Andrew Valentine
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apvalentine.bsky.social
Andrew Valentine
@apvalentine.bsky.social
62 followers 39 following 7 posts
Assoc. Prof., Durham University
Inverse theory, ML, seismology, geophysics & computation.
https://valentineap.github.io/
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apvalentine.bsky.social
In particular, if we have already run McMC for each state individually, Carlin & Chib's approach lets us build a trans-conceptual ensemble by resampling the resulting ensembles.

Go read doi.org/10.1029/2024... to find out more and see some examples of this idea applied to real problems!

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An ensemble resampler provides an efficient means of constructing a trans-conceptual ensemble from multiple single-concept ensembles.
August 27, 2025 at 12:59 PM
apvalentine.bsky.social
An alternative comes from the work of Carlin & Chib (1999). Instead of working across multiple different parameter spaces, combine them all into a single 'product space'. Of course, this increases the dimension of the search space (= bad), but in practice some simplification may be possible.

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Carlin & Chib (1995) combine separate states into a single 'product space' and add an indicator variable to identify the active state.
August 27, 2025 at 12:59 PM
apvalentine.bsky.social
In some cases this problem can be tackled using reversible-jump McMC (Green, 1995) to switch between the different physical theories (or 'conceptual states'). See, e.g., 'trans-dimensional' sampling. However, this requires us to know the Jacobian of the transformation between states...

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Reversible jump McMC can explore, and step between, parameter spaces of different dimension.
August 27, 2025 at 12:59 PM
apvalentine.bsky.social
🧪 Monte Carlo methods can help characterise unknown parameters within a physical model. But what if we have multiple competing physical theories? Trans-conceptual sampling may be the answer...

Just out in JGR, w/M. Sambridge & J. Hauser: doi.org/10.1029/2024...

@durhamearthsci.bsky.social

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An illustration of three classes of ensemble representing an Earth model whose properties only vary with depth. The fixed-dimensional ensemble shows three Earth models each with three layers, whose thicknesses and seismic velocities all vary. The trans-dimensional ensemble is similar but with variable numbers of layers. In contrast, the trans-conceptual ensemble allows Earth models to have variable character as well. The first containing a single linear gradient, the second multiple layers and an inclined fault, while the third has undulating layers. Each ensemble class is a subset of those to its right. Fig 1 from Sambridge, Valentine & Hauser, 2025, JGR.
August 27, 2025 at 12:59 PM