Hidden role of anion exchange reactions in nucleation of colloidal nanocrystals

We investigate the processes involved in the nucleation of colloidal lead selenide nanoparticles. Our studies show that an unusual pathway - an anion exchange reaction, causes the nucleation of lead selenide nanocrystals. In this process, one quantum dot is transformed into another due to a substitution of its constituent anions. The existence of this pathway was never anticipated perhaps due to its unusually rapid kinetics. The nucleation and growth kinetics of colloidal lead selenide quantum dots are found to fit well to a two-step process. The rate constant associated with the anion exchange process is found to be four orders of magnitude greater than that of the nanocrystal growth. The complete consumption of the initial oxide nanoparticle thus provides a sharp, temporally well-defined nucleation event.

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.