.pj_xi = np.zeros(num_swaps)
        """The posterior of chain j at the position of i."""
        self.pj_xj = np.zeros(num_swaps)
        """The posterior of chain j at the position of j."""
        self.delta_test_posteriors = np.zeros(num_swaps)
        """The posterior probability ratio for swap/noswap."""
        self.swap_alphas = np.zeros(num_swaps)
        """The random number used to accept/reject the swap."""
        self.swap_accepts = np.zeros(num_swaps, dtype=bool)
        """Booleans indicating accepted swaps."""
        self.swap_rejects = np.zeros(num_swaps, dtype=bool)
        """Booleans indicating rejected swaps."""
        self.swap_iter = 0
        """Current swap iteration (runs to ``nsteps / swap_period``)"""
Example #3
0
    def __init__(self, opts, num_chains, max_temp, min_temp=1, swap_period=20):
        self.options = opts
        self.max_temp = max_temp
        self.min_temp = min_temp
        self.swap_period = swap_period

        self.iter = 0
        """Current step iteration (runs to ``nsteps``)."""
        self.chains = []
        """The set of chains in the temperature series."""

        # Calculate the temperature series
        temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains)
        # Initialize each of the chains
        for i, temp in enumerate(temps):
            chain = MCMC(opts)
            chain.options.T_init = temp
            chain.initialize()
            chain.iter = chain.start_iter
            self.chains.append(chain)

        # Initialize arrays for storing swap info
        num_swaps = self.options.nsteps / swap_period
        self.swap_proposals = np.zeros((num_swaps, 2))
        """Each swap proposal is stored as [i, j] row in this array."""
        self.pi_xi = np.zeros(num_swaps)
        """The posterior of chain i at the position of i."""
        self.pi_xj = np.zeros(num_swaps)
        """The posterior of chain i at the position of j."""
        self.pj_xi = np.zeros(num_swaps)
        """The posterior of chain j at the position of i."""
        self.pj_xj = np.zeros(num_swaps)
        """The posterior of chain j at the position of j."""
        self.delta_test_posteriors = np.zeros(num_swaps)
        """The posterior probability ratio for swap/noswap."""
        self.swap_alphas = np.zeros(num_swaps)
        """The random number used to accept/reject the swap."""
        self.swap_accepts = np.zeros(num_swaps, dtype=bool)
        """Booleans indicating accepted swaps."""
        self.swap_rejects = np.zeros(num_swaps, dtype=bool)
        """Booleans indicating rejected swaps."""
        self.swap_iter = 0
        """Current swap iteration (runs to ``nsteps / swap_period``)"""
Example #4
0
def fit_gaussian(nsteps):
    num_dimensions = 1
    # Create the dummy model
    means = 10 ** np.random.rand(num_dimensions)
    variances = np.random.rand(num_dimensions)
    g = GaussianFit(means, variances)

    # Create the options
    opts = MCMCOpts()
    opts.model = g
    opts.estimate_params = g.parameters
    opts.initial_values = [1]
    opts.nsteps = nsteps
    opts.anneal_length = nsteps/10
    opts.T_init = 1
    opts.use_hessian = False
    opts.seed = 1
    opts.norm_step_size = 1
    opts.likelihood_fn = g.likelihood
    opts.step_fn = step

    # Create the MCMC object
    mcmc = MCMC(opts)
    mcmc.initialize()
    mcmc.estimate()
    mcmc.prune(nsteps/10, 1)

    plt.ion()
    for i in range(mcmc.num_estimate):
        mean_i = np.mean(mcmc.positions[:,i])
        var_i = np.var(mcmc.positions[:, i])
        print "True mean: %f" % means[i]
        print "Sampled mean: %f" % mean_i
        print "True variance: %f" % variances[i]
        print "Sampled variance: %f" % var_i
        plt.figure()
        (heights, points, lines) = plt.hist(mcmc.positions[:,i], bins=50,
                                        normed=True)
        plt.plot(points, norm.pdf(points, loc=means[i],
             scale=np.sqrt(variances[i])), 'r')

