arXiv subjects

Peter Mueller

Publications and source records attributed to Peter Mueller.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Bayesian Clustering with Regression for Unaligned Longitudinal Binary Data

We propose a generalized Bayesian clustering with regression model for unaligned longitudinal binary outcomes, motivated by seizure diary data from the Human Epilepsy Project. Seizure diaries are sparse, irregularly observed, and vary enormously across patients. A single fully-specified generative model tends to be either misspecified or computationally inefficient. We address the challenge by two strategies. We set up a regression by way of clustering as model-based clustering using a mixture model. For the latter, we take a generalized Bayesian perspective which replaces the full likelihood with a loss-based update using a generalized likelihood. We combine a trajectory similarity loss and a regression loss, so that clustering is informed by both trajectory similarity and the prediction of outcomes The trajectory similarity loss is constructed by representing each trajectory as an (empirical) distribution of subsequences, called reads, and then is defined based on the sliced Wasserstein distance between these empirical distributions. This loss allows alignment-free comparison of sequences that are irregularly observed or temporally misaligned, and it scales quasi-linearly in trajectory length. The regression loss is the negative log-likelihood of a probit regression. A prior on the cluster-specific parameters is defined by way of a Dirichlet process prior on the mixing measure.

stat.ME↗

arXiv2026

Distributional Determinantal Point Process for Repulsive Clustering of Distributions

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.

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arXiv2026

A Mixed Self-Exciting Process to Model Epileptic Seizures

Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a process we call seizure clustering. Motivated by seizure diary data collected over three years from 407 individuals newly diagnosed with focal epilepsy in the Human Epilepsy Project (HEP), we propose a Bayesian mixed Hawkes process model that addresses seizure clustering and heterogeneity between individuals. In the Hawkes process, the intensity is accelerated each time an event occurs, through the composition of background and excitation intensity functions. The proposed model incorporates a Weibull baseline intensity to model a trend in background seizure rates over time, while the excitation process accounts for seizure clustering within individuals. We model heterogeneity among individuals by including covariates and random effects in both the background and excitation intensities. In the HEP study, the average time between primary and secondary seizures within an individual is 1.57 (95\% CrI: 1.43, 1.70) days, with an average of 2.20 (1.96, 2.47) seizures per cluster. We demonstrate that omitting random effects in the presence of heterogeneity leads to underestimation of the background intensity and overestimation of excitation rates.

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arXiv2026

Bayesian Nonparametrics: Principles and Practice

This extended preface [to the Book `Bayesian Nonparametrics', Cambridge University Press, 2010, by NL Hjort, CC Holmes, P Mueller, SG Walker] is meant to explain why you are right to be curious about Bayesian nonparametrics -- why you may actually need it and how you can manage to understand it and use it. The preface also serves as an introductory chapter, giving an overview of the aims and contents of the book. We also explain the background for how the book came into existence, delve briefly on the history of the still relatively young field of Bayesian nonparametrics, and offer some concluding remarks, pertaining to various challenges and likely future developments of the area.

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arXiv2026

Vertical Consensus Inference for High-Dimensional Random Partition

We review recently proposed Bayesian approaches for clustering high-dimensional data. After identifying the main limitations of available approaches, we introduce an alternative framework based on vertical consensus inference (VCI) to mitigate the curse of dimensionality in high-dimensional Bayesian clustering. VCI builds on the idea of consensus Monte Carlo by dividing the data into multiple shards (smaller subsets of variables), performing posterior inference on each shard, and then combining the shard-level posteriors to obtain a consensus posterior. The key distinction is that VCI splits the data vertically, producing vertical shards that retain the same number of observations but have lower dimensionality. We use an entropic regularized Wasserstein barycenter to define a consensus posterior. The shard-specific barycenter weights are constructed to favor shards that provide meaningful partitions, distinct from a trivial single cluster or all singleton clusters, favoring balanced cluster sizes and precise shard-specific posterior random partitions. We show that VCI can be interpreted as a variational approximation to the posterior under a hierarchical model with a generalized Bayes prior. For relatively low-dimensional problems, experiments suggest that VCI closely approximates inference based on clustering the entire multivariate data. For high-dimensional data and in the presence of many noninformative dimensions, VCI introduces a new framework for model-based and principled inference on random partitions. Although our focus here is on random partitions, VCI can be applied to any dimension-independent parameters and serves as a bridge to emerging areas in statistics such as consensus Monte Carlo, optimal transport, variational inference, and generalized Bayes.

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arXiv2026

Bayesian Multiple Multivariate Density-Density Regression

We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core idea is to define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors and to quantify deviations from the observed response using the sliced Wasserstein (SW) distance. Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework, enabling principled uncertainty quantification without requiring a fully specified likelihood. The inference process can be seen as an instance of an inverse SWB problem. We establish theoretical guarantees, including the stability of the SWB under perturbations of marginals and barycenter weights, sample complexity of the generalized likelihood, and posterior consistency. For practical inference, we introduce a differentiable approximation of the SWB and a smooth reparameterization to handle the simplex constraint on barycenter weights, allowing efficient gradient-based MCMC sampling. We demonstrate MDDR in an application to inference for population-scale single-cell data. Posterior analysis under the MDDR model in this example includes inference on communication between multiple source/sender cell types and a target/receiver cell type. The proposed approach provides accurate fits, reliable predictions, and interpretable posterior estimates of barycenter weights, which can be used to construct sparse cell-cell communication networks.

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arXiv2025

Bayesian Multivariate Density-Density Regression

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing in spaces of differing dimensions. We utilize a generalized Bayes framework, circumventing the need for a fully specified likelihood by employing the sliced Wasserstein distance to measure the discrepancy between fitted and observed distributions. This choice not only handles high-dimensional data and varying sample sizes efficiently but also facilitates a Metropolis-adjusted Langevin algorithm (MALA) for posterior inference. Furthermore, we establish the posterior consistency of our generalized Bayesian approach, ensuring that the posterior distribution concentrates around the true parameters as the sample size increases. Through simulations and application to a population-scale single-cell dataset, we show that Bayesian DDR provides robust fits, superior predictive performance compared to traditional methods, and valuable insights into complex biological interactions.

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arXiv2025

DPGLM: A Semiparametric Bayesian GLM with Inhomogeneous Normalized Random Measures

We introduce a novel varying-weight dependent Dirichlet process (DDP) model that extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM. We show that the resulting model takes the form of an inhomogeneous completely random measure that arises from exponential tilting of a normalized completely random measure. Building on familiar posterior sampling methods for mixtures with respect to normalized random measures, we introduce posterior simulation in the resulting model. We validate the proposed methodology through extensive simulation studies and illustrate its application using data from a speech intelligibility study.

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arXiv2024

Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al., 2022). We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing estimation of the mixing measure (or mixture) as an inference target. One of the key features is the model-agnostic nature of the approach, which remains valid under arbitrarily complex dependence structures in the underlying sampling model. Using a decision-theoretic framework, our method identifies a point estimate by minimizing posterior expected loss. A loss function is defined as a discrepancy between mixing measures. Estimating the mixing measure implies inference on the mixture density and the random partition. Exploiting the discrete nature of the mixing measure, we use a version of sliced Wasserstein distance. We introduce two specific variants for Gaussian mixtures. The first, mixed sliced Wasserstein, applies generalized geodesic projections on the product of the Euclidean space and the manifold of symmetric positive definite matrices. The second, sliced mixture Wasserstein, leverages the linearity of Gaussian mixture measures for efficient projection

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arXiv2024

The Auger-Meitner Radioisotope Microscope: an instrument for characterization of Auger electron multiplicities and energy distributions

