Monte Carlo Adjusted Profile

pypomp.mcap(parameter: ArrayLike, loglik: ArrayLike, *, level: float = 0.95, span: float = 0.75, n_grid: int = 1000, loess_degree: int = 2) → MCAPResult

Compute Monte Carlo-adjusted profile (MCAP) confidence intervals.

Constructs a profile likelihood confidence interval accommodating both Monte Carlo noise in the profile and statistical uncertainty in the likelihood function (Ionides et al. 2017 [1]).

Parameters:

• parameter (array-like) – Parameter values at which log-likelihoods were evaluated.

• loglik (array-like) – Log-likelihood values corresponding to parameter.

• level (float, optional) – Confidence level for the interval. Defaults to 0.95.

• span (float, optional) – Span parameter for the LOESS smoother. Defaults to 0.75.

• n_grid (int, optional) – Number of grid points for evaluating the smoothed log-likelihood. Defaults to 1000.

• loess_degree (int, optional) – Polynomial degree for the LOESS smoother. Defaults to 2.

Returns:

Object containing the computed confidence interval and SE decomposition.

Return type:

MCAPResult

References

[1]

Ionides, Edward L., Carles Bretó, Joonha Park, R. A. Smith, and Aaron A. King. “Monte Carlo profile confidence intervals for dynamic systems.” Journal of The Royal Society Interface 14, no. 132 (2017): 20170126. https://doi.org/10.1098/rsif.2017.0126.

class pypomp.mcap.MCAPResult(level: float, mle: float, ci: Tuple[float | None, float | None], delta: float, se_stat: float, se_mc: float, se_total: float, fit: Dict[str, NDArray[floating[Any]]], quadratic_max: float, quadratic_coef: Dict[str, float], vcov: NDArray[floating[Any]])

Bases: object

Results of a Monte Carlo adjusted profile (MCAP) analysis.

Attributes

MCAPResult.level: float

The confidence level of the profile likelihood confidence interval.

MCAPResult.mle: float

The maximum likelihood estimate of the focal parameter, taken as the argmax of the smoothed profile.

MCAPResult.ci: Tuple[float | None, float | None]

The profile likelihood confidence interval (lower, upper).

MCAPResult.delta: float

The log-likelihood threshold used to define the confidence interval, relative to the maximum.

MCAPResult.se_stat: float

The standard error due to statistical uncertainty (sampling variance).

MCAPResult.se_mc: float

The standard error due to Monte Carlo noise in the likelihood estimates.

MCAPResult.se_total: float

The total standard error, calculated as the root sum of squares of se_stat and se_mc.

MCAPResult.fit: Dict[str, NDArray[floating[Any]]]

A dictionary containing the grid of parameters (‘parameter’), the smoothed log-likelihood values (‘smoothed’), and the local quadratic fit values (‘quadratic’).

MCAPResult.quadratic_max: float

The parameter value that maximizes the local quadratic fit.

MCAPResult.quadratic_coef: Dict[str, float]

c - ax^2 + bx.

Type:

The coefficients of the local quadratic fit

MCAPResult.vcov: NDArray[floating[Any]]

The variance-covariance matrix of the quadratic coefficients a and b.