# Neural Posterior Estimation

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.

Bayesian parameter inference for extreme-mass-ratio inspirals (EMRIs) has relied on narrow priors centered on the true parameters or Markov chains initialized near them, information real observations do not provide. A deep-learning-assisted framework first uses a neural network to produce approximate posteriors from the data and shrink the search region, then particle swarm optimization finds a high-likelihood starting point, and staged Markov chain Monte Carlo sampling produces the final posteriors. On two noise-free six-month simulated signals, the resulting posteriors agree closely with reference analyses initialized near the true values, and once the network is trained each signal takes about ten hours.

Bayesian parameter inference for extreme-mass-ratio inspirals (EMRIs) has relied on narrow priors centered on the true parameters or Markov chains initialized near them, information real observations do not provide. A deep-learning-assisted framework first uses a neural network to produce approximate posteriors from the data and shrink the search region, then particle swarm optimization finds a high-likelihood starting point, and staged Markov chain Monte Carlo sampling produces the final posteriors. On two noise-free six-month simulated signals, the resulting posteriors agree closely with reference analyses initialized near the true values, and once the network is trained each signal takes about ten hours.

Seasonal influenza models are routinely asked to recommend an antiviral coverage tier from weekly reported cases, yet a well-calibrated parameter posterior does not make that tier identifiable. A decision-relevance score weighted by the variance of the decision margin measures how much of that variance comes from directions the data failed to shrink; on a 192-cell synthetic grid the bounded posterior still flipped the plug-in action in 26.7% of cells, and the plug-in rule lost 11.7% of the oracle's value. On 204 real FluView region-seasons, widening the reporting-rate prior raised the main arm from 0.476 to 0.733 while the scale-invariant control stayed near zero.

Seasonal influenza models are routinely asked to recommend an antiviral coverage tier from weekly reported cases, yet a well-calibrated parameter posterior does not make that tier identifiable. A decision-relevance score weighted by the variance of the decision margin measures how much of that variance comes from directions the data failed to shrink; on a 192-cell synthetic grid the bounded posterior still flipped the plug-in action in 26.7% of cells, and the plug-in rule lost 11.7% of the oracle's value. On 204 real FluView region-seasons, widening the reporting-rate prior raised the main arm from 0.476 to 0.733 while the scale-invariant control stayed near zero.