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Source code for pastas.objective_functions

"""This module contains the objective functions that can be used with the pastas 
`EmceeSolve` solver.   

"""

from numpy import log, pi
from pandas import DataFrame


[docs]class GaussianLikelihood: """Gaussian likelihood function. Notes ----- The Gaussian log-likelihood function is defined as: .. math:: \\log(L) = -\\frac{N}{2}\\log(2\\pi\\sigma^2) + \\frac{\\sum_{i=1}^N - \\epsilon_i^2}{2\\sigma^2} where :math:`N` is the number of observations, :math:`\\sigma^2` is the variance of the residuals, and :math:`\\epsilon_i` is the residual at time :math:`i`. The parameter :math:`\\sigma^2` need to be estimated. """ _name = "GaussianLikelihood"
[docs] def __init__(self): self.nparam = 1
[docs] def get_init_parameters(self, name: str) -> DataFrame: """Get the initial parameters for the log-likelihood function. Parameters ---------- name: str Name of the log-likelihood function. Returns ------- parameters: DataFrame Initial parameters for the log-likelihood function. """ parameters = DataFrame( columns=["initial", "pmin", "pmax", "vary", "stderr", "name", "dist"] ) parameters.loc[name + "_sigma"] = (0.05, 1e-10, 1, True, 0.01, name, "uniform") return parameters
[docs] def compute(self, rv, p): """Compute the log-likelihood. Parameters ---------- rv: array Residuals of the model. p: array or list Parameters of the log-likelihood function. Returns ------- ln: float Log-likelihood """ sigma = p[-1] N = rv.size ln = -0.5 * N * log(2 * pi * sigma) + sum(-(rv**2) / (2 * sigma)) return ln
[docs]class GaussianLikelihoodAr1: """Gaussian likelihood function with AR1 autocorrelated residuals. Notes ----- The Gaussian log-likelihood function with AR1 autocorrelated residual is defined as: .. math:: \\log(L) = -\\frac{N-1}{2}\\log(2\\pi\\sigma^2) + \\frac{\\sum_{i=1}^N - (\\epsilon_i - \\phi \\epsilon_{i-\\Delta t})^2} {2\\sigma^2} where :math:`N` is the number of observations, :math:`\\sigma^2` is the variance of the residuals, :math:`\\epsilon_i` is the residual at time :math:`i` and :math:`\\mu` is the mean of the residuals. :math:`\\Delta t` is the time step between the observations. :math:`\\phi` is the autoregressive parameter. The parameters :math:`\\phi` and :math:`\\sigma^2` need to be estimated. """ _name = "GaussianLikelihoodAr1"
[docs] def __init__(self): self.nparam = 2
[docs] def get_init_parameters(self, name: str) -> DataFrame: """Get the initial parameters for the log-likelihood function. Parameters ---------- name: str Name of the log-likelihood function. Returns ------- parameters: DataFrame Initial parameters for the log-likelihood function. """ parameters = DataFrame( columns=["initial", "pmin", "pmax", "vary", "stderr", "name", "dist"] ) parameters.loc[name + "_sigma"] = (0.05, 1e-10, 1, True, 0.01, name, "uniform") parameters.loc[name + "_theta"] = ( 0.5, 1e-10, 0.99999, True, 0.2, name, "uniform", ) return parameters
[docs] def compute(self, rv, p): """Compute the log-likelihood. Parameters ---------- rv: array Residuals of the model. p: array or list Parameters of the log-likelihood function. Returns ------- ln: float Log-likelihood. """ sigma = p[-2] theta = p[-1] N = rv.size ln = -(N - 1) / 2 * log(2 * pi * sigma) + sum( -((rv[1:] - theta * rv[0:-1]) ** 2) / (2 * sigma) ) return ln