1,089 research outputs found
Bayesian spline-based hidden Markov models with applications to actimetry data and sleep analysis
B-spline-based hidden Markov models employ B-splines to specify the emission distributions, offering a more flexible modeling approach to data than conventional parametric HMMs. We introduce a Bayesian framework for inference, enabling the simultaneous estimation of all unknown model parameters including the number of states. A parsimonious knot configuration of the B-splines is identified by the use of a trans-dimensional Markov chain sampling algorithm, while model selection regarding the number of states can be performed based on the marginal likelihood within a parallel sampling framework. Using extensive simulation studies, we demonstrate the superiority of our methodology over alternative approaches as well as its robustness and scalability. We illustrate the explorative use of our methods for data on activity in animals, that is whitetip-sharks. The flexibility of our Bayesian approach also facilitates the incorporation of more realistic assumptions and we demonstrate this by developing a novel hierarchical conditional HMM to analyse human activity for circadian and sleep modeling. Supplementary materials for this article are available online
Bayesian CART models for insurance claims frequency
The accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easy to interpret. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. In addition to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Simulations and real insurance data will be used to illustrate the applicability of these models
Bayesian Forecasting in Economics and Finance: A Modern Review
The Bayesian statistical paradigm provides a principled and coherent approach
to probabilistic forecasting. Uncertainty about all unknowns that characterize
any forecasting problem -- model, parameters, latent states -- is able to be
quantified explicitly, and factored into the forecast distribution via the
process of integration or averaging. Allied with the elegance of the method,
Bayesian forecasting is now underpinned by the burgeoning field of Bayesian
computation, which enables Bayesian forecasts to be produced for virtually any
problem, no matter how large, or complex. The current state of play in Bayesian
forecasting in economics and finance is the subject of this review. The aim is
to provide the reader with an overview of modern approaches to the field, set
in some historical context; and with sufficient computational detail given to
assist the reader with implementation.Comment: The paper is now published online at:
https://doi.org/10.1016/j.ijforecast.2023.05.00
Identifiable and interpretable nonparametric factor analysis
Factor models have been widely used to summarize the variability of
high-dimensional data through a set of factors with much lower dimensionality.
Gaussian linear factor models have been particularly popular due to their
interpretability and ease of computation. However, in practice, data often
violate the multivariate Gaussian assumption. To characterize higher-order
dependence and nonlinearity, models that include factors as predictors in
flexible multivariate regression are popular, with GP-LVMs using Gaussian
process (GP) priors for the regression function and VAEs using deep neural
networks. Unfortunately, such approaches lack identifiability and
interpretability and tend to produce brittle and non-reproducible results. To
address these problems by simplifying the nonparametric factor model while
maintaining flexibility, we propose the NIFTY framework, which parsimoniously
transforms uniform latent variables using one-dimensional nonlinear mappings
and then applies a linear generative model. The induced multivariate
distribution falls into a flexible class while maintaining simple computation
and interpretation. We prove that this model is identifiable and empirically
study NIFTY using simulated data, observing good performance in density
estimation and data visualization. We then apply NIFTY to bird song data in an
environmental monitoring application.Comment: 50 pages, 17 figure
Bayesian computation in astronomy: novel methods for parallel and gradient-free inference
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the author that aim to facilitate Bayesian data analysis for the next generation of astronomical observations and theoretical models.
The first part of this thesis familiarises the reader with the notion of probability and its relevance for science through the prism of Bayesian reasoning, by introducing the key constituents of the theory and discussing its best practices. The second part includes a pedagogical introduction to the principles of Bayesian computation motivated by the geometric characteristics of probability distributions and followed by a detailed exposition of various methods including Markov chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC) and Nested Sampling (NS). Finally, the third part presents two novel computational methods and their respective software implementations.
The first such development is Ensemble Slice Sampling (ESS), a new class of MCMC algorithms that extend the applicability of the standard Slice Sampler by adaptively tuning its only hyperparameter and utilising an ensemble of parallel walkers in order to efficiently handle strong correlations between parameters. The parallel, black–box and gradient-free nature of the method renders it ideal for use in combination with computationally expensive and non–differentiable models often met in astronomy. ESS is implemented in Python in the well–tested and open-source software package called zeus that is specifically designed to tackle the computational challenges posed by modern astronomical and cosmological analyses. In particular, use of the code requires minimal, if any, hand–tuning of hyperparameters while its performance is insensitive to linear correlations and it can scale up to thousands of CPUs without any extra effort.
