DeepAI
Log In Sign Up

Sequential Bayesian Experimental Design for Implicit Models via Mutual Information

03/20/2020
by   Steven Kleinegesse, et al.
0

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

READ FULL TEXT
10/23/2018

Efficient Bayesian Experimental Design for Implicit Models

Bayesian experimental design involves the optimal allocation of resource...
02/19/2020

Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation

Implicit stochastic models, where the data-generation distribution is in...
05/10/2021

Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds

We introduce a framework for Bayesian experimental design (BED) with imp...
06/03/2021

MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories

Simulation-based inference enables learning the parameters of a model ev...
07/04/2019

Sequential Experimental Design for Functional Response Experiments

Understanding functional response within a predator-prey dynamic is esse...
08/30/2022

Model-robust Bayesian design through Generalised Additive Models for monitoring submerged shoals

Optimal sampling strategies are critical for surveys of deeper coral ree...
03/14/2021

A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to...