A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Adaptive plasticity in hatching age: a response to predation risk trade-offs.

The life histories of many animals are characterized by niche shifts, the timing of which can strongly affect fitness. In the tree frog Agalychnis callidryas, which has arboreal eggs, there is a trade-off between predation risks before and after hatching. When eggs are attacked by snakes, tadpoles escape by hatching rapidly and falling into the water below. Eggs not attacked by snakes hatch later, when newly emerged tadpoles are less vulnerable to aquatic predators. Plasticity in hatching allows embryos to use immediate, local information on risk of mortality to make instantaneous behavioral decisions about hatching and the accompanying shift from arboreal to aquatic habitats.