DETECTING PHYLODIVERSITY-DEPENDENT DIVERSIFICATION WITH A GENERAL PHYLOGENETIC INFERENCE FRAMEWORK

Diversity-dependent diversification models have been extensively used to study the effect of ecological limits and feedback of community structure on species diversification processes, such as speciation and extinction. Current diversity-dependent diversification models characterise ecological limits by carrying capacities for species richness. Such ecological limits have been justified by niche filling arguments: as species diversity increases, the number of available niches for diversification decreases. However, as species diversify they may diverge from one another phenotypically, which may open new niches for new species. Alternatively, this phenotypic divergence may not affect the species diversification process or even inhibit further diversification. Hence, it seems natural to explore the consequences of phylogenetic diversity-dependent (or phylodiversity-dependent) diversification. Current likelihood methods for estimating diversity-dependent diversification parameters cannot be used for this, as phylodiversity is continuously changing as time progresses and species form and become extinct. Here, we present a new method based on Monte Carlo Expectation-Maximization (MCEM), designed to perform statistical inference on a general class of species diversification models and implemented in the R package emphasis. We use the method to fit phylodiversity-dependent diversification models to 14 phylogenies, and compare the results to the fit of a richness-dependent diversification model. We find that in a number of phylogenies, phylogenetic divergence indeed spurs speciation even though species richness reduces it. Not only do we thus shine a new light on diversity-dependent diversification, we also argue that our inference framework can handle a large class of diversification models for which currently no inference method exists.

Estimating cell-type-specific DNA methylation effects in heterogeneous cellular populations

Aim: To develop a method for estimating cell-specific effects in epigenomic association studies in the presence of cell type heterogeneity. Materials & methods: We utilized Monte Carlo Expectation-Maximization (MCEM) algorithm with Metropolis–Hastings sampler to reconstruct the ‘missing’ cell-specific methylations and to estimate their associations with phenotypes free of confounding by cell type proportions. Results: Simulations showed reliable performance of the method under various settings including when the cell type is rare. Application to a real dataset recapitulated the directly measured cell-specific methylation pattern in whole blood. Conclusion: This work provides a framework to identify important cell groups and account for cell type composition useful for studying the role of epigenetic changes in human traits and diseases.

Fast Iterative Combinatorial Auctions via Bayesian Learning

Iterative combinatorial auctions (CAs) are often used in multibillion dollar domains like spectrum auctions, and speed of convergence is one of the crucial factors behind the choice of a specific design for practical applications. To achieve fast convergence, current CAs require careful tuning of the price update rule to balance convergence speed and allocative efficiency. Brero and Lahaie (2018) recently introduced a Bayesian iterative auction design for settings with singleminded bidders. The Bayesian approach allowed them to incorporate prior knowledge into the price update algorithm, reducing the number of rounds to convergence with minimal parameter tuning. In this paper, we generalize their work to settings with no restrictions on bidder valuations. We introduce a new Bayesian CA design for this general setting which uses Monte Carlo Expectation Maximization to update prices at each round of the auction. We evaluate our approach via simulations on CATS instances. Our results show that our Bayesian CA outperforms even a highly optimized benchmark in terms of clearing percentage and convergence speed.

INVESTIGATING BARGAINING POWER OF FARMERS AND PROCESSORS IN IRAN'S DAIRY MARKET

The farm-gate price of raw milk in Iran is determined annually in negotiations among representatives of dairy processors, milk producers, and government officials. This study estimates the average bargaining power of dairy farmers and processors, through applying the generalized axiomatic Nash approach in a bilateral bargaining model. We employ annual data from 1990 to 2013 to estimate econometric representation of a bilateral bargaining model using a Monte Carlo expectation maximization algorithm. Results imply a higher bargaining power of 0.69 for processors, compared with 0.31 for farmers. This asymmetry of bargaining power causes unequal allocation of gains in the milk market.

A quantile variant of the expectation–maximization algorithm and its application to parameter estimation with interval data

The expectation–maximization algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The expectation–maximization is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the expectation–maximization algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo expectation–maximization algorithm. The Monte Carlo expectation–maximization uses a random sample to estimate the integral at each E-step. But the problem with the Monte Carlo expectation–maximization is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes computational burden. In this paper, we propose what we refer to as the quantile variant of the expectation–maximization algorithm. We prove that the proposed method has an accuracy of [Formula: see text], while the Monte Carlo expectation–maximization method has an accuracy of [Formula: see text]. Thus, the proposed method possesses faster and more stable convergence properties when compared with the Monte Carlo expectation–maximization algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided.