On roads showing significant violations of posted speed limits, one measure of the safety effect of speeding is the difference between the road's actual accident count and the count that would have occurred if the posted speed limit had been strictly obeyed. An estimate of this accident reduction can be had by computing the probability that speeding was a necessary condition for each of set of accidents. This is an instance of assessing individual probabilities of causation, which is generally not possible absent prior knowledge of causal structure. For traffic accidents such prior knowledge is often available and this paper illustrates how, for a commonly occurring class of vehicle/pedestrian accidents, approaches to uncertainty and causal analyses appearing in the accident reconstruction literature can be unified using Bayesian networks. Measured skidmarks, pedestrian throw distances, and pedestrian injury severity are treated as evidence, and using the Gibbs Sampling routine BUGS, the posterior probability distribution over exogenous variables, such as the vehicle's initial speed, location, and driver reaction time, is computed. This posterior distribution is then used to compute the "probability of necessity" for speeding.

It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of "instrumental variables" sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or trek can be computed directly from the parameter values associated with each edge in the path or trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.These properties are exploited in search procedures. It is also known that properties (2)-(5) do not hold for all Bayes nets with binary variables. We show that (1) holds for all Bayes nets with binary variables and (5) holds for all singly trek-connected Bayes nets of that kind. We further show that all five properties hold for Bayes nets with any DAG and binary variables parameterized with noisy-or and noisy-and gates.

It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete data and a given node ordering this division is a myth, by showing that cross entropy methods for checking conditional independence are mathematically identical to methods based upon discriminating between models by their overall goodness-of-fit logarithmic scores.

In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used to estimate how the distribution of an effect will respond to a manipulation of its causes, even in the presence of unmeasured common causes (confounders). In typical instrumental variable estimation, instruments are chosen based on domain knowledge. There is currently no statistical test for validating a variable as an instrument. In this paper, we introduce the concept of semi-instrument, which generalizes the concept of instrument. We show that in the framework of additive models, under certain conditions, we can test whether a variable is semi-instrumental. Moreover, adding some distribution assumptions, we can test whether two semi-instruments are instrumental. We give algorithms to estimate the p-value that a random variable is semi-instrumental, and the p-value that two semi-instruments are both instrumental. These algorithms can be used to test the experts' choice of instruments, or to identify instruments automatically.

We present two sampling algorithms for probabilistic confidence inference in Bayesian networks. These two algorithms (we call them AIS-BN-mu and AIS-BN-sigma algorithms) guarantee that estimates of posterior probabilities are with a given probability within a desired precision bound. Our algorithms are based on recent advances in sampling algorithms for (1) estimating the mean of bounded random variables and (2) adaptive importance sampling in Bayesian networks. In addition to a simple stopping rule for sampling that they provide, the AIS-BN-mu and AIS-BN-sigma algorithms are capable of guiding the learning process in the AIS-BN algorithm. An empirical evaluation of the proposed algorithms shows excellent performance, even for very unlikely evidence.

We propose a new directed graphical representation of utility functions, called UCP-networks, that combines aspects of two existing graphical models: generalized additive models and CP-networks. The network decomposes a utility function into a number of additive factors, with the directionality of the arcs reflecting conditional dependence of preference statements - in the underlying (qualitative) preference ordering - under a {em ceteris paribus} (all else being equal) interpretation. This representation is arguably natural in many settings. Furthermore, the strong CP-semantics ensures that computation of optimization and dominance queries is very efficient. We also demonstrate the value of this representation in decision making. Finally, we describe an interactive elicitation procedure that takes advantage of the linear nature of the constraints on "`tradeoff weights" imposed by a UCP-network. This procedure allows the network to be refined until the regret of the decision with minimax regret (with respect to the incompletely specified utility function) falls below a specified threshold (e.g., the cost of further questioning.

An instrument is a random variable thatallows the identification of parameters inlinear models when the error terms arenot uncorrelated.It is a popular method used in economicsand the social sciences that reduces theproblem of identification to the problemof finding the appropriate instruments.Few years ago, Pearl introduced a necessarytest for instruments that allows the researcher to discard those candidatesthat fail the test.In this paper, we make a detailed study of Pearl's test and the general model forinstruments. The results of this studyinclude a novel interpretation of Pearl'stest, a general theory of instrumentaltests, and an affirmative answer to aprevious conjecture. We also presentnew instrumentality tests for the casesof discrete and continuous variables.

This paper presents a sound and completecalculus for causal relevance, based onPearl's functional models semantics.The calculus consists of axioms and rulesof inference for reasoning about causalrelevance relationships.We extend the set of known axioms for causalrelevance with three new axioms, andintroduce two new rules of inference forreasoning about specific subclasses ofmodels.These subclasses give a more refinedcharacterization of causal models than the one given in Halpern's axiomatizationof counterfactual reasoning.Finally, we show how the calculus for causalrelevance can be used in the task ofidentifying causal structure from non-observational data.

The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.

Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the conditioning is either based on the minimum, or the product operator. Benferhat et al. (1999) have investigated the connections between min-based graphs and possibilistic logic bases (made of classical formulas weighted in terms of certainty). This paper deals with a more difficult issue : the product-based graphical representations of possibilistic bases, which provides an easy structural reading of possibilistic bases. Moreover, this paper also provides another reading of possibilistic bases in terms of comparative preferences of the form "in the context p, q is preferred to not q". This enables us to explicit preferences underlying a set of goals with different levels of priority.