Description Usage Arguments Value References See Also

Computes gradient of Q-function with respect to log(c(lambda,phi)) for EM algorithm from Cao et al. (2000) for their smoothed model.

1 | ```
grad_smoothed(logtheta, c, M, rdiag, eta0, sigma0, V, eps.lambda, eps.phi)
``` |

`logtheta` |
numeric vector (length k+1) of log(lambda) (1:k) and log(phi) (last entry) |

`c` |
power parameter in model of Cao et al. (2000) |

`M` |
matrix (n x k) of conditional expectations for OD flows, one time per row |

`rdiag` |
numeric vector (length k) containing diagonal of conditional covariance matrix R |

`eta0` |
numeric vector (length k+1) containing value for log(c(lambda, phi)) from previous time (or initial value) |

`sigma0` |
covariance matrix (k+1 x k+1) of log(c(lambda, phi)) from previous time (or initial value) |

`V` |
evolution covariance matrix (k+1 x k+1) for log(c(lambda, phi)) (random walk) |

`eps.lambda` |
numeric small positive value to add to lambda for numerical stability; typically 0 |

`eps.phi` |
numeric small positive value to add to phi for numerical stability; typically 0 |

numeric vector of same length as logtheta containing calculated gradient

J. Cao, D. Davis, S. Van Der Viel, and B. Yu. Time-varying network tomography: router link data. Journal of the American Statistical Association, 95:1063-75, 2000.

Other CaoEtAl: `Q_iid`

;
`Q_smoothed`

; `R_estep`

;
`grad_iid`

; `locally_iid_EM`

;
`m_estep`

; `phi_init`

;
`smoothed_EM`

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