Bayes and the Law: Cambridge event and new review paper

When we set up the Bayes and the Law network in 2012 we made the following assertion:

Proper use of statistics and probabilistic reasoning has the potential to improve dramatically the efficiency, transparency and fairness of the criminal justice system and the accuracy of its verdicts, by enabling the relevance of evidence – especially forensic evidence - to be meaningfully evaluated and communicated. However, its actual use in practice is minimal, and indeed the most natural way to handle probabilistic evidence (Bayes) has generally been shunned. 

The first workshop (30th August to 2nd September 2016)  that is part of our 6-month programme "Probability and Statistics in Forensic Science" at the Issac Newton Institute of Mathematics Cambridge directly addresses the above assertion and seeks to understand the scope, limitations, and barriers of using statistics and probability in court. The Workshop brings together many of the world's leading academics and pracitioners (including lawyers) in this area. Information on the programme and how to participate can be found here.

A new review paper* "Bayes and the Law" has just been published in Annual Review of Statistics and Its Application.

This paper reviews the potential and actual use of Bayes in the law and explains the main reasons for its lack of impact on legal practice. These include misconceptions by the legal community about Bayes’ theorem, over-reliance on the use of the likelihood ratio and the lack of adoption of modern computational methods. The paper argues that Bayesian Networks (BNs), which automatically produce the necessary Bayesian calculations, provide an opportunity to address most concerns about using Bayes in the law.

*Full citation:

Fenton N.E, Neil M, Berger D, “Bayes and the Law”, Annual Review of Statistics and Its Application, Volume 3, pp51-77, June 2016 http://dx.doi.org/10.1146/annurev-statistics-041715-033428. Pre-publication version is here and the Supplementary Material is here.

Using expert judgment to build better decision support models

The 'big data' juggernaut seems to be rumbling along with many oblivious to the limitations of what pure machine learning techniques can really achieve in most important applications. We have written here before about the dangers of 'learning' from data alone (no matter how 'big' the data is).

Contrary to the narrative being sold by many in the big data community, if you want accurate predictions and improved decision-making then, invariably, you need to incorporate human knowledge and judgment. Much of the research in the BAYES-KNOWLEDGE project is concerned with building better decision-support models - normally Bayesian networks (BNs) - by incorporating knowledge and data.

There are two major steps to building a BN model for a decision analysis problem:

1. Identify the key variables and which ones directly influence each other.   
2. Define the probability tables for each variable conditioned on its parents

We have been reporting on this blog about various recent papers from the project that have addressed these steps, most in the context of case studies*, while some of the project work on combining judgement and data to learn the probability tables has been incorporated into the BAYES-KNOWLEDGE tool on the Agenarisk platform.

Now new research (supported jointly by BAYES-KNOWLEDGE and the China Scholarship Council) has been published in the top ranked journal "Decision Support Systems" that describes an important advance in defining the probability tables of a BN. The paper shows that, in practice, many of the variables in a BN model are related by certain types of 'monotonic constraints'.  As a very simple example consider a model in which the variable "Lung cancer" has the parent "Smoking". Although we do not know the exact relationship between these variables it is known that as probability values of "Smoking" increase so do the probability values of "Lung cancer". So this is an example of a positive monotonic constraint. It turns out that, even with fairly minimal data, it is possible to exploit an expert's knowledge about the existence of monotonic constraints to learn complete probability tables that lead to accurate and useful models. This is important because most approaches to incorporating expert judgement to define the probability tables requires the expert to consider multiple combinations of variables states.

The full citation for this new paper is:

Zhou, Y., Fenton, N. E., Zhu, C. (2016), "An Empirical Study of Bayesian Network Parameter Learning with Monotonic Causality Constraints", Decision Support Systems. http://dx.doi.org/10.1016/j.dss.2016.05.001 pre-publication pdf version here. 

*See:

• Bayesian networks for Cost, Benefit and Risk Analysis of Agricultural Development Projects
• Turning poorly structured data into intelligent Bayesian Network models for medical decision support
• Improving BNs by learning from similar ones

Bayesian networks for Cost, Benefit and Risk Analysis of Agricultural Development Projects

Successful implementation of major projects requires careful management of uncertainty and risk. Yet, uncertainty is rarely effectively calculated when analysing project costs and benefits. In the case of major agricultural and other development projects in Africa this challenge is especially important.

A paper just published* in the journal Experts Systems with Applications presents a Bayesian network (BN) modelling framework to calculate the costs, benefits, and return on investment of a project over a specified time period, allowing for changing circumstances and trade-offs. Marianne Gadeberg and Eike Luedeling have written an overview of the work here.

The framework uses hybrid and dynamic BNs containing both discrete and continuous variables over multiple time stages. The BN framework calculates costs and benefits based on multiple causal factors including the effects of individual risk factors, budget deficits, and time value discounting, taking account of the parameter uncertainty of all continuous variables. The framework can serve as the basis for various project management assessments and is illustrated using a case study of an agricultural development project. The work was a collaboration between the World Agroforestry Centre (ICRAF), Nairobi, Kenya, the Risk Information Management Group at Queen Mary (as part of the BAYES-KNOWLEDGE project) and Agena Ltd.

*The full reference is:

Yet, B., Constantinou, A., Fenton, N., Neil, M., Luedeling, E., & Shepherd, K. (2016). "A Bayesian Network Framework for Project Cost, Benefit and Risk Analysis with an Agricultural Development Case Study" . Expert Systems with Applications, Volume 60, 30 October 2016, Pages 141–155. DOI: 10.1016/j.eswa.2016.05.005. 

Until July 2016 the full published pdf is available for free.  A permanent pre-publication pdf is available here.

See also: Can we build a better project: assessing complexities in development projects

Acknowledgements: Part of this work was performed under the auspices of EU project ERC-2013-AdG339182-BAYES_KNOWLEDGE and part under ICRAF Contract No SD4/2012/214 issued to Agena. We acknowledge support from the Water, Land and Ecosystems (WLE) program of the Consultative Group on International Agricultural Research (CGIAR).