Search

Summary: Semi‐supervised learning is being extensively applied to estimate classifiers from training data in which not all the labels of the feature vectors are available. We present gmmsslm, an R package for estimating the Bayes' classifier from such partially classified data in the case where the feature vector has a multivariate Gaussian (normal) distribution in each of the pre‐defined classes. Our package implements a recently proposed Gaussian mixture modelling framework that incorporates a missingness mechanism for the missing labels in which the probability of a missing label is represented via a logistic model with covariates that depend on the entropy of the feature vector. Under this framework, it has been shown that the accuracy of the Bayes' classifier formed from the Gaussian mixture model fitted to the partially classified training data can even have lower error rate than if it were estimated from the sample completely classified. This result was established in the particular case of two Gaussian classes with a common covariance matrix. Here we focus on the effective implementation of an algorithm for multiple Gaussian classes with arbitrary covariance matrices. A strategy for initialising the algorithm is discussed and illustrated. The new package is demonstrated on some real data. [ABSTRACT FROM AUTHOR]

The focus of this paper is impulse noise reduction in digital color images. The most popular noise reduction schemes are the vector median filter and its many variants that operate by minimizing the aggregate distance from one pixel to every other pixel in a chosen window. This minimizing operation determines the most confirmative pixel based on its similarity to the chosen window and replaces the central pixel of the window with the determined one. The peer group filters, unlike the vector median filters, determine a set of pixels that are most confirmative to the window and then perform filtering over the determined set. Using a set of pixels in the filtering process rather than one pixel is more helpful as it takes into account the full information of all the pixels that seemingly contribute to the signal. Hence, the peer group filters are found to be more robust to noise. However, the peer group for each pixel is computed deterministically using thresholding schemes. A wrong choice of the threshold will easily impair the filtering performance. In this paper, we propose a peer group filtering approach using principles of Bayesian probability theory and clustering. Here, we present a method to compute the probability that a pixel value is clean (not corrupted by impulse noise) and then apply clustering on the probability measure to determine the peer group. The key benefit of this proposal is that the need for thresholding in peer group filtering is completely avoided. Simulation results show that the proposed method performs better than the conventional vector median and peer group filtering methods in terms of noise reduction and structural similarity, thus validating the proposed approach. [ABSTRACT FROM AUTHOR]

Technological innovations in the materials and biological sciences ensure more consistent raw materials as production process inputs while IT improves material attribute discernment. When raw materials of two types are to be sorted, we provide a Bayesian information processing model with three parameters, one each to summarize product consistency, signals to discern raw material attributes, and incentives to correctly categorize materials. Consistency and discernment substitute when mis-categorization costs are symmetric. They can complement when mis-categorization into the prevalent type is heavily penalized. A single commodity market emerges whenever consistency is near 100 % but otherwise two may arise. A Catalyst Effect occurs whereby improvements in materials and biological technologies first increases demand for both discernment and consistency but then eliminates demand for discernment while further boosting demand for consistency. [ABSTRACT FROM AUTHOR]

Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes' rule. The degree of true belief is quantified by means of active information I + : a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent's strength of belief in a true proposition has increased in comparison with the ignorant person ( I + > 0 ), or the strength of belief in a false proposition has decreased ( I + < 0 ). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus. [ABSTRACT FROM AUTHOR]

Bayesian Reasoning is both a fundamental idea of probability and a key model in applied sciences for evaluating situations of uncertainty. Bayesian Reasoning may be defined as the dealing with, and understanding of, Bayesian situations. This includes various aspects such as calculating a conditional probability (performance), assessing the effects of changes to the parameters of a formula on the result (covariation) and adequately interpreting and explaining the results of a formula (communication). Bayesian Reasoning is crucial in several non-mathematical disciplines such as medicine and law. However, even experts from these domains struggle to reason in a Bayesian manner. Therefore, it is desirable to develop a training course for this specific audience regarding the different aspects of Bayesian Reasoning. In this paper, we present an evidence-based development of such training courses by considering relevant prior research on successful strategies for Bayesian Reasoning (e.g., natural frequencies and adequate visualizations) and on the 4C/ID model as a promising instructional approach. The results of a formative evaluation are described, which show that students from the target audience (i.e., medicine or law) increased their Bayesian Reasoning skills and found taking part in the training courses to be relevant and fruitful for their professional expertise. [ABSTRACT FROM AUTHOR]

• This study explores the multi-dimensional features of the round-trip carsharing usage pattern. • Stop time thresholds are determined by considering different rental time. • The impact of price incentives on carsharing usage is discussed. Users' usage of carsharing and parking spaces has obvious peak hours. • Hotspots in the spatial distribution of activities are identified. In recent years, the concept of carsharing is rapidly gaining popularity in China, and the round-trip carsharing has become a common mode. However, few studies have revealed the role of round-trip carsharing in users' travel. In this study, the round-trip GPS data provided by a carsharing company in Beijing, China is used to analyze the users' usage patterns based on their trip chains. Through the extraction and analysis of trip information, all trip chains are grouped into three clusters, each of which has a different usage pattern. Then the consumption features and the shared car pick-up and return time of these three patterns are discussed. Further, the Bayes' rule is used to predict the activity purpose, and the proportion and spatial distribution of different purposes are analyzed. Results reveal that the carsharing program presents multiple usage patterns to meet the different travel needs of users. Price incentives like coupons, discounts, and packages can attract more shared car trips. Users' demand for price incentives increases with longer travel distance and time. Also, users' usage of vehicles and parking spaces has obvious peak hours. The spatial distribution of user activities has distinctly different hotspots. This paper can be beneficial for operators to set a reasonable pricing plan and provide better services. [ABSTRACT FROM AUTHOR]

The general lines of Bayesian modeling (BM) in the study of perception are outlined here. The main thesis argued here is that BM works well only in the so-called secondary processes of perception, and in particular in cases of imperfect discriminability between stimuli, or when a judgment is required, or in cases of multistability. In cases of "primary processes," on the other hand, it is often arbitrary and anyway superfluous, as with the laws of Gestalt. However, it is pointed out that in these latter cases, simpler and more well-established methodologies already exist, such as signal detection theory and individual choice theory. The frequent recourse to arbitrary values of a priori probabilities is also open to question. [ABSTRACT FROM AUTHOR]

• A close-to-ideal performance is achieved for gait-based gender classification. • The robust design of the proposed method allows it to work with occluded frames. • Elliptic Fourier descriptors are explored for an alternative feature set. • LDA with Bayes' rule is taken as an alternative to SVM for classification. • The CASIA-B and TUM-GAID datasets are considered for experimental evaluation. The incorporation of soft biometrics can significantly increase the performance of hard biometric systems. Gender is found to be the most popular soft biometric that can be derived from human gait. The state of the art produces accuracies up to 98% but are constrained by the necessity of requiring a complete gait cycle to function properly. We propose to remove this requirement using pose-based voting (PBV) – a method which treats every frame as a labeled instance. Linear discriminant analysis (LDA) is used in conjunction with the Bayes' rule for classification as an alternative to the popular support vector machine (SVM). The robust design of this technique facilitates the system to cope with partially occluded gait cycles with minimal loss in classification accuracy. Furthermore, when multiple cycles are taken to account, the error becomes negligibly small. We also investigate the applicability of elliptic Fourier descriptors and and depth gait histograms for the gait-based gender classification problem. The efficiency of our approach is evaluated using all view angles of the CASIA-B gait database and the TUM-GAID database under prescribed test conditions. [ABSTRACT FROM AUTHOR]

Structural monitoring and control utilize vibration measurements acquired by a sensor network. Combined empirical and analytical virtual sensing is introduced to estimate full-field dynamic response of a structure using a limited number of sensors. Bayesian empirical virtual sensing technique is developed to obtain less noisy estimates of sensor data. Then, analytical virtual sensing utilizes the expansion algorithm to compute the full-field response. If the sensor noise is known, virtual sensors are more accurate than the corresponding physical measurements with any number of sensors in the network. Often, the measurement error has to be estimated. The upper bound of the sensor noise variance is derived, and the effect of the noise estimation error on the accuracy of virtual sensors is studied. Numerical simulations are performed for a structure subject to unknown random excitation in order to validate the proposed virtual sensing algorithms. Displacement and strain sensor networks with different numbers of sensors and different noise models are studied. [ABSTRACT FROM AUTHOR]

Highlights • We show what incidence/prevalence a disease can have when all monitoring rounds return only negative samples. • Samples repeated in time are properly accounted for using a simple epidemic model. • An approximation of the sampling model is provided for practical use. • It is exemplified deriving appropriate monitoring programs for 3 epidemics. Abstract Monitoring for disease requires subsets of the host population to be sampled and tested for the pathogen. If all the samples return healthy, what are the chances the disease was present but missed? In this paper, we developed a statistical approach to solve this problem considering the fundamental property of infectious diseases: their growing incidence in the host population. The model gives an estimate of the incidence probability density as a function of the sampling effort, and can be reversed to derive adequate monitoring patterns ensuring a given maximum incidence in the population. We then present an approximation of this model, providing a simple rule of thumb for practitioners. The approximation is shown to be accurate for a sample size larger than 20, and we demonstrate its use by applying it to three plant pathogens: citrus canker, bacterial blight and grey mould. [ABSTRACT FROM AUTHOR]

Abstract In this study, impact of initial ensembles on posterior distribution of ensemble-based assimilation methods is statistically analyzed. Along with, sampling performance as well as uncertainty quantification of these methods are compared in terms of their ability to accurately and consistently evaluate unknown reservoir model parameters and reservoir future performance. For this purpose, a synthetic test problem, which is a small but highly nonlinear reservoir model under two-phase flow, is utilized. Subsequently, different initial ensemble sets are considered and are updated through the assimilation process performed on the test problem using ensemble-based assimilation methods. Afterwards, consistency of the updated ensemble sets of permeability field as well as consistency of the predicted ensemble sets of cumulative water production have been assessed to reveal dependence of assimilation methods to the initial ensembles. Results of multi-sample hypothesis tests clearly disclose the inconsistencies between different updated ensemble sets of permeability field, and also between different predicted ensemble sets of cumulative water production. This is probably due to spurious correlations among the updated ensemble members within each set. Furthermore, the effects of ensemble size and type of the observation data on the associated inconsistency are investigated. Highlights • Performance of the ensemble-based assimilation methods is compared. • Dependence of assimilation methods to initial ensemble is examined. • Hypothesis tests are used to disclose inconsistency between different ensemble sets. • Effects of ensemble size and observation type on the inconsistency are analyzed. • A synthetic 1D reservoir model is considered for assessment purposes. [ABSTRACT FROM AUTHOR]

Summary: This contribution shows a simple implementation of Monte Carlo simulation method when presenting Bayes' rule. The implementation is carried out in the environment of Microsoft Excel spreadsheets by means of a generator of random numbers. The empiric results gained by simulation serve to confirm the correctness of the chosen procedures in calculations using Bayes' formula. [ABSTRACT FROM AUTHOR]

The kernel Bayes' rule has been proposed as a nonparametric kernelbased method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the way of incorporating the prior in the kernel Bayes' rule is unnatural. In particular, we show that under some reasonable conditions, the posterior in the kernel Bayes' rule is completely unaffected by the prior, which seems to be irrelevant in the context of Bayesian inference. We consider that this phenomenon is in part due to the fact that the assumptions in the kernel Bayes' rule do not hold in general. [ABSTRACT FROM AUTHOR]

The evidential basis for disease management decision making is provided by data relating to risk factors. The decision process involves an assessment of the evidence leading to taking (or refraining from) action on the basis of a prediction. The primary objective of the decision process is to identify-at the time the decision is made-the control action that provides the best predicted end-of-season outcome, calculated in terms of revenue or another appropriate metric. Data relating to disease risk factors may take a variety of forms (e.g., continuous, discrete, categorical) on measurement scales in a variety of units. Log10-likelihood ratios provide a principled basis for the accumulation of evidence based on such data and allow predictions to be made via Bayesian updating of prior probabilities. [ABSTRACT FROM AUTHOR]

The quality of water of the river has a significant impact on human population and livestock in basin area. Six water quality indicators are monitored from the gauging stations of Brahmani River to assess the changing trends in the quality of water. The conventional Aggregative Index Evaluation method is applied to know the overall water quality index for its intended use. Further, in this study, Bayes’ rule is applied for comprehensive assessment. The likelihood estimates are obtained from the normal distribution and is pre-owned for posterior probability calculation through Bayes’ rule. Finally, the indicator weights are estimated by Shannon’s entropy weight method. The consequences of analysis specified that the indicator, CODMn, is affecting the quality of water more in Panposh downstream. Biological oxygen demand, TA as CaCO3, NH4–N and Nitrate-N are closely related to domestic pollution and agricultural non-point source pollution. The overall quality of water is improved during dry seasons than during wet seasons due to the dilution of pollutants. Comprehensive evaluation indicates that the water is acceptable for second grade surface source protection zones for centralised drinking water. [ABSTRACT FROM PUBLISHER]

The orbitofrontal cortex (OFC) has been implicated in both the representation of "state," in studies of reinforcement learning and decision making, and also in the representation of schemas,' in studies of episodic memory. Both of these cognitive constructs require a similar inference about the underlying situation or "latent cause" that generates our observations at any given time. The statistically optimal solution to this inference problem is to use Bayes' rule to compute a posterior probability distribution over latent causes. To test whether such a posterior probability distribution is represented in the OFC, we tasked human participants with inferring a probability distribution over four possible latent causes, based on their observations. Using fMRI pattern similarity analyses, we found that BOLD activity in the OFC is best explained as representing the (log-transformed) posterior distribution over latent causes. Furthermore, this pattern explained OFC activity better than other task-relevant alternatives, such as the most probable latent cause, the most recent observation, or the uncertainty over latent causes. [ABSTRACT FROM AUTHOR]

We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use themuch criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our set-up can and should be interpreted as a generalization of the classicalmethodology, allowingmore flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice. [ABSTRACT FROM AUTHOR]

Uniparental genetic markers, mitochondrial DNA (mtDNA) and Y chromosomal DNA, are widely used for the inference of human ancestry. However, the resolution of ancestral origins based on mtDNA haplotypes is limited by the fact that such haplotypes are often found to be distributed across wide geographical regions. We have addressed this issue here by combining two sources of ancestry information that have typically been considered separately: historical records regarding population origins and genetic information on mtDNA haplotypes. To combine these distinct data sources, we applied a Bayesian approach that considers historical records, in the form of prior probabilities, together with data on the geographical distribution of mtDNA haplotypes, formulated as likelihoods, to yield ancestry assignments from posterior probabilities. This combined evidence Bayesian approach to ancestry assignment was evaluated for its ability to accurately assign sub-continental African ancestral origins to Afro-Colombians based on their mtDNA haplotypes. We demonstrate that the incorporation of historical prior probabilities via this analytical framework can provide for substantially increased resolution in sub-continental African ancestry assignment for members of this population. In addition, a personalized approach to ancestry assignment that involves the tuning of priors to individual mtDNA haplotypes yields even greater resolution for individual ancestry assignment. Despite the fact that Colombia has a large population of Afro-descendants, the ancestry of this community has been understudied relative to populations with primarily European and Native American ancestry. Thus, the application of the kind of combined evidence approach developed here to the study of ancestry in the Afro-Colombian population has the potential to be impactful. The formal Bayesian analytical framework we propose for combining historical and genetic information also has the potential to be widely applied across various global populations and for different genetic markers. [ABSTRACT FROM AUTHOR]

In recent years, “reproducibility” has emerged as a key factor in evaluating x applications of statistics to the biomedical sciences, for example, learning predictors of disease phenotypes from high-throughput “omics” data. In particular, “validation” is undermined when error rates on newly acquired data are sharply higher than those originally reported. More precisely, when data are collected fromm“studies” representing possibly different subphenotypes, more generally different mixtures of subphenotypes, the error rates in cross-study validation (CSV) are observed to be larger than those obtained in ordinary randomized cross-validation (RCV), although the “gap” seems to close asmincreases. Whereas these findings are hardly surprising for a heterogenous underlying population, this discrepancy is then seen as a barrier to translational research. We provide a statistical formulation in the large-sample limit: studies themselves are modeled as components of a mixture and all error rates are optimal (Bayes) for a two-class problem. Our results cohere with the trends observed in practice and suggest what is likely to be observed with large samples and consistent density estimators, namely, that the CSV error rate exceeds the RCV error rates for anym, the latter (appropriately averaged) increases withm, and both converge to the optimal rate for the whole population. [ABSTRACT FROM PUBLISHER]

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities-especially the ones that involve Bayes' rule-with the help of such traditional approaches as formula use or conversion to natural frequencies. The truth table approach is an alternative method for explaining the concept and calculation procedure of conditional probability and Bayes' rule. [ABSTRACT FROM AUTHOR]

To most biologists, the exact meaning of confidence intervals is very difficult to grasp, though such intervals are shown in many of our papers as measures of data variability. One of the reasons lies in the fact that the traditional way of teaching confidence intervals suggests much more than they actually deliver. Therefore, working with biologists, statistics teachers need a convincing way of introducing this topic and, to my experience, Monte Carlo simulation offers some opportunities. However, understanding the crude meaning of frequentist confidence intervals may be disappointing for biologists, who might be seduced by the intuitive appeal of Bayesian credible intervals. [ABSTRACT FROM AUTHOR]

We consider approaches to explanation within the cognitive sciences that begin with Marr's computational level (e.g., purely Bayesian accounts of cognitive phenomena) or Marr's implementational level (e.g., reductionist accounts of cognitive phenomena based only on neural-level evidence) and argue that each is subject to fundamental limitations which impair their ability to provide adequate explanations of cognitive phenomena. For this reason, it is argued, explanation cannot proceed at either level without tight coupling to the algorithmic and representation level. Even at this level, however, we argue that additional constraints relating to the decomposition of the cognitive system into a set of interacting subfunctions (i.e., a cognitive architecture) are required. Integrated cognitive architectures that permit abstract specification of the functions of components and that make contact with the neural level provide a powerful bridge for linking the algorithmic and representational level to both the computational level and the implementational level. [ABSTRACT FROM AUTHOR]

This paper focuses on the update step of Bayesian nonlinear filtering. We first derive the unscented Gaussian likelihood approximation filter (UGLAF), which provides a Gaussian approximation to the likelihood by applying the unscented transformation to the inverse of the measurement function. The UGLAF approximation is accurate in the cases where the unscented Kalman filter (UKF) is not and the other way round. As a result, we propose the adaptive UGLAF (AUGLAF), which selects the best approximation to the posterior (UKF or UGLAF) based on the Kullback–Leibler divergence. This enables AUGLAF to outperform both the UKF and UGLAF. [ABSTRACT FROM AUTHOR]

Philosophers have argued that people ought to change their graded beliefs via Bayes' rule. Recent work in psychology indicates that people sometimes violate that rule by attending to explanatory factors. Results from computational modeling suggest that such violations may actually be rational. [ABSTRACT FROM AUTHOR]

The concept of indicated prevention has proliferated in psychiatry, and accumulating evidence suggests that it may indeed be possible to prevent or delay the onset of a first episode of psychosis though adequate interventions in individuals deemed at clinical high risk (CHR) for such an event. One challenge undermining these efforts is the relatively poor predictive accuracy of clinical assessments used in practice for CHR individuals, often leading to diagnostic and therapeutic uncertainty reflected in clinical guidelines promoting a 'watch and wait' approach to CHR patients. Using data from published studies, and employing predictive models based on the odds-ratio form of Bayes' rule, we simulated scenarios where clinical interview, neurocognitive testing, structural magnetic resonance imaging and electrophysiology are part of the initial assessment process of a CHR individual (extended diagnostic approach). Our findings indicate that for most at-risk patients, at least three of these assessments are necessary to arrive at a clinically meaningful differentiation into high- intermediate-, and low-risk groups. In particular, patients with equivocal results in the initial assessments require additional diagnostic testing to produce an accurate risk profile forming part of the comprehensive initial assessment. The findings may inform future research into reliable identification and personalized therapeutic targeting of CHR patients, to prevent transition to full-blown psychosis. [ABSTRACT FROM AUTHOR]

A soft sensor predicts the values of some process variable y that is difficult to measure. To maintain the predictive ability of a soft sensor model, adaptation mechanisms are applied to soft sensors. However, even these adaptive soft sensors cannot predict the y-values of various process states in chemical plants, and it is difficult to ensure the predictive ability of such models on a long-term basis. Therefore, we propose a method that combines online support vector regression (OSVR) with an ensemble learning system to adapt to nonlinear and time-varying changes in process characteristics and various process states in a plant. Several OSVR models, each of which has an adaptation mechanism and is updated with new data, predict y-values. A final predicted y-value is calculated based on those predicted y-values and Bayes' rule. We analyze a numerical dataset and two real industrial datasets, and demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights: [•] We develop a probability-based online learning method for fuzzy inference systems. [•] Our online learning is built upon the statistical concept of maximum a posteriori. [•] Experiments show that our method can balance between model accuracy and simplicity. [•] Empirical results show our model can handle large and nonstationary data stream. [Copyright &y& Elsevier]

Drinking water distribution system models have been increasingly utilized in the development and implementation of contaminant warning systems. This study proposes a Bayesian approach for probabilistic contamination source identification using a beta-binomial conjugate pair framework to identify contaminant source locations and times and compares the performance of this algorithm to previous work based on a Bayes' rule approach. The proposed algorithm is capable of directly assigning a probability to a potential source location and updating the probability through the use of a backtracking algorithm and Bayesian statistics. The evaluation of the performance associated with the two algorithms was conducted by a simple comparison, as well as a simulation study in terms of a conservative chemical intrusion event through both a small skeletonized network and a large all-pipe distribution system network. Results from the simple comparison showed that the beta-binomial approach was more responsive to changes in sensor signals. In terms of intrusion events, the beta-binomial approach was more selective than the Bayes' rule approach in identifying potential source node-time pairs and provided the flexibility to account for multiple possible injection locations. [ABSTRACT FROM AUTHOR]

Some say that researchers who study humans are locked in to frameworks of epistemic assumptions from which there can be no escape. We explain, on the contrary, how researchers who disagree may nevertheless reconcile their differences. Freedom from the epistemic dungeon is made possible by practices that convert beliefs into testable hypotheses, which are then tested. Such practices are the engines of scientific progress. To clarify misunderstandings about practices of hypothesis testing, we discuss Bayes' rule, a mathematically perfect algebra for belief revision. To illustrate both the benefits and inevitable limitations of scientific research on religion, we work through the details of a recent national questionnaire study that revealed five different types of supernatural believers. [ABSTRACT FROM AUTHOR]

A kernel method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The posterior is likewise an RKHS mean of a weighted sample. The estimator for the expectation of a function of the posterior is derived, and rates of consistency are shown. Some representative applications of the kernel Bayes' rule are presented, including Bayesian computation without likelihood and filtering with a nonparametric state-space model. [ABSTRACT FROM AUTHOR]

We frame behavior in classical conditioning experiments as the product of normative statistical inference. According to this theory, animals learn an internal model of their environment from experience. The basic building blocks of this internal model are latent causes-explanatory constructs inferred by the animal that partition observations into coherent clusters. Generalization of conditioned responding from one cue to another arises from the animal's inference that the cues were generated by the same latent cause. Through a wide range of simulations, we demonstrate where the theory succeeds and where it fails as a general account of classical conditioning. [ABSTRACT FROM AUTHOR]

We devise a filtering algorithm to approximate the first two moments of the posterior probability density function (PDF). The novelties of the algorithm are in the update step. If the likelihood has a bounded support, we can use a modified prior distribution that meets Bayes' rule exactly. Applying a Kalman filter (KF) to the modified prior distribution, referred to as truncated Kalman filter (TKF), can vastly improve the performance of the conventional Kalman filter, particularly when the measurements are informative relative to the prior. The application of the TKF to practical problems in which the measurement noise PDF has unbounded support is achieved by imposing several approximating assumptions which are valid only when the measurements are informative. This implies that we adaptively choose between an approximation to the KF or the TKF according to the information provided by the measurement. The resulting algorithm based on the unscented transformation is referred to as truncated unscented KF. [ABSTRACT FROM PUBLISHER]

This paper presents a novel iterative active learning (AL) technique aimed at defining effective multitemporal training sets to be used for the supervised detection of land-cover transitions in a pair of remote sensing images acquired on the same area at different times. The proposed AL technique is developed in the framework of the Bayes' rule for compound classification. At each iteration, it selects the pair of spatially aligned unlabeled pixels in the two images that are classified with the maximum uncertainty. These pixels are then labeled by an external supervisor and included in the training set. The uncertainty of a pair of pixels is assessed by the joint entropy defined by considering two possible different simplifying assumptions: 1) class-conditional independence and 2) temporal independence between multitemporal images. Accordingly, different algorithms are introduced. The proposed joint-entropy-based AL algorithms for compound classification are compared with each other and with a marginal-entropy-based AL technique (in which the entropy is computed separately on single-date images) applied to the postclassification comparison method. The experimental results obtained on two multispectral and multitemporal data sets show the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Abstract: Introducing adaptive metric has been shown to improve the results of distance-based classification algorithms. Existing methods are often computationally intensive, either in the training or in the classification phase. We present a novel algorithm that we call Cluster-Based Adaptive Metric (CLAM) classification. It first determines the number of clusters in each class of a training set and then computes the parameters of a Mahalanobis distance for each cluster. The derived Mahalanobis distances are then used to estimate the probability of cluster- and, subsequently, class-membership. We compare the proposed algorithm with other classification algorithms using 10 different data sets. The proposed CLAM algorithm is as effective as other adaptive metric classification algorithms yet it is simpler to use and in many cases computationally more efficient. [Copyright &y& Elsevier]

Abstract: In the study of perceptual organization, the Occamian simplicity principle (which promotes efficiency) and the Helmholtzian likelihood principle (which promotes veridicality) have been claimed to be equivalent. Proposed models of these principles may well yield similar outcomes (especially in everyday situations), but as argued here, claims that the principles are equivalent confused subjective probabilities (which are used