A. P. Dawid

Independence properties of directed markov fields

We investigate directed Markov fields over finite graphs without positivity assumptions on the densities involved. A criterion for conditional independence of two groups of variables given a third is given and named as the directed, global Markov property. We give a simple proof of the fact that the directed, local Markov property and directed, global Markov property are equivalent and – in the case of absolute continuity w. r. t. a product measure – equivalent to the recursive factorization of densities. It is argued that our criterion is easy to use, it is sharper than that given by Kiiveri, Speed, and Carlin and equivalent to that of Pearl. It follows that our criterion cannot be sharpened.

The Well-Calibrated Bayesian

Abstract Suppose that a forecaster sequentially assigns probabilities to events. He is well calibrated if, for example, of those events to which he assigns a probability 30 percent, the long-run proportion that actually occurs turns out to be 30 percent. We prove a theorem to the effect that a coherent Bayesian expects to be well calibrated, and consider its destructive implications for the theory of coherence.

Causal Inference without Counterfactuals

Abstract A popular approach to the framing and answering of causal questions relies on the idea of counterfactuals: Outcomes that would have been observed had the world developed differently; for example, if the patient had received a different treatment. By definition, one can never observe such quantities, nor assess empirically the validity of any modeling assumptions made about them, even though ones conclusions may be sensitive to these assumptions. Here I argue that for making inference about the likely effects of applied causes, counterfactual arguments are unnecessary and potentially misleading. An alternative approach, based on Bayesian decision analysis, is presented. Properties of counterfactuals are relevant to inference about the likely causes of observed effects, but close attention then must be given to the nature and context of the query, as well as to what conclusions can and cannot be supported empirically. In particular, even in the absence of Statistical uncertainty, such inferences m...

Applications of a general propagation algorithm for probabilistic expert systems

A probabilistic expert system provides a graphical representation of a joint probability distribution which can be used to simplify and localize calculations. Jensenet al. (1990) introduced a ‘flow-propagation’ algorithm for calculating marginal and conditional distributions in such a system. This paper analyses that algorithm in detail, and shows how it can be modified to perform other tasks, including maximization of the joint density and simultaneous ‘fast retraction’ of evidence entered on several variables.

Probabilistic Expert Systems for Forensic Inference from Genetic Markers

We present a number of real and fictitious examples in illustration of a new approach to analysing complex cases of forensic identification inference. This is effected by careful restructuring of the relevant pedigrees as a Probabilistic Expert System. Existing software can then be used to perform the required inferential calculations. Specific complications which are readily handled by this approach include missing data on one or more relevant individuals, and genetic mutation. The method is particularly valuable for disputed paternity cases, but applies also to certain criminal cases.

Probabilistic expert systems for DNA mixture profiling

We show how probabilistic expert systems can be used to structure and solve complex cases of forensic identification involving DNA traces that might be mixtures of several DNA profiles. In particular, this approach can readily handle cases where the number of contributors to the mixture cannot be regarded as known in advance. The flexible modularity of the networks used also allows us to handle still more complex cases, for example where the finding of a mixed DNA trace is compounded by such features as missing individuals or the possibility of unobserved alleles.

Non-fatherhood or mutation? A probabilistic approach to parental exclusion in paternity testing

The occurrence of germline mutations at microsatellite loci poses problems in ascertaining non-fatherhood status in paternity testing. We describe the appropriate probabilistic analysis for computing the likelihood ratio in favour of paternity while allowing for mutation, for all 18 relevant combinations of seemingly incompatible parental genotypes. We allow arbitrary and possibly different mutation rates in paternal and maternal germlines. We describe a stationary mutation model for expressing the required allele-specific transition mutation rates in terms of overall mutation rates, and compare the likelihood ratios calculated from this and from other mutation models suggested in the literature. We also show how to derive an upper bound on the likelihood ratio, depending only on the overall mutation rate.

On testing the validity of sequential probability forecasts

Events are observed sequentially, and at each stage a probability for the next event is assessed. We consider the relationship between the sequence of probability forecasts and the sequence of outcomes. We argue that the forecasts may be considered “empirically valid” when both these sequences are consistent with a common joint distribution for the events. To aid in assessing validity, we introduce various test statistics that measure, in a natural way, the empirical performance of the probability forecasts in the light of the outcomes obtained. It is shown that under the null hypothesis of forecast validity, such statistics will, after suitable normalization, have a Standard normal (or chi-squared) distribution, virtually irrespective of the common joint distribution supposed to underlie both sequences.

Probability, Causality and the Empirical World: A Bayes–de Finetti–Popper– Borel Synthesis

This article expounds a philosophical approach to Probability and Causality: a synthesis of the personalist Bayesian views of de Finetti and Popper’s falsificationist programme. A falsification method for probabilistic or causal theories, based on “Borel criteria,” is described. It is argued that this minimalist approach, free of any distracting metaphysical inputs, provides the essential support required for the conduct and advance of Science.

Likelihood and Bayesian Inference from Selectively Reported Data

Abstract If the reported data of an experiment have been subject to selection, then inference from such data should be modified accordingly. We investigate the modification required to the face-value likelihood. In particular, we derive conditions under which no modification is necessary and the data can be taken at face value.