# Simulation-Based Inference

Recombination and mutation rates vary along bacterial genomes, the two signals overlap, and clonal relationships confound inference, while earlier methods often assumed a constant mutation rate or relied on a small set of summary statistics. This work trains a simulator-based neural posterior estimator conditioned on a fixed clonal genealogy to infer local recombination and mutation rates for each gene segment, then applies a circular posterior-propagated Difference-of-Gaussians detector that carries posterior uncertainty into hotspot calls. On simulated data the inferred rates track the true values and credible intervals narrow as gene length grows; candidate hotspots are reported for three real datasets in the Bacillus cereus group, Staphylococcus aureus and Escherichia coli.

Recombination and mutation rates vary along bacterial genomes, the two signals overlap, and clonal relationships confound inference, while earlier methods often assumed a constant mutation rate or relied on a small set of summary statistics. This work trains a simulator-based neural posterior estimator conditioned on a fixed clonal genealogy to infer local recombination and mutation rates for each gene segment, then applies a circular posterior-propagated Difference-of-Gaussians detector that carries posterior uncertainty into hotspot calls. On simulated data the inferred rates track the true values and credible intervals narrow as gene length grows; candidate hotspots are reported for three real datasets in the Bacillus cereus group, Staphylococcus aureus and Escherichia coli.

In hierarchical Bayesian inversion, putting the forward model inside the likelihood means every posterior evaluation costs one forward solve per cell. A triangular transport-map likelihood trained once per design now serves every cell, and is used to infer contact angle and capillary length from photographs of a hole in a thin liquid film. At a synthetic validation design the map's posteriors agree with direct sampling in the wetting properties and pass simulation-based calibration; a single posterior needs several hundred times fewer forward-model evaluations than a gradient-free ensemble sampler, and further posteriors at the same design add no forward solve.

In hierarchical Bayesian inversion, putting the forward model inside the likelihood means every posterior evaluation costs one forward solve per cell. A triangular transport-map likelihood trained once per design now serves every cell, and is used to infer contact angle and capillary length from photographs of a hole in a thin liquid film. At a synthetic validation design the map's posteriors agree with direct sampling in the wetting properties and pass simulation-based calibration; a single posterior needs several hundred times fewer forward-model evaluations than a gradient-free ensemble sampler, and further posteriors at the same design add no forward solve.

Weak-lensing shear data from the third year of the Dark Energy Survey (DES Y3) have been analysed cosmologically with the integrated three-point correlation function (i3PCF), a higher-order statistic that correlates local aperture mass with surrounding shear, and for the first time a three-point shear statistic on survey data is treated with fully simulation-based inference. Jointly with the two-point correlation functions, the i3PCF is detected at a signal-to-noise ratio of 12.8, and the figure of merit in the Ωm–S8–w space roughly doubles over two-point statistics alone, with the gain coming from angular scales where baryonic effects are subdominant.

Weak-lensing shear data from the third year of the Dark Energy Survey (DES Y3) have been analysed cosmologically with the integrated three-point correlation function (i3PCF), a higher-order statistic that correlates local aperture mass with surrounding shear, and for the first time a three-point shear statistic on survey data is treated with fully simulation-based inference. Jointly with the two-point correlation functions, the i3PCF is detected at a signal-to-noise ratio of 12.8, and the figure of merit in the Ωm–S8–w space roughly doubles over two-point statistics alone, with the gain coming from angular scales where baryonic effects are subdominant.

Posterior inference over phylogenetic trees has depended on likelihoods, which become intractable once real processes such as insertions, deletions or site selection are modeled. This family of conditional generative models builds a tree step by step, bottom-up, middle-out or top-down, and is trained with a discrete diffusion objective; on real and synthetic data it recovers MCMC posteriors more closely than the prior simulation-based method Phyloformer 2, matches IQ-Tree on simple data, and is reliably more accurate on more realistic complex models.

Posterior inference over phylogenetic trees has depended on likelihoods, which become intractable once real processes such as insertions, deletions or site selection are modeled. This family of conditional generative models builds a tree step by step, bottom-up, middle-out or top-down, and is trained with a discrete diffusion objective; on real and synthetic data it recovers MCMC posteriors more closely than the prior simulation-based method Phyloformer 2, matches IQ-Tree on simple data, and is reliably more accurate on more realistic complex models.

Estimating the frequencies of host-symbiont coevolution events used to require reconstructing a host tree and then reconciling the symbiont tree against it, so tree-inference error propagated into the result. Fox instead uses a transformer to output the relative frequencies of cospeciation, host switching, loss and duplication directly from the host and symbiont multiple sequence alignments and their mapping, paying the simulation cost once at training time and processing each new system in a single forward pass. On the independent simulator treeducken, Fox reached a mean absolute error of 0.060 on the 92 datasets AmoCoala completed, against 0.131 for AmoCoala, while running more than three orders of magnitude faster.

Estimating the frequencies of host-symbiont coevolution events used to require reconstructing a host tree and then reconciling the symbiont tree against it, so tree-inference error propagated into the result. Fox instead uses a transformer to output the relative frequencies of cospeciation, host switching, loss and duplication directly from the host and symbiont multiple sequence alignments and their mapping, paying the simulation cost once at training time and processing each new system in a single forward pass. On the independent simulator treeducken, Fox reached a mean absolute error of 0.060 on the 92 datasets AmoCoala completed, against 0.131 for AmoCoala, while running more than three orders of magnitude faster.

A simulation-based inference framework jointly learns a low-dimensional summary statistic and an amortized posterior estimator with non-asymptotic guarantees: in exponential-family and smooth-model settings, the training size needed for a target accuracy grows only polynomially with observation dimension, not exponentially as in classical nonparametric conditional distribution estimation.

A simulation-based inference framework jointly learns a low-dimensional summary statistic and an amortized posterior estimator with non-asymptotic guarantees: in exponential-family and smooth-model settings, the training size needed for a target accuracy grows only polynomially with observation dimension, not exponentially as in classical nonparametric conditional distribution estimation.