parameter estimation
Definition
Parameter estimation refers to the statistical process of quantifying the effects, both interaction and main effects, of variables in a model to characterize its probability distribution. In the Ising model, parameter estimation is complicated by an intractable normalizing constant that grows exponentially with the number of variables, making exact maximum likelihood estimation computationally feasible only for small graphs. To address this challenge, maximum pseudolikelihood estimation methods—specifically joint pseudolikelihood (JPL) and disjoint pseudolikelihood (DPL) approximations—provide computationally efficient alternatives that yield consistent estimators, though their finite-sample performance relative to exact likelihood methods varies depending on network structure and sample size.
Sources: Keetelaar et al. (2024)
Related Terms
Applications
Parameter Estimation and Network Structure
The choice between parameter estimation methods depends on the network's structure; simulations show that the DPL is more efficient for sparse networks, while the JPL performs better for dense networks.
Sources: Keetelaar et al. (2024)
Parameter Estimation and Sample Size
Parameter estimation methods for the Ising model exhibit different performance characteristics across finite sample sizes. Maximum pseudolikelihood estimation based on JPL is a stable estimation method that accurately approximates maximum likelihood estimates across various conditions, whereas maximum pseudolikelihood estimation based on DPL only works well for large sample sizes.
Sources: Keetelaar et al. (2024)
