Parameter Estimation

EMRI parameter estimation: waveform generation, Fisher matrix, SNR, and Cramér-Rao bounds.

ParameterEstimation drives the core computational pipeline: it generates LISA TDI waveforms using the few package, computes the signal-to-noise ratio, and — for detections above the SNR threshold — evaluates the full Fisher information matrix via a 5-point finite-difference stencil to obtain Cramér-Rao lower bounds on all 14 EMRI parameters.

class master_thesis_code.parameter_estimation.parameter_estimation.ParameterEstimation(waveform_generation_type, parameter_space, *, use_gpu=True, use_five_point_stencil=True)[source]

Bases: object

EMRI waveform-based parameter estimation using the LISA Fisher information matrix.

Generates LISA TDI waveforms via the few package, computes the noise-weighted signal-to-noise ratio, and — for detections above the SNR threshold — evaluates the full \(14 \times 14\) Fisher matrix using a 5-point finite-difference stencil to obtain Cramér-Rao lower bounds on all EMRI parameters.

Variables:

  • parameter_space (master_thesis_code.datamodels.parameter_space.ParameterSpace) – 14-parameter EMRI configuration space.

  • lisa_response_generator (Any) – LISA TDI response generator for the full 5-year observation.

  • snr_check_generator (Any) – LISA TDI response generator for the 1-year SNR pre-check.

  • dt (int) – Time sampling interval in seconds.

  • T (float) – Observation time in years.

Parameters:

  • waveform_generation_type (WaveGeneratorType)

  • parameter_space (ParameterSpace)

  • use_gpu (bool)

  • use_five_point_stencil (bool)

SNR_analysis()[source]
Return type:

None

T: float = 5
compute_Cramer_Rao_bounds()[source]
Return type:

dict

compute_fisher_information_matrix()[source]
Return type:

Any

compute_signal_to_noise_ratio(use_snr_check_generator=False)[source]
Parameters:

use_snr_check_generator (bool)

Return type:

float

dt: int = 10
finite_difference_derivative()[source]

Compute partial derivative of the currently set parameters w.r.t. the provided parameter.

Parameters:

parameter_symbol (str) – parameter w.r.t. which the derivative is taken (Note: symbol string has to coincide with that in the ParameterSpace list!)

Returns:

data series of derivative

Return type:

cp.array[float]

five_point_stencil_derivative()[source]

Compute partial derivatives for all parameters using the 5-point stencil method.

Uses the O(epsilon^4) central-difference stencil for each of the 14 EMRI parameters, matching the API of finite_difference_derivative() so the two methods are interchangeable in compute_fisher_information_matrix().

Returns:

Dictionary mapping parameter symbol to its derivative array.

Raises:

ParameterOutOfBoundsError – If the stencil would evaluate outside parameter bounds.

Return type:

dict[str, Any]

References

Vallisneri (2008), arXiv:gr-qc/0703086 — derivative accuracy for Fisher matrices.

flush_pending_results()[source]

Write all buffered Cramér-Rao bound rows to disk and clear the buffer.

Call this at the end of a simulation run to ensure no results are lost. Rows are grouped by simulation index so a single read/write per file replaces one read/write per detection (the previous behaviour).

Return type:

None

generate_lisa_response(update_parameter_dict={}, use_snr_check_generator=False)[source]
Parameters:

  • update_parameter_dict (dict[str, Any])

  • use_snr_check_generator (bool)

Return type:

Any

lisa_response_generator: Any
parameter_space: ParameterSpace
save_cramer_rao_bound(cramer_rao_bound_dictionary, snr, simulation_index, host_galaxy_index=-1)[source]
Parameters:

  • cramer_rao_bound_dictionary (dict)

  • snr (float)

  • simulation_index (int)

  • host_galaxy_index (int)

Return type:

None

save_snr_analysis(snr, parameter_set_index)[source]
Parameters:
Return type:

None

scalar_product_of_functions(tdi_channels_a, tdi_channels_b)[source]

LISA noise-weighted inner product between two TDI waveforms.

Implements the standard gravitational-wave inner product:

\[\langle h_1 \mid h_2 \rangle = 4 \,\mathrm{Re} \sum_{\alpha \in \{A, E\}} \int_{f_\min}^{f_\max} \frac{\tilde{h}_1^\alpha(f)\, \tilde{h}_2^{\alpha *}(f)}{S_n^\alpha(f)} \, df\]

summed over TDI channels, where \(S_n^\alpha(f)\) is the one-sided noise PSD from power_spectral_density().

This is the computational hot path: it is called \(O(N_\theta^2)\) times per Fisher matrix (105 calls for 14 parameters using the 5-point stencil).

Parameters:

  • tdi_channels_a (ndarray[tuple[Any, ...], dtype[float64]]) – TDI waveform array of shape (n_channels, n_samples).

  • tdi_channels_b (ndarray[tuple[Any, ...], dtype[float64]]) – TDI waveform array of shape (n_channels, n_samples).

Returns:

Real-valued inner product \(\langle h_1 \mid h_2 \rangle\).

Return type:

float

snr_check_generator: Any