    mean_err = np.zeros(len(mcmc.positions))
    var_err = np.zeros(len(mcmc.positions))
    for i in range(len(mcmc.positions)):
        mean_err[i] = (means[0] - np.mean(mcmc.positions[:i+1,0]))
        var_err[i] = (variances[0] - np.var(mcmc.positions[:i+1,0]))
    plt.figure()
    plt.plot(mean_err)
    plt.plot(var_err)

    return mcmc
Example #5
0
def fit_twod_gaussians(nsteps):
    means_x = [ 0.1, 0.5, 0.9,
                0.1, 0.5, 0.9,
                0.1, 0.5, 0.9]
    means_y = [0.1, 0.1, 0.1,
               0.5, 0.5, 0.5,
               0.9, 0.9, 0.9]
    sd = 0.01
    tdg = TwoDGaussianFit(means_x, means_y, sd ** 2)

    # Create the options
    opts = MCMCOpts()
    opts.model = tdg
    opts.estimate_params = tdg.parameters
    opts.initial_values = [1.001, 1.001]
    opts.nsteps = nsteps
    opts.anneal_length = nsteps/10
    opts.T_init = 1
    opts.use_hessian = False
    opts.seed = 1
    opts.norm_step_size = 0.1
    opts.likelihood_fn = tdg.likelihood
    opts.step_fn = step

    mcmc = MCMC(opts)
    mcmc.initialize()
    mcmc.estimate()

    plt.ion()
    fig = plt.figure()
    mcmc.prune(0, 20)
    plt.scatter(mcmc.positions[:,0], mcmc.positions[:,1])
    ax = fig.gca()
    for x, y in zip(means_x, means_y):
        circ = plt.Circle((x, y), radius=2*sd, color='r', fill=False)
        ax.add_patch(circ)
    plt.xlim((-0.5, 1.5))
    plt.ylim((-0.5, 1.5))
    plt.show()

    return mcmc
Example #6
0
    # Create temperature array based on number of workers (excluding master)
    temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains-1)

    # Create the options
    opts = MCMCOpts()
    opts.model = tdg
    opts.estimate_params = tdg.parameters
    opts.initial_values = [1.001, 1.001]
    opts.nsteps = nsteps
    opts.anneal_length = 0 # necessary so cooling does not occur
    opts.T_init = temps[rank - 1] # Use the temperature for this worker
    opts.use_hessian = False
    opts.seed = 1
    opts.norm_step_size = 0.1
    opts.likelihood_fn = tdg.likelihood

    mcmc = MCMC(opts)
    mcmc.initialize()

    # The master coordinates when swaps occur ---------
    if rank == 0:
        pt = PT_MPI_Master(comm, rank, opts, swap_period, num_chains)
        pt.run()
    # Everyone else runs MCMC steps and swaps when told -----------
    else:
        pt = PT_MPI_Worker(comm, rank, mcmc, swap_period)
        pt.run()



Example #7
0
    sd = 0.01
    tdg = TwoDGaussianFit(means_x, means_y, sd**2)

    # Create temperature array based on number of workers (excluding master)
    temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains - 1)

    # Create the options
    opts = MCMCOpts()
    opts.model = tdg
    opts.estimate_params = tdg.parameters
    opts.initial_values = [1.001, 1.001]
    opts.nsteps = nsteps
    opts.anneal_length = 0  # necessary so cooling does not occur
    opts.T_init = temps[rank - 1]  # Use the temperature for this worker
    opts.use_hessian = False
    opts.seed = 1
    opts.norm_step_size = 0.1
    opts.likelihood_fn = tdg.likelihood

    mcmc = MCMC(opts)
    mcmc.initialize()

    # The master coordinates when swaps occur ---------
    if rank == 0:
        pt = PT_MPI_Master(comm, rank, opts, swap_period, num_chains)
        pt.run()
    # Everyone else runs MCMC steps and swaps when told -----------
    else:
        pt = PT_MPI_Worker(comm, rank, mcmc, swap_period)
        pt.run()