Research

Turning an expected information gain into a probability of detection on the one sky we actually observe.

Problem

The Kullback–Leibler divergence is the standard criterion for deciding whether a cosmological model is distinguishable from the null. But KL is an expected information gain, averaged over an ensemble of hypothetical universes. It says nothing about the probability of detection on a single realization.

Contribution

Derived the exact sampling distribution of the log-likelihood ratio between two Gaussian models — a generalized non-central χ² — and used it to convert expected information gain into a detection probability, with ROC curves and calibrated interval coverage.

Result

Yields correctly calibrated error estimates in regimes where standard statistical errors mislead. Supplies the frequentist validation layer that learned ratio estimators (NRE) currently lack, and connects directly to Bayesian experimental design, where the KL divergence is the standard expected utility. The framework is model-agnostic; cosmic topology is the case study.

Manuscript in preparation Likelihood-ratio inferenceInformation theoryDetection probability

A direction I am moving into: replacing an intractable MCMC scan with amortized neural inference, and proving the replacement is honest.

Problem

MCMC-based Bayesian parameter estimation is the bottleneck in topology searches, which must scan manifold size, orientation and observer position simultaneously.

Contribution

The plan is amortized neural inference with variational-autoencoder likelihood emulators trained on simulated CMB covariances, benchmarked against a validated MCMC baseline on the same posterior, with simulation-based calibration and coverage tests as the acceptance criterion rather than an afterthought. My existing work on the exact likelihood-ratio distribution is what makes that validation step well-defined.

Result

Early stage — no results yet. This is a research direction I intend to develop, not completed work.

Planned direction Simulation-based inferenceNeural emulatorsBayesian computation

If space is compact, the CMB is no longer described by a power spectrum. Someone has to compute what replaces it.

Problem

Non-trivial topology breaks statistical isotropy, so the CMB is no longer described by an angular power spectrum alone — it requires full non-diagonal covariance matrices across all ℓm, ℓ'm'.

Contribution

Derived the first tensor-sector (spin-2) eigenmodes and covariances for compact Euclidean manifolds, and showed that topology alone generates parity-odd TB/EB correlations — a new observational channel for primordial gravitational waves. Built CMBtopology, a GPU-parallelized HPC package now used collaboration-wide.

Result

Three first-author JCAP papers; a fourth in preparation.

Ongoing CMB statisticsEigenmode analysisGPU / HPC

A rare machine-learning problem where the optimal answer is computable, so the network's loss can be measured rather than assumed.

Problem

Likelihood-based identification of the underlying manifold from CMB maps is accurate but expensive.

Contribution

Showed that classifiers trained on simulated CMB maps recover near-likelihood-level discrimination between manifolds at a fraction of the cost.

Result

Because the ground-truth likelihood is computable in this problem, the learned model's discrepancy from the optimal decision rule can be measured rather than assumed — a property almost no applied machine-learning setting offers.

JCAP 09 (2024) 057 Machine learningModel comparisonCMB

The same question as the cosmology work, asked of a different system: how much evidence does one noisy measurement actually carry?

Problem

LLM benchmarks report accuracy without uncertainty, so rankings are unstable and the inference procedure behind a reported number is rarely stated.

Contribution

Co-developed a Bayesian evaluation framework replacing Pass@k with Dirichlet-posterior estimates and credible intervals, giving stable rankings from far fewer samples; released as the open-source Scorio toolkit. Also formalized test-time scaling as budgeted search over a transformer's prefix tree, with reproducibility standards for reporting it.

Result

Accepted to the ICLR 2026 main conference. The work is now being extended to reinforcement learning, where calibrated evaluation shapes the training signal itself.

ICLR 2026 Bayesian evaluationInference-time scalingLLMs

Complex scalar-field dark matter in the non-relativistic limit — effective field theory, canonical transformations and multi-field axion models (advisor: M. H. Namjoo). Cosmological perturbation theory, inflation and primordial non-Gaussianity using xAct (advisor: H. Firouzjahi).