Towards black-box parameter estimation

• URL: http://arxiv.org/abs/2303.15041v2
• Date: Mon, 19 Feb 2024 11:19:12 GMT
• Title: Towards black-box parameter estimation
• Authors: Amanda Lenzi and Haavard Rue
• Abstract summary: We develop new black-box procedures to estimate parameters of statistical models based on weak parameter structure assumptions. For well-structured likelihoods with frequent occurrences, this is achieved by pre-training a deep neural network on an extensive simulated database.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on simulating parameters that sufficiently reproduce the observed data, and, at present, there is a lack of efficient methods to produce these simulations. We develop new black-box procedures to estimate parameters of statistical models based only on weak parameter structure assumptions. For well-structured likelihoods with frequent occurrences, such as in time series, this is achieved by pre-training a deep neural network on an extensive simulated database that covers a wide range of data sizes. For other types of complex dependencies, an iterative algorithm guides simulations to the correct parameter region in multiple rounds. These approaches can successfully estimate and quantify the uncertainty of parameters from non-Gaussian models with complex spatial and temporal dependencies. The success of our methods is a first step towards a fully flexible automatic black-box estimation framework.

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