Assessing evidence and testing appropriate hypotheses

It is crucial to identify the most appropriate hypotheses if one is to apply probabilistic reasoning to evaluate and properly understand the impact of evidence. Subtle changes to the choice of a prosecution hypothesis can result in drastically different posterior probabilities to a defence hypothesis from the same evidence. To illustrate the problem we consider a real case in which probabilistic arguments assumed that the prosecution hypothesis “both babies were murdered” was the appropriate alternative to the defence hypothesis “both babies died of Sudden Infant Death Syndrome (SIDS)”. Since it would have been sufficient for the prosecution to establish just one murder, a more appropriate alternative hypothesis was “at least one baby was murdered”. Based on the same assumptions used by one of the probability experts who examined the case, the prior odds in favour of the defence hypothesis over the double murder hypothesis are 30 to 1. However, the prior odds in favour of the defence hypothesis over the alternative ‘at least one murder’ hypothesis are only 5 to 2. Assuming that the medical and other evidence has a likelihood ratio of 5 in favour of the prosecution hypothesis results in very different conclusions about the posterior probability of the defence hypothesis

Rigorously assessing software reliability and safety

This paper summarises the state of the art in the assessment of software reliability and safety ("dependability"), and describes some promising developments. A sound demonstration of very high dependability is still impossible before operation of the software; but research is finding ways to make rigorous assessment increasingly feasible. While refined mathematical techniques cannot take the place of factual knowledge, they can allow the decision-maker to draw more accurate conclusions from the knowledge that is available

A Note on UK Covid19 death rates by religion: which groups are most at risk?

4 pages, 1 figureThere has been great concern in the UK that people from the BAME (Black And Minority Ethnic) community have a far higher risk of dying from Covid19 than those of other ethnicities. However, the overall fatalities data from the Government's ONS (Office of National Statistics) most recent report on deaths by religion shows that Jews (very few of whom are classified as BAME) have a much higher risk than those of religions (Hindu, Sikh, Muslim) with predominantly BAME people. This apparently contradictory result is, according to the ONS statistical analysis, implicitly explained by age as the report claims that, when 'adjusted for age' Muslims have the highest fatality risk. However, the report fails to provide the raw data to support this. There are many factors other than just age that must be incorporated into any analysis of the observed data before making definitive conclusions about risk based on religion/ethnicity. We propose the need for a causal model for this. If we discount unknown genetic factors, then religion and ethnicity have NO impact at all on a person's Covid19 death risk once we know their age, underlying medical conditions, work/living conditions, and extent of social distancing

PROFITING FROM ARBITRAGE AND ODDS BIASES OF THE EUROPEAN FOOTBALL GAMBLING MARKET

A gambling market is usually described as being inefficient if there are one or more betting strategies that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This paper examines the online European football gambling market based on 14 European football leagues over a period of seven years, from season 2005/06 to 2011/12 inclusive, and takes into consideration the odds provided by numerous bookmaking firms. Contrary to common misconceptions, we demonstrate that the accuracy of bookmakers' odds has not improved over this period. More importantly, our results question market efficiency by demonstrating high profitability on the basis of consistent odds biases and numerous arbitrage opportunities

Calculating the Likelihood Ratio for Multiple Pieces of Evidence

27 pages, 12 figures27 pages, 12 figuresWhen presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA comes from the suspect', and is defined as the probability of the evidence if the hypothesis is true divided by the probability of the evidence if the hypothesis is false. The LR is a valid measure of probative value because, by Bayes Theorem, the higher the LR is, the more our belief in the probability the hypothesis is true increases after observing the evidence. The LR is popular because it measures the probative value of evidence without having to make any explicit assumptions about the prior probability of the hypothesis. However, whereas the LR can in principle be easily calculated for a distinct single piece of evidence that relates directly to a specific hypothesis, in most realistic situations 'the evidence' is made up of multiple dependent components that impact multiple different hypotheses. In such situations the LR cannot be calculated . However, once the multiple pieces of evidence and hypotheses are modelled as a causal Bayesian network (BN), any relevant LR can be automatically derived using any BN software application

Fallacy of Federalism in Foreign Affairs: State and Local Foreign Policy Trade Restrictions, The

State and local foreign trade restrictions represent the convergence of two main threads of the globalization of the U.S. experience, and raise a serious challenge to the historic allocation of foreign policy responsibility to the federal government. The internationalization of state and local economies is the first thread. The second is the heightened efforts of state, city and county governments to play a role in foreign affairs and foreign policy decisions. Where they meet finds states and cities using their new-found international economic leverage to influence not only United States\u27 foreign policy, but the domestic policies of foreign nations as well. At a time when economic sanctions are emerging as the weapons of choice in maintaining international order, these state and local efforts threaten to undermine the authority and effectiveness of United States\u27 foreign policy