idmtools_calibra.algorithms.fisher_inf_matrix module¶
- idmtools_calibra.algorithms.fisher_inf_matrix.perturbed_points(center, xmin, xmax, m=10, n=5, sample_size=1, resolution_raw=None)[source]¶
Having the estimated optimal point (θ*), the next step is generating a set of perturbed points (samples). At this step, you can specify the size of perturbation (resolution). In case you do not input the perturbation size (resolution_raw=None), the script will pick a perturbation using the given range for each parameter (Xmin-Xmax). You need to allocate per-realization (M) and cross-realization (N). Note that \(M>p^2\), where p is the number of parameters (size of θ). The number of cross-realization (N) should be set depending on the uncertainty of the model at the given final point (θ*). To choose N, you can use Chebyshev’s inequality.
You can allocate number of replicates of the model (n). The log-likelihood at each point obtains from n replicates of the model with different run numbers. Then these n replicates are used to compute the likelihood at that point. When we have a model with high uncertainty, the easiest way to compute the likelihood might be taking average of the multiple (n) replicates of the model run to compute the likelihood. Note that the algorithm only accepts n=1 now. But the Cramer Rao script has the potential to accept higher n, whenever a smoothing technique which requires multiple replicates of the model for computing the likelihood be added to the Analyzers.
- Parameters:
center – center point 1xp nparray
xmin – minimum of parameters 1xp nparray
xmax – maximum of parameters 1xp nparray
m – number of Hessian estimates scalar-positive integer
n – number of pseudodata vectors scalar-positive integer
sample_size – sample size scalar-positive integer
resolution_raw – minimum meaningful perturbation for each parameter 1xp nparray
- Returns:
perturbed points (4MNn x 4+p) nparray
- Return type:
X_perturbed
- idmtools_calibra.algorithms.fisher_inf_matrix.compute_fisher_inf_matrix(center_point, df_ll_points, data_columns)[source]¶
Compute the Fisher Information matrix using the LL of perturbed points
Computation of the Fisher information matrix (covariance matrix) This step returns a p×p covariance matrix, called Σ.
Atiye Alaeddini, 12/15/2017
- Parameters:
center_point – center point (1 x p) nparray
df_ll_points – Log Likelihood of points DataFrame
data_columns – List of columns to filter points with
- Returns:
Fisher Information matrix (p x p) np array
- Return type:
Fisher
- idmtools_calibra.algorithms.fisher_inf_matrix.sample_cov_ellipse(cov, pos, num_of_pts=10)[source]¶
Sample ‘num_of_pts’ points from the specified covariance matrix (cov).
- Parameters:
cov – 2-D array_like, The covariance matrix (inverse of fisher matrix). It must be symmetric and positive-semidefinite for proper sampling.
pos – 1-D array_like, The location of the center of the ellipse, Mean of the multi variate distribution
num_of_pts – The number of sample points.
- Returns:
ndarray of the drawn samples, of shape (num_of_pts,).
- idmtools_calibra.algorithms.fisher_inf_matrix.trunc_gauss(mu, sigma, low_bound, high_bound, num_of_pts, batch_size=100)[source]¶