In statistical modeling, making accurate predictions based on incomplete or imperfect data is a common challenge. One approach to address this issue is SBI (Slice-Based Inference), which involves dividing the parameter space into smaller regions called slices and estimating the posterior distribution within each slice separately. However, when the model is misspecified, SBI methods may not always produce accurate results. This review aims to demystify complex concepts related to SBI under model misspecification by using everyday language and engaging metaphors or analogies.
Introduction
Imagine you’re trying to build a jigsaw puzzle with missing pieces. You might start by dividing the puzzle into smaller sections, hoping that each section will be easier to complete. This is similar to what SBI does in statistical modeling – it divides the parameter space into smaller regions called slices, making it easier to estimate the posterior distribution within each slice.
Challenges with SBI under Model Misspecification
However, just like the jigsaw puzzle analogy, things can get tricky when some of the pieces are missing or misplaced. In statistical modeling, this means that the model may not be accurate enough to capture the true relationship between the data and parameters. When this happens, SBI methods may not produce accurate results, leading to overconfident predictions or incorrect conclusions.
Combining SBI with Likelihood-Based Importance Sampling
One way to address these challenges is by combining SBI methods with likelihood-based importance sampling (Dax et al., 2023a). This involves using the inferred estimate from SBI as a proposal distribution for importance sampling. Think of it like this – if you’re still struggling to complete the jigsaw puzzle, you might use a different approach by attaching additional pieces that are more likely to fit together based on their shape and color. In this case, the additional pieces represent the inferred estimate from SBI, which can help guide the importance sampling process to produce more accurate results.
Conclusion
In conclusion, SBI is a powerful tool for statistical modeling under model misspecification, but it’s essential to understand its limitations and potential biases. By combining SBI with likelihood-based importance sampling, we can improve the accuracy of our predictions and avoid overconfident conclusions. Just like completing a jigsaw puzzle requires patience and persistence, SBI methods require careful consideration of the model assumptions and the choice of prior distributions to produce reliable results.
