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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities

Which feature of the likelihood for a Markov multiple-state model with constant intensities allows each intensity to be estimated separately?

The likelihood is a product of separate factors, one per transition type, each of the form intensity raised to the number of transitions times exp of minus intensity times time in state. Because each factor contains one parameter, each intensity can be maximised separately.

  1. AThe likelihood factorises into separate terms for each intensity, each of the form mu_ij^d_ij exp(-mu_ij v_i)Correct
  2. BAll intensities must be equal under the Markov assumption
  3. CThe total time in each state is always identical
  4. DThe number of transitions is fixed in advance for every pair of states
  5. The likelihood depends only on the final state occupied by each life

Explanation

The likelihood is a product over pairs (i,j) of terms mu_ij^d_ij exp(-mu_ij v_i). Each term involves only one intensity, so maximising each term separately gives the MLE of that intensity.

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