Maximum Likelihood Inference for Multivariate Frailty Models Using an Automated Monte Carlo EM Algorithm

We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.     

Sum-of-squares rank upper bounds for matching problems

The matching problem is one of the most studied combinatorial optimization problems in the context of extended formulations and convex relaxations. In this paper we provide upper bounds for the rank of the sum-of-squares/Lasserre hierarchy for a family of matching problems. In particular, we show that when the problem formulation is strengthened by incorporating the objective function in the constraints, the hierarchy requires at most \(\left\lceil \frac{k}{2} \right\rceil \) levels to refute the existence of a perfect matching in an odd clique of size \(2k+1\).     

Unpacking the circular economy: A problematizing review

Transitioning to a circular economy (CE) model has been proposed to solve many grand environmental challenges. While research on CE has been extensively reviewed, less is known about the implicit underlying assumptions of this work. Understanding these assumptions is critical as they typically go unchallenged yet play a significant role in shaping research fields. In this paper we conduct a problematizing review to critically analyse and make explicit the in-house, root metaphor and ideological assumptions that inform the framing of CE. Firstly, we demonstrate various in-house assumptions about CE, such as an emphasis on the business case for CE and the relationship between CE and corporate sustainability. Secondly, root metaphor assumptions include circularity and industrial relationships resembling biological metabolisms. Finally, the dominant ideological assumptions-neoliberalism and ecological modernization-guide scholarly thinking about growth, consumption and profit maximization. Based on our analysis and drawing on the ongoing CE debates within broader environmental studies, we suggest new agendas for future research. We contribute to the growing literature on CE in business, management and organization studies by identifying assumptions that may be misleading or limiting for future CE research, as well as to the conversations on grand challenges by discussing the implications of how challenges and solutions are framed.