Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions

In latent variable models parameter estimation can be implemented by using the joint or the marginal likelihood, based on independence or conditional independence assumptions. The same dilemma occurs within the Bayesian framework with respect to the estimation of the Bayesian marginal (or integrated) likelihood, which is the main tool for model comparison and averaging. In most cases, the Bayesian marginal likelihood is a high dimensional integral that cannot be computed analytically and a plethora of methods based on Monte Carlo integration (MCI) are used for its estimation. In this work, it is shown that the joint MCI approach makes subtle use of the properties of the adopted model, leading to increased error and bias in finite settings. The sources and the components of the error associated with estimators under the two approaches are identified here and provided in exact forms. Additionally, the effect of the sample covariation on the Monte Carlo estimators is examined. In particular, even under independence assumptions the sample covariance will be close to (but not exactly) zero which surprisingly has a severe effect on the estimated values and their variability. To address this problem, an index of the sample's divergence from independence is introduced as a multivariate extension of covariance. The implications addressed here are important in the majority of practical problems appearing in Bayesian inference of multi-parameter models with analogous structures

Conceptual modelling for simulation Part I: definition and requirements

Conceptual modelling is probably the most important aspect of a simulation study. It is also the most difficult and least understood. Over 40 years of simulation research and practice have provided only limited information on how to go about designing a simulation conceptual model. This paper, the first of two, discusses the meaning of conceptual modelling and the requirements of a conceptual model. Founded on existing literature, a definition of a conceptual model is provided. Four requirements of a conceptual model are described: validity, credibility, utility and feasibility. The need to develop the simplest model possible is also discussed. Owing to a paucity of advice on how to design a conceptual model, the need for a conceptual modelling framework is proposed. Built on the foundations laid in this paper, a conceptual modelling framework is described in the paper that follows