jesterTOV.inference.likelihoods.radio.RadioTimingLikelihood

class RadioTimingLikelihood(psr_name, mean, std, m_min=0.1, penalty_value=0.0)

Bases: LikelihoodBase

Likelihood for radio pulsar mass measurements constraining maximum NS mass.

This likelihood evaluates how well an equation of state’s maximum TOV mass (M_TOV) is consistent with an observed pulsar mass measurement. Since we observe a specific pulsar (with some measurement uncertainty) but don’t know its true mass relative to the theoretical maximum, we must marginalize over all possible true masses between some minimum value and M_TOV.

The marginalization assumes: - The measured mass follows a Gaussian distribution: \(M_{\text{obs}} \sim \mathcal{N}(M_{\text{true}}, \sigma)\) - The true mass has a uniform prior: \(P(M_{\text{true}} | M_{\text{TOV}}) = 1/(M_{\text{TOV}} - m_{\text{min}})\) for \(M_{\text{true}} \in [m_{\text{min}}, M_{\text{TOV}}]\)

This gives the marginal likelihood.

\[\mathcal{L}(M_{\text{TOV}} | M_{\text{obs}}, \sigma) = \frac{1}{M_{\text{TOV}} - m_{\text{min}}} \int_{m_{\text{min}}}^{M_{\text{TOV}}} \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left[-\frac{(m - M_{\text{obs}})^2}{2\sigma^2}\right] dm\]

where the integration is evaluated analytically via the Gaussian CDF.

Parameters:

• psr_name (str) – Pulsar designation for identification (e.g., “J1614-2230”, “J0740+6620”). Used for logging and tracking which pulsar constraint is being applied.

• mean (float) – Measured pulsar mass in solar masses (\(M_{\odot}\)). This is typically the reported value from timing analysis.

• std (float) – Measurement uncertainty (\(1\sigma\)) in solar masses. This combines statistical and systematic uncertainties from the timing analysis.

• m_min (float, optional) – Minimum mass for the integration lower bound in solar masses. This should be well below any physical neutron star mass to avoid truncation effects. Recommended to not touch this parameter. Default is 0.1 \(M_{\odot}\).

• penalty_value (float, optional) – Log-likelihood penalty for invalid TOV solutions (M_TOV ≤ m_min). Default is 0.0.

Variables:

• psr_name (str) – Pulsar designation

• mean (float) – Observed mass mean in solar masses

• std (float) – Observed mass uncertainty in solar masses

• m_min (float) – Minimum mass for integration (solar masses)

• penalty_value (float) – Log-likelihood penalty for invalid TOV solutions

Notes

Invalid TOV solutions (M_TOV ≤ m_min) receive a large negative log-likelihood penalty to effectively exclude them from the posterior.

The implementation uses log-space arithmetic throughout to avoid numerical underflow when combining with other log-likelihoods.

See also

GWLikelihood

Gravitational wave constraints on mass and tidal deformability

NICERLikelihood

X-ray timing constraints on mass and radius

Examples

Create a likelihood for PSR J0740+6620 (Fonseca et al. 2021: 2.08 ± 0.07 \(M_{\odot}\)):

>>> from jesterTOV.inference.likelihoods import RadioTimingLikelihood
>>> likelihood = RadioTimingLikelihood("J0740+6620", mean=2.08, std=0.07)
>>> params = {"masses_EOS": jnp.array([1.0, 1.5, 2.0, 2.2])}  # Example TOV masses
>>> log_like = likelihood.evaluate(params, data={})

Create a more precise likelihood for PSR J1614-2230 (narrower uncertainty):

>>> likelihood_j1614 = RadioTimingLikelihood("J1614-2230", mean=1.94, std=0.06)

__init__(psr_name, mean, std, m_min=0.1, penalty_value=0.0)

Methods

__init__(psr_name, mean, std[, m_min, ...])
evaluate(params)	Evaluate the marginalized log-likelihood for the pulsar mass measurement.

Attributes

data	The data for the likelihood.
model	The model for the likelihood.
psr_name
mean
std
m_min
penalty_value

evaluate(params)

Evaluate the marginalized log-likelihood for the pulsar mass measurement.

This method computes the marginal likelihood by: 1. Extracting the maximum TOV mass from the EOS 2. Computing standardized z-scores for the integration bounds 3. Evaluating the Gaussian CDF at the upper and lower bounds 4. Computing the CDF difference in log-space for numerical stability 5. Applying the 1/(M_TOV - m_min) normalization factor

Parameters:

params (dict[str, Float | Array]) –

Dictionary containing TOV solution outputs from the transform. Required keys:

• ”masses_EOS” : Array of neutron star masses (solar masses) at different central pressures. The maximum value is taken as M_TOV.

Return type:

Float

Returns:

Float – Natural logarithm of the marginalized likelihood. Returns a large negative penalty for invalid EOSs (M_TOV ≤ m_min), which indicates TOV integration failure or unphysical EOS.

Notes

Any NaN or infinity values in the result should not be replaced with -jnp.inf as this will cause some samplers to have numerical problems.

m_min: float

mean: float

penalty_value: float

psr_name: str

std: float