Bayesian Flashcards
(15 cards)
Why did you choose a Bayesian hierarchical framework for your models?
- flexible modelling of complex structured data
- incorporating uncertainty at multiple levels
- incorporates prior information, updating beliefs based on the data
- naturally accommodates missing values as unknown quantities which are estimated during MCMC
- allows for posterior predictive model checking where uncertainty in parameter estimates can be quantified
What are the benefits of using MCMC for inference?
- accurate approximation of posterior distributions, especially when closed-form solutions are unavailable
- uncertainty quantification through credible intervals
- complex model flexibility, including non-standard likelihoods and latent variable structures
What are the advantages of using Bayesian inference in the context of compositional data?
- integration over uncertainty in parameter estimation and predictions
- handling of structural zeros and missing values without imputation
- use of count-based models (e.g. GDM), directly working with observed data and incorporating prior knowledge.
- flexibility in modelling hierarchical structures in compositional datasets
How does your hierarchical model handle structural zeros without imputation?
- addressed by using model-based approaches
- no need for arbitrary imputation; instead, zeros are treated as valid outcomes within the probabilistic framework
- accounted for through splitting the data based on presence and absence of zeros in the components or explicit modelling the through distributions that allow for zeros (e.g. GDM).
How do Bayesian models help with missing data?
- handled through the posterior distribution, where missing values are drawn from distributions during MCMC
What sampling methods did you use and why?
- MCMC (Markov Chain Monte Carlo)
- necessary due to the non-conjugate and hierarchical structure of the models
- allowed flexible posterior exploration
How did you specify priors in your Bayesian models, and how sensitive are your results to them?
- used mainly weakly informative
- allowing the posterior to be data-driven, without over reliance on the prior
- For example, Dirichlet and Beta priors were used for compositional proportions, while Normal priors were set on spline coefficients and latent variables
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Can you explain how latent variables were used in your models?
- Forensic: clustering labels
- Time Series: HMM - latent hidden states
- Spatial: spatial penalised regression splines
- allowed capturing unobserved structure, enhancing flexibility and interpretability
What is the role of NIMBLE in your modelling?
NIMBLE was chosen because:
* NIMBLE is a flexible and efficient package for fitting a wide range of statistical models, particularly those that are computationally intensive and involve complex hierarchical structures
* NIMBLE models are written in the BUGS language and then compiled automatically into C++, which allows for fast execution
* results in efficient MCMC sampling
* ability to handle custom distributions (e.g. GDM)
* flexibility in writing model-specific samplers
* integration of R-based model specification with compiled C++ speed
How do you ensure convergence in your MCMC chains?
- visual inspection of trace plots
- potential Scale Reduction Factor (PSRF)
- running multiple chains with different initial values
How did you handle model uncertainty?
- model comparison using posterior predictive model checks, cross-validation and predictive performance metrics (e.g., Brier Score, ECE).
- latent variables where necessary to accommodate uncertainty in class membership, HMM states or spatial variation These approaches allowed you to quantify both parameter and structural uncertainty in predictions.
What is the PSRF and how did you use it?
- used to assess convergence of MCMC chains
- ensure multiple chains converged to the same posterior distribution
- ratio between-chain and within-chain
- PSRF close to 1 indicates convergence
How does your thesis contribute to the field of Bayesian statistics?
- developing GDM-based hierarchical models for multilevel compositional data
- incorporating custom distributions and latent variables for non-standard data types.
- demonstrating Bayesian decision support for real-world applications (e.g., forensic, public health, ecology).
Why were custom distributions necessary in your implementation?
- standard distributions (e.g., Multinomial, Dirichlet) were insufficient for modelling specific data
- GDM offers more flexibility - not written in many probabilistic programming tools
- implemented custom likelihood functions in NIMBLE to accommodate these structures within a Bayesian framework.
Explain the hierarchical aspect of each method?
- Forensic: multiple measurements per fragment, multiple fragments per item - hierarchical model with multiple levels
- COVID-19: weekly counts per variant per country - HMM with group-specifc parameters (each country / variant)
- Trees: proportions of tree species over a grid - splines with group-specific parameters (each tree type)
