Package pylal :: Module upper_limit_utils

Module upper_limit_utils

Functions

margLikelihoodMonteCarlo(VTs, lambs, mu, mcerrs=None)
This function marginalizes the loudest event likelihood over unknown Monte Carlo errors, assumed to be independent between each experiment.

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margLikelihood(VTs, lambs, mu, calerr=0, mcerrs=None)
This function marginalizes the loudest event likelihood over unknown Monte Carlo and calibration errors.

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integral_element(mu, pdf)
Returns an array of elements of the integrand dP = p(mu) dmu for a density p(mu) defined at sample values mu ; samples need not be equally spaced.

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normalize_pdf(mu, pofmu)
Takes a function pofmu defined at rate sample values mu and normalizes it to be a suitable pdf.

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compute_upper_limit(mu_in, post, alpha=0.9)
Returns the upper limit mu_high of confidence level alpha for a posterior distribution post on the given parameter mu.

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compute_lower_limit(mu_in, post, alpha=0.9)
Returns the lower limit mu_low of confidence level alpha for a posterior distribution post on the given parameter mu.

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confidence_interval_min_width(mu, post, alpha=0.9)
Returns the minimal-width confidence interval [mu_low, mu_high] of confidence level alpha for a posterior distribution post on the parameter mu.

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hpd_coverage(mu, pdf, thresh)
Integrates a pdf over mu taking only bins where the mean over the bin is above a given threshold This gives the coverage of the HPD interval for the given threshold.

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hpd_threshold(mu_in, post, alpha, tol)
For a PDF post over samples mu_in, find a density threshold such that the region having higher density has coverage of at least alpha, and less than alpha plus a given tolerance.

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hpd_credible_interval(mu_in, post, alpha=0.9, tolerance=1e-3)
Returns the minimum and maximum rate values of the HPD (Highest Posterior Density) credible interval for a posterior post defined at the sample values mu_in.

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integrate_efficiency(dbins, eff, err=0, logbins=False)

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compute_efficiency(f_dist, m_dist, dbins)
Compute the efficiency as a function of distance for the given sets of found and missed injection distances.

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mean_efficiency_volume(found, missed, dbins)

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volume_montecarlo(found, missed, distribution_param, distribution, limits_param, max_param=None, min_param=None)
Compute the sensitive volume and standard error using a direct Monte Carlo integral

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filter_injections_by_mass(injs, mbins, bin_num, bin_type, bin_num2=None)
For a given set of injections (sim_inspiral rows), return the subset of injections that fall within the given mass range.

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compute_volume_vs_mass(found, missed, mass_bins, bin_type, dbins=None, distribution_param=None, distribution=None, limits_param=None, max_param=None, min_param=None)
Compute the average luminosity an experiment was sensitive to given the sets of found and missed injections and assuming luminosity is uniformly distributed in space.

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log_volume_derivative_fit(x, vols)
Performs a linear least squares to log(vols) as a function of x.

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get_loudest_event(connection, coinc_table="coinc_inspiral", datatype="exclude_play")

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Function Details

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margLikelihood(VTs, lambs, mu, calerr=0, mcerrs=None)

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This function marginalizes the loudest event likelihood over unknown Monte Carlo and calibration errors. The vector VTs is the sensitive volumes for independent searches and lambs is the vector of loudest event likelihood. The statistical errors are assumed to be independent between each experiment while the calibration errors are applied the same in each experiment.

integral_element(mu, pdf)

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Returns an array of elements of the integrand dP = p(mu) dmu for a density p(mu) defined at sample values mu ; samples need not be equally spaced. Uses a simple trapezium rule. Number of dP elements is 1 - (number of mu samples).

normalize_pdf(mu, pofmu)

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Takes a function pofmu defined at rate sample values mu and normalizes it to be a suitable pdf. Both mu and pofmu must be arrays or lists of the same length.

compute_upper_limit(mu_in, post, alpha=0.9)

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Returns the upper limit mu_high of confidence level alpha for a posterior distribution post on the given parameter mu. The posterior need not be normalized.

compute_lower_limit(mu_in, post, alpha=0.9)

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Returns the lower limit mu_low of confidence level alpha for a posterior distribution post on the given parameter mu. The posterior need not be normalized.

hpd_credible_interval(mu_in, post, alpha=0.9, tolerance=1e-3)

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Returns the minimum and maximum rate values of the HPD (Highest Posterior Density) credible interval for a posterior post defined at the sample values mu_in. Samples need not be uniformly spaced and posterior need not be normalized.

Will not return a correct credible interval if the posterior is multimodal and the correct interval is not contiguous; in this case will over-cover by including the whole range from minimum to maximum mu.

compute_efficiency(f_dist, m_dist, dbins)

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Compute the efficiency as a function of distance for the given sets of found and missed injection distances. Note that injections that do not fit into any dbin get lost :(.

volume_montecarlo(found, missed, distribution_param, distribution, limits_param, max_param=None, min_param=None)

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Compute the sensitive volume and standard error using a direct Monte Carlo integral

* distribution_param, D: parameter of the injections used to generate a distribution over distance
  - may be 'distance', 'chirp_distance"
* distribution: form of the distribution over the parameter
  - 'log' (uniform in log D), 'uniform' (uniform in D), 'distancesquared' (uniform in D**2),
    'volume' (uniform in D***3)
  - It is assumed that injections were carried out over a range of D such that sensitive
    volume due to signals at distances < D_min is negligible and efficiency at distances
    > D_max is negligibly small
* limits_param, Dlim: parameter specifying limits in which injections were made
  - may be 'distance', 'chirp_distance'
* max_param: maximum value of Dlim out to which injections were made, if None the maximum 
  value among all found and missed injections will be used
* min_param: minimum value of Dlim at which injections were made - needed to normalize
  the log distance integral correctly.  If None, for the log distribution the minimum
  value among all found and missed injections will be used

compute_volume_vs_mass(found, missed, mass_bins, bin_type, dbins=None, distribution_param=None, distribution=None, limits_param=None, max_param=None, min_param=None)

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Compute the average luminosity an experiment was sensitive to given the sets of found and missed injections and assuming luminosity is uniformly distributed in space.

If distance_param and distance_distribution are not None, use an unbinned Monte Carlo integral (which optionally takes max_distance and min_distance parameters) for the volume and error Otherwise use a simple efficiency * distance**2 binned integral In either case use distance bins to return the efficiency in each bin