The next contribution includes the introduction of Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates effective sampling of probability distributions with non–trivial geometry. PMC utilises a Normalising Flow (NF) in order to decorrelate the parameters of the distribution and then proceeds by sampling from the preconditioned target distribution using an adaptive SMC scheme. PMC, through its Python implementation pocoMC, achieves excellent sampling performance, including accurate estimation of the model evidence, for highly correlated, non–Gaussian, and multimodal target distributions. Finally, the code is directly parallelisable, manifesting linear scaling up to thousands of CPUs
Mean-field Variational Inference via Wasserstein Gradient Flow
Variational inference, such as the mean-field (MF) approximation, requires
certain conjugacy structures for efficient computation. These can impose
unnecessary restrictions on the viable prior distribution family and further
constraints on the variational approximation family. In this work, we introduce
a general computational framework to implement MF variational inference for
Bayesian models, with or without latent variables, using the Wasserstein
gradient flow (WGF), a modern mathematical technique for realizing a gradient
flow over the space of probability measures. Theoretically, we analyze the
algorithmic convergence of the proposed approaches, providing an explicit
expression for the contraction factor. We also strengthen existing results on
MF variational posterior concentration from a polynomial to an exponential
contraction, by utilizing the fixed point equation of the time-discretized WGF.
Computationally, we propose a new constraint-free function approximation method
using neural networks to numerically realize our algorithm. This method is
shown to be more precise and efficient than traditional particle approximation
methods based on Langevin dynamics
Reasoning about quantities and concepts: studies in social learning
We live and learn in a ‘society of mind’. This means that we form beliefs not
just based on our own observations and prior expectations but also based on the
communications from other people, such as our social network peers. Across seven
experiments, I study how people combine their own private observations with other
people’s communications to form and update beliefs about the environment. I will
follow the tradition of rational analysis and benchmark human learning against optimal Bayesian inference at Marr’s computational level. To accommodate human
resource constraints and cognitive biases, I will further contrast human learning
with a variety of process level accounts. In Chapters 2–4, I examine how people
reason about simple environmental quantities. I will focus on the effect of dependent information sources on the success of group and individual learning across a
series of single-player and multi-player judgement tasks. Overall, the results from
Chapters 2–4 highlight the nuances of real social network dynamics and provide
insights into the conditions under which we can expect collective success versus
failures such as the formation of inaccurate worldviews. In Chapter 5, I develop a
more complex social learning task which goes beyond estimation of environmental
quantities and focuses on inductive inference with symbolic concepts. Here, I investigate how people search compositional theory spaces to form and adapt their
beliefs, and how symbolic belief adaptation interfaces with individual and social
learning in a challenging active learning task. Results from Chapter 5 suggest that
people might explore compositional theory spaces using local incremental search;
and that it is difficult for people to use another person’s learning data to improve
upon their hypothesis
Personalized Treatment Selection via Product Partition Models with Covariates
Precision medicine is an approach for disease treatment that defines
treatment strategies based on the individual characteristics of the patients.
Motivated by an open problem in cancer genomics, we develop a novel model that
flexibly clusters patients with similar predictive characteristics and similar
treatment responses; this approach identifies, via predictive inference, which
one among a set of treatments is better suited for a new patient. The proposed
method is fully model-based, avoiding uncertainty underestimation attained when
treatment assignment is performed by adopting heuristic clustering procedures,
and belongs to the class of product partition models with covariates, here
extended to include the cohesion induced by the Normalized Generalized Gamma
process. The method performs particularly well in scenarios characterized by
considerable heterogeneity of the predictive covariates in simulation studies.
A cancer genomics case study illustrates the potential benefits in terms of
treatment response yielded by the proposed approach. Finally, being
model-based, the approach allows estimating clusters' specific response
probabilities and then identifying patients more likely to benefit from
personalized treatment.Comment: 31 pages, 7 figure
Cosmology with the Laser Interferometer Space Antenna
The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe
Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data
Mixed Membership Models (MMMs) are a popular family of latent structure
models for complex multivariate data. Instead of forcing each subject to belong
to a single cluster, MMMs incorporate a vector of subject-specific weights
characterizing partial membership across clusters. With this flexibility come
challenges in uniquely identifying, estimating, and interpreting the
parameters. In this article, we propose a new class of Dimension-Grouped MMMs
(Gro-Ms) for multivariate categorical data, which improve parsimony and
interpretability. In Gro-Ms, observed variables are partitioned into groups
such that the latent membership is constant for variables within a group but
can differ across groups. Traditional latent class models are obtained when all
variables are in one group, while traditional MMMs are obtained when each
variable is in its own group. The new model corresponds to a novel
decomposition of probability tensors. Theoretically, we derive transparent
identifiability conditions for both the unknown grouping structure and model
parameters in general settings. Methodologically, we propose a Bayesian
approach for Dirichlet Gro-Ms to inferring the variable grouping structure
and estimating model parameters. Simulation results demonstrate good
computational performance and empirically confirm the identifiability results.
We illustrate the new methodology through applications to a functional
disability survey dataset and a personality test dataset
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