Using Bayes' rule to define the value of evidence from syndromic surveillance

In this work we propose the adoption of a statistical framework used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial "evidence" of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence (V). Using Bayes' rule, the prior odds for an ongoing outbreak are multiplied by V to obtain the posterior odds. This approach was applied to time series on the number of horses showing clinical respiratory symptoms or neurological symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent reasoning process suitable for supporting decision makers. The value of evidence can be translated into a verbal statement, as often done in forensics or used for the production of risk maps. Furthermore, a Bayesian approach offers seamless integration of data from syndromic surveillance with results from predictive modeling and with information from other sources such as disease introduction risk assessments.

Using Bayesian networks with rule extraction to infer the risk of weed infestation in a corn-crop

This paper describes the modeling of a weed infestation risk inference system that implements a collaborative inference scheme based on rules extracted from two Bayesian network classifiers. The first Bayesian classifier infers a categorical variable value for the weed-crop competitiveness using as input categorical variables for the total density of weeds and corresponding proportions of narrow and broad-leaved weeds. The inferred categorical variable values for the weed-crop competitiveness along with three other categorical variables extracted from estimated maps for the weed seed production and weed coverage are then used as input for a second Bayesian network classifier to infer categorical variables values for the risk of infestation. Weed biomass and yield loss data samples are used to learn the probability relationship among the nodes of the first and second Bayesian classifiers in a supervised fashion, respectively. For comparison purposes, two types of Bayesian network structures are considered, namely an expert-based Bayesian classifier and a naive Bayes classifier. The inference system focused on the knowledge interpretation by translating a Bayesian classifier into a set of classification rules. The results obtained for the risk inference in a corn-crop field are presented and discussed. (C) 2009 Elsevier Ltd. All rights reserved.

The ex-Ante non-optimality of the Dempster-Schafer updating rule for ambiguous beliefs

The most widely used updating rule for non-additive probalities is the Dempster-Schafer rule. Schmeidles and Gilboa have developed a model of decision making under uncertainty based on non-additive probabilities, and in their paper “Updating Ambiguos Beliefs” they justify the Dempster-Schafer rule based on a maximum likelihood procedure. This note shows in the context of Schmeidler-Gilboa preferences under uncertainty, that the Dempster-Schafer rule is in general not ex-ante optimal. This contrasts with Brown’s result that Bayes’ rule is ex-ante optimal for standard Savage preferences with additive probabilities.

Linear Bayes policy for learning in contextual-bandits

Machine and Statistical Learning techniques are used in almost all online advertisement systems. The problem of discovering which content is more demanded (e.g. receive more clicks) can be modeled as a multi-armed bandit problem. Contextual bandits (i.e., bandits with covariates, side information or associative reinforcement learning) associate, to each specific content, several features that define the “context” in which it appears (e.g. user, web page, time, region). This problem can be studied in the stochastic/statistical setting by means of the conditional probability paradigm using the Bayes’ theorem. However, for very large contextual information and/or real-time constraints, the exact calculation of the Bayes’ rule is computationally infeasible. In this article, we present a method that is able to handle large contextual information for learning in contextual-bandits problems. This method was tested in the Challenge on Yahoo! dataset at ICML2012’s Workshop “new Challenges for Exploration & Exploitation 3”, obtaining the second place. Its basic exploration policy is deterministic in the sense that for the same input data (as a time-series) the same results are obtained. We address the deterministic exploration vs. exploitation issue, explaining the way in which the proposed method deterministically finds an effective dynamic trade-off based solely in the input-data, in contrast to other methods that use a random number generator.

Continuous opinions and discrete actions in opinion dynamics problems

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors, and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.