We describe a new instrument, the Argonne Auger Radioisotope Microscope (ARM), capable of characterizing the Auger electron emission of radionuclides, including candidates relevant in nuclear medicine. Our approach relies on event-by-event ion-electron coincidence, time-of-flight, and spatial readout measurement to determine correlated electron multiplicity and energy distributions of Auger decays. We present a proof-of-principle measurement with the ARM using X-ray photoionization of stable krypton beyond the K-edge and identify a bifurcation in the electron multiplicity distribution depending on the emission of K-LX electrons. Extension of the ARM to the characterization of radioactive sources of Auger electron emissions is enabled by the combination of two recent developments: (1) cryogenic buffer gas beam technology to introduce Auger emitters into the detection region with well-defined initial conditions, and (2) large-area micro-channel plate detectors with multi-hit detection capabilities to simultaneously detect multiple electrons emitted in a single decay. The ARM will generate new experimental data on Auger multiplicities that can be used to benchmark atomic relaxation and decay models. This data will provide insight into the low-energy regime of Auger electrons where intensity calculations are most challenging and experimental data is limited. In particular, accurate multiplicity data of the low-energy regime can be used to inform oncological dosimetry models, where electron energies less than 500 eV are known to be most effective in damaging DNA and cell membranes.

physics.ins-det↗

arXiv2024

Clustering and Meta-Analysis Using a Mixture of Dependent Linear Tail-Free Priors

We propose a novel nonparametric Bayesian approach for meta-analysis with event time outcomes. The model is an extension of linear dependent tail-free processes. The extension includes a modification to facilitate (conditionally) conjugate posterior updating and a hierarchical extension with a random partition of studies. The partition is formalized as a Dirichlet process mixture. The model development is motivated by a meta-analysis of cancer immunotherapy studies. The aim is to validate the use of relevant biomarkers in the design of immunotherapy studies. The hypothesis is about immunotherapy in general, rather than about a specific tumor type, therapy and marker. This broad hypothesis leads to a very diverse set of studies being included in the analysis and gives rise to substantial heterogeneity across studies

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arXiv2024

A VUV light source for enhanced production of metastable krypton and xenon beams

We demonstrate excitation of metastable krypton and xenon beams using a vacuum ultraviolet lamp and directly compare the performance of this method to metastable excitation based on a radiofrequency-driven plasma discharge. In our apparatus, lamp-based metastable excitation outperforms the plasma discharge across a wide range of beam flux values relevant for Atom Trap Trace Analysis (ATTA). Moreover, we do not observe significant degradation in lamp performance after over 160 hours of operation. We find that lamp-based excitation is particularly advantageous at the smallest and largest beam fluxes tested, demonstrating the utility of this approach both for improving krypton ATTA and for enabling the detection of radioactive xenon isotopes using ATTA. Finally, we demonstrate an additional enhancement to lamp-based metastable excitation efficiency and stability by applying an external magnetic field.

physics.atom-ph↗

arXiv2023

Regression with Variable Dimension Covariates

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the ubiquitous nature of regression problems and the abundance of related methods and results there is a surprising gap in the literature. There are no well established methods for regression with a varying dimension covariate vectors, despite the common occurrence of such problems. In this paper we review some recent related papers proposing varying dimension regression by way of random partitions.

math.ST↗

arXiv2023

Implementing an electronic sideband offset lock for precision spectroscopy in radium

We demonstrate laser frequency stabilization with at least 6 GHz of offset tunability using an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) on a titanium sapphire laser at 714 nm and we apply this technique to the precision spectroscopy of $^{226}$Ra, and $^{225}$Ra. By locking the laser to a single resonance of a high finesse optical cavity and adjusting the lock offset, we determine the frequency difference between the magneto-optical trap (MOT) transitions in the two isotopes to be $2630.0\pm0.3$ MHz, a factor of 29 more precise than the previously available data. Using the known value of the hyperfine splitting of the $^{3}P_{1}$ level, we calculate the isotope shift for the $^{1}S_{0}$ to $^{3}P_{1}$ transition to be $2267.0\pm2.2$ MHz, which is a factor of 8 more precise than the best available value. Our technique could be applied to countless other atomic systems to provide unprecedented precision in isotope shift spectroscopy and other relative frequency comparisons.

physics.atom-ph↗

arXiv2023

Graph-Aligned Random Partition Model (GARP)

Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the biological relations of the clusters. The increasing availability of large genomic data requires new statistical tools to perform model-based clustering and infer the relationship between homogeneous subgroups of units. Motivated by single-cell RNA applications we develop a novel dependent mixture model to jointly perform cluster analysis and align the clusters on a graph. Our flexible graph-aligned random partition model (GARP) exploits Gibbs-type priors as building blocks, allowing us to derive analytical results on the graph-aligned random partition's probability mass function (pmf). We derive a generalization of the Chinese restaurant process from the pmf and a related efficient and neat MCMC algorithm to perform Bayesian inference. We perform posterior inference on real single-cell RNA data from mice stem cells. We further investigate the performance of our model in capturing the underlying clustering structure as well as the underlying graph by means of simulation studies.

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arXiv2022

A cryogenic SRAM based arbitrary waveform generator in 14 nm for spin qubit control

Realization of qubit gate sequences require coherent microwave control pulses with programmable amplitude, duration, spacing and phase. We propose an SRAM based arbitrary waveform generator for cryogenic control of spin qubits. We demonstrate in this work, the cryogenic operation of a fully programmable radio frequency arbitrary waveform generator in 14 nm FinFET technology. The waveform sequence from a control processor can be stored in an SRAM memory array, which can be programmed in real time. The waveform pattern is converted to microwave pulses by a source-series-terminated digital to analog converter. The chip is operational at 4 K, capable of generating an arbitrary envelope shape at the desired carrier frequency. Total power consumption of the AWG is 40-140mW at 4 K, depending upon the baud rate. A wide signal band of 1-17 GHz is measured at 4 K, while multiple qubit control can be achieved using frequency division multiplexing at an average spurious free dynamic range of 40 dB. This work paves the way to optimal qubit control and closed loop feedback control, which is necessary to achieve low latency error mitigation

quant-ph↗

arXiv2022

A system design approach toward integrated cryogenic quantum control systems

In this paper, we provide a system level perspective on the design of control electronics for large scale quantum systems. Quantum computing systems with high-fidelity control and readout, coherent coupling, calibrated gates, and reconfigurable circuits with low error rates are expected to have superior quantum volumes. Cryogenic CMOS plays a crucial role in the realization of scalable quantum computers, by minimizing the feature size, lowering the cost, power consumption, and implementing low latency error correction. Our approach toward achieving scalable feed-back based control systems includes the design of memory based arbitrary waveform generators (AWG's), wide band radio frequency analog to digital converters, integrated amplifier chain, and state discriminators that can be synchronized with gate sequences. Digitally assisted designs, when implemented in an advanced CMOS node such as 7 nm can reap the benefits of low power due to scaling. A qubit readout chain demands several amplification stages before the digitizer. We propose the co-integration of our in-house developed InP HEMT LNAs with CMOS LNA stages to achieve the required gain at the digitizer input with minimal area. Our approach using high impedance matching between the HEMT LNA and the cryogenic CMOS receiver can relax the design constraints of an inverter-based CMOS LNA, paving the way toward a fully integrated qubit readout chain. The qubit state discriminator consists of a digital signal processor that computes the qubit state from the digitizer output and a pre-determined threshold. The proposed system realizes feedback-based optimal control for error mitigation and reduction of the required data rate through the serial interface to room temperature electronics.

quant-ph↗

arXiv2022

A Recommender System Based on a Double Feature Allocation Model

A collaborative filtering recommender system predicts user preferences by discovering common features among users and items. We implement such inference using a Bayesian double feature allocation model, that is, a model for random pairs of subsets. We use an Indian buffet process (IBP) to link users and items to features. Here a feature is a subset of users and a matching subset of items. By training feature-specific rating effects, we predict ratings. We use MovieLens Data to demonstrate posterior inference in the model and prediction of user preferences for unseen items compared to items they have previously rated. Part of the implementation is a novel semi-consensus Monte Carlo method to accomodate large numbers of users and items, as is typical for related applications. The proposed approach implements parallel posterior sampling in multiple shards of users while sharing item-related global parameters across shards.

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