# Fine-Tuning the Odds in Bayesian Networks

arXiv: https://arxiv.org/abs/2105.14371 · HTML: https://mlsanity.com/paper/2105.14371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 29 May 2021.

## Builds on (most cited first, 15 of 15)

- [A storm is Coming: A Modern Probabilistic Model Checker](https://mlsanity.com/paper/1702.04311/) (2017)
- [Parameter Synthesis for Markov Models: Faster Than Ever](https://mlsanity.com/paper/1602.05113/) (2016)
- [Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination](https://mlsanity.com/paper/1709.02093/) (2017)
- [Synthesis in pMDPs: A Tale of 1001 Parameters](https://mlsanity.com/paper/1803.02884/) (2018)
- [The Complexity of Reachability in Parametric Markov Decision Processes](https://mlsanity.com/paper/2009.13128/) (2020)
- [Making Sensitivity Analysis Computationally Efficient](https://mlsanity.com/paper/1301.3868/) (2013)
- [Accelerating Parametric Probabilistic Verification](https://mlsanity.com/paper/1312.3979/) (2013)
- [Sequential Convex Programming for the Efficient Verification of Parametric MDPs](https://mlsanity.com/paper/1702.00063/) (2017)
- [Are Parametric Markov Chains Monotonic?](https://mlsanity.com/paper/1907.08491/) (2019)
- [Fast Parametric Model Checking through Model Fragmentation](https://mlsanity.com/paper/2102.01490/) (2021)
- [Sensitivity Analysis for Probability Assessments in Bayesian Networks](https://mlsanity.com/paper/1303.1470/) (2013)
- [Bayesian Inference by Symbolic Model Checking](https://mlsanity.com/paper/2007.15071/) (2020)
- [Accelerated Model Checking of Parametric Markov Chains](https://mlsanity.com/paper/1805.05672/) (2018)
- [Constrained Bayesian Networks: Theory, Optimization, and Applications](https://mlsanity.com/paper/1705.05326/) (2017)
- [Analysis of Bayesian Networks via Prob-Solvable Loops](https://mlsanity.com/paper/2007.09450/) (2020)

## Built on by (most cited first, 3 of 3)

- [Abstraction-Refinement for Hierarchical Probabilistic Models](https://mlsanity.com/paper/2206.02653/) (2022)
- [Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks](https://mlsanity.com/paper/2406.05764/) (2024)
- [Finding an ε-close Variation of Parameters in Bayesian Networks](https://mlsanity.com/paper/2305.10051/) (2023)

## Abstract (arXiv)

This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in parametric Markov chains. Our techniques are applicable to arbitrarily many, possibly dependent parameters that may occur in various CPTs. This lifts the severe restrictions on parameters, e.g., by restricting the number of parametrized CPTs to one or two, or by avoiding parameter dependencies between several CPTs, in existing works for parametric Bayes networks (pBNs). We describe how our techniques can be used for various pBN synthesis problems studied in the literature such as computing sensitivity functions (and values), simple and difference parameter tuning, ratio parameter tuning, and minimal change tuning. Experiments on several benchmarks show that our prototypical tool built on top of the probabilistic model checker Storm can handle several hundreds of parameters.