39,858 research outputs found
Local robustness of Bayesian parametric inference and observed likelihoods
Here a new class of local separation measures over prior densities is
studied and their usefulness for examining prior to posterior robustness
under a sequence of observed likelihoods, possibly erroneous, illustrated.
It is shown that provided an approximation to a prior distribution satisfies certain mild smoothness and tail conditions then prior to posterior
inference for large samples is robust, irrespective of whether the priors
are grossly misspecified with respect to variation distance and irrespective of the form or the validity of the observed likelihood. Furthermore
it is usually possible to specify error bounds explicitly in terms of statistics associated with the posterior associated with the approximating prior
and asumed prior error bounds. These results apply in a general multivariate setting and are especially easy to interpret when prior densities
are approximated using standard families or multivariate prior densities
factorise
Equivalence Classes of Staged Trees
In this paper we give a complete characterization of the statistical
equivalence classes of CEGs and of staged trees. We are able to show that all
graphical representations of the same model share a common polynomial
description. Then, simple transformations on that polynomial enable us to
traverse the corresponding class of graphs. We illustrate our results with a
real analysis of the implicit dependence relationships within a previously
studied dataset.Comment: 18 pages, 4 figure
Tree cumulants and the geometry of binary tree models
In this paper we investigate undirected discrete graphical tree models when
all the variables in the system are binary, where leaves represent the
observable variables and where all the inner nodes are unobserved. A novel
approach based on the theory of partially ordered sets allows us to obtain a
convenient parametrization of this model class. The construction of the
proposed coordinate system mirrors the combinatorial definition of cumulants. A
simple product-like form of the resulting parametrization gives insight into
identifiability issues associated with this model class. In particular, we
provide necessary and sufficient conditions for such a model to be identified
up to the switching of labels of the inner nodes. When these conditions hold,
we give explicit formulas for the parameters of the model. Whenever the model
fails to be identified, we use the new parametrization to describe the geometry
of the unidentified parameter space. We illustrate these results using a simple
example.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ338 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Directed expected utility networks
A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, such as, for example, conditional utility independence and generalized additive independence, have more recently started to appear. In this paper, we define a new graphical model, called a directed expected utility network, whose edges depict both probabilistic and utility conditional independences. These embed a very flexible class of utility models, much larger than those usually conceived in standard influence diagrams. Our graphical representation and various transformations of the original graph into a tree structure are then used to guide fast routines for the computation of a decision problemâs expected utilities. We show that our routines generalize those usually utilized in standard influence diagramsâ evaluations under much more restrictive conditions. We then proceed with the construction of a directed expected utility network to support decision makers in the domain of household food security
The Dependence of Routine Bayesian Model Selection Methods on Irrelevant Alternatives
Bayesian methods - either based on Bayes Factors or BIC - are now widely used
for model selection. One property that might reasonably be demanded of any
model selection method is that if a model is preferred to a model
, when these two models are expressed as members of one model class
, this preference is preserved when they are embedded in a
different class . However, we illustrate in this paper that with
the usual implementation of these common Bayesian procedures this property does
not hold true even approximately. We therefore contend that to use these
methods it is first necessary for there to exist a "natural" embedding class.
We argue that in any context like the one illustrated in our running example of
Bayesian model selection of binary phylogenetic trees there is no such
embedding
Conditionally externally Bayesian pooling operators in chain graphs
We address the multivariate version of Frenchâs group decision problem where the m members of a group, who are jointly responsible for the decisions they should make, wish to combine their beliefs about the possible values of n random variables into the group consensus probability distribution. We shall assume the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed partially complete chain graph (PCG) we define in the paper. However, the members diverge about the actual conditional probability distributions for the variables in the common PCG. The combination algorithm we suggest they adopt is one which demands, at least on learning information which is common to the members and which preserves the originally agreed PCG structure, that the pools of conditional
distributions associated with the PCG are externally Bayesian (EB). We propose a characterization for such conditionally EB (CEB) poolings which is more general and flexible than the characterization proposed by Genest, McConway and Schervish. In particular, such a generalization allows the weights attributed to the joint probability assessments of different individuals in the pool to differ across the distinct components of each joint density. We show that the groupâs commitment to being CEB on chain elements can be accomplished by the group being EB on the whole PCG
when the group also agrees to perform the conditional poolings in an ordering compatible with evidence propagation in the graph
Bayesian decision support for complex systems with many distributed experts
Complex decision support systems often consist of component modules which, encoding the judgements of panels of domain experts, describe a particular sub-domain of the overall system. Ideally these modules need to be pasted together to provide a comprehensive picture of the whole process. The challenge of building such an integrated system is that, whilst the overall qualitative features are common knowledge to all, the explicit forecasts and their associated uncertainties are only expressed individually by each panel, resulting from its own analysis. The structure of the integrated system therefore needs to facilitate the coherent piecing together of these separate evaluations. If such a system is not available there is a serious danger that this might drive decision makers to incoherent and so indefensible policy choices. In this paper we develop a graphically based framework which embeds a set of conditions, consisting of the agreement usually made in practice of certain probability and utility models, that, if satisfied in a given context, are sufficient to ensure the composite system is truly coherent. Furthermore, we develop new message passing algorithms entailing the transmission of expected utility scores between the panels, that enable the uncertainties within each module to be fully accounted for in the evaluation of the available alternatives in these composite systems
Using graphical models and multi-attribute utility theory for probabilistic uncertainty handling in large systems, with application to nuclear emergency management
Although many decision-making problems involve uncertainty, uncertainty handling within large decision support systems (DSSs) is challenging. One domain where uncertainty handling is critical is emergency response management, in particular nuclear emergency response, where decision making takes place in an uncertain, dynamically changing environment. Assimilation and analysis of data can help to reduce these uncertainties, but it is critical to do this in an efficient and defensible way. After briefly introducing the structure of a typical DSS for nuclear emergencies, the paper sets up a theoretical structure that enables a formal Bayesian decision analysis to be performed for environments like this within a DSS architecture. In such probabilistic DSSs many input conditional probability distributions are provided by different sets of experts overseeing different aspects of the emergency. These probabilities are then used by the decision maker (DM) to find her optimal decision. We demonstrate in this paper that unless due care is taken in such a composite framework, coherence and rationality may be compromised in a sense made explicit below. The technology we describe here builds a framework around which Bayesian data updating can be performed in a modular way, ensuring both coherence and efficiency, and provides sufficient unambiguous information to enable the DM to discover her expected utility maximizing policy
Trends in Black-White Church Integration
Historically, the separation of blacks and whites in churches was well known (Gilbreath 1995; Schaefer 2005). Even in 1968, about four years after the passage of the landmark Civil Rights Act of 1964, Dr. Martin Luther King, Jr. still said that eleven o\u27clock on Sunday is the most segregated hour of the week (Gilbreath 1995:1). His reference was to the entrenched practice of black and white Americans who worshiped separately in segregated congregations even though as Christians, their faith was supposed to bring them together to love each other as brothers and sisters. King\u27s statement was not just a casual observation. One of the few places that civil rights workers failed to integrate was churches. Black ministers and their allies were at the forefront of the church integration movement, but their stiffest opposition often came from white ministers. The irony is that belonging to the same denomination could not prevent the racial separation of their congregations. In 1964, when a group of black women civil rights activists went to a white church in St. Augustine, Florida to attend a Sunday service, the women were met by a phalanx of white people with their arms linked to keep the activists out (Bryce 2004). King\u27s classic Letter from a Birmingham Jail was a response to white ministers who criticized him and the civil rights movement after a major civil rights demonstration (King [2002])
Regulating autonomous agents facing conflicting objectives : a command and control example
UK military commanders have a degree of devolved decision
authority delegated from command and control (C2) regulators,
and they are trained and expected to act rationally and accountably. Therefore from a Bayesian perspective they should be subjective expected utility maximizers. In fact they largely appear
to be so. However when current tactical objectives conflict with
broader campaign objective there is a strong risk that fielded
commanders will lose rationality and coherence. By systematically analysing the geometry of their expected utilities, arising
from a utility function with two attributes, we demonstrate in
this paper that even when a remote C2 regulator can predict
only the likely broad shape of her agents' marginal utility functions it is still often possible for her to identify robustly those
settings where the commander is at risk of making inappropriate
decisions
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