Imperfectly credible disinflation under endogenous time-ependent pricing

The real effects of an imperfectly credible disinflation depend critically on the extent of price rigidity. Therefore, the study of how policymakers’ credibility affects the outcome of an announced disinflation should not be dissociated from the analysis of the determinants of the frequency of price adjustments. In this paper we examine how credibility affects the outcome of a disinflation in a model with endogenous timedependent pricing rules. Both the initial degree of price ridigity, calculated optimally, and, more notably, the changes in contract length during disinflation play an important role in the explanation of the effects of imperfect credibility. We initially evaluate the costs of disinflation in a setup where credibility is exogenous, and then allow agents to use Bayes rule to update beliefs about the “type” of monetary authority that they face. In both cases, the interaction between the endogeneity of time-dependent rules and imperfect credibility increases the output costs of disinflation, but the pattern of the output path is more realistic in the case with learning.

Solving the Levins' paradox in the logistic model to the population growth

We introduce a new method to improve Markov maps by means of a Bayesian approach. The method starts from an initial map model, wherefrom a likelihood function is defined which is regulated by a temperature-like parameter. Then, the new constraints are added by the use of Bayes rule in the prior distribution. We applied the method to the logistic map of population growth of a single species. We show that the population size is limited for all ranges of parameters, allowing thus to overcome difficulties in interpretation of the concept of carrying capacity known as the Levins paradox. © Published under licence by IOP Publishing Ltd.

Estimating the probability for a protein to have a new fold: A statistical computational model

Structural genomics aims to solve a large number of protein structures that represent the protein space. Currently an exhaustive solution for all structures seems prohibitively expensive, so the challenge is to define a relatively small set of proteins with new, currently unknown folds. This paper presents a method that assigns each protein with a probability of having an unsolved fold. The method makes extensive use of protomap, a sequence-based classification, and scop, a structure-based classification. According to protomap, the protein space encodes the relationship among proteins as a graph whose vertices correspond to 13,354 clusters of proteins. A representative fold for a cluster with at least one solved protein is determined after superposition of all scop (release 1.37) folds onto protomap clusters. Distances within the protomap graph are computed from each representative fold to the neighboring folds. The distribution of these distances is used to create a statistical model for distances among those folds that are already known and those that have yet to be discovered. The distribution of distances for solved/unsolved proteins is significantly different. This difference makes it possible to use Bayes' rule to derive a statistical estimate that any protein has a yet undetermined fold. Proteins that score the highest probability to represent a new fold constitute the target list for structural determination. Our predicted probabilities for unsolved proteins correlate very well with the proportion of new folds among recently solved structures (new scop 1.39 records) that are disjoint from our original training set.

Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.

Investigating Giant (Gt) Repression in the Formation of Partially Overlapping Pair-Rule Stripes

Drosophila pair-rule genes are expressed in striped patterns with a precise order of overlap between stripes of different genes. We investigated the role of Giant (Gt) in the regulation of even-skipped, hairy, runt, and fushi tarazu stripes formed in the vicinity of Gt expression domains. In gt null embryos, specific stripes of eve, h, run, and ftz are disrupted. With an ectopic expression system, we verified that stripes affected in the mutant are also repressed. Simultaneously hybridizing gt misxpressing embryos with two pair-rule gene probes, we were able to distinguish differences in the repression of pairs of stripes that overlap extensively. Together, our results showed Gt repression roles in the regulation of two groups of partially overlapping stripes and that Gt morphogen activity is part of the mechanism responsible for the differential positioning of these stripes borders. We discuss the possibility that other factors regulate Gt stripe targets as well. Developmental Dynamics 239:2989-2999, 2010. (C) 2010 Wiley-Liss, Inc.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Violation of Kohler's rule by the magnetoresistance of a quasi-two-dimensional organic metal

The interlayer magnetoresistance of the quasi-two-dimensional metal alpha-(BEDT-TTF)(2)KHg(SCN)(4) is considered. In the temperature range from 0.5 to 10 K and for fields up to 10 T the magnetoresistance has a stronger temperature dependence than the zero-field resistance. Consequently Kohler's rule is not obeyed for any range of temperatures or fields. This means that the magnetoresistance cannot be described in terms of semiclassical transport on a single Fermi surface with a single scattering time. Possible explanations for the violations of Kohler's rule are considered, both within the framework of semiclassical transport theory and involving incoherent interlayer transport. The issues considered are similar to those raised by the magnetotransport of the cuprate superconductors. [S0163-1829(98)13219-8].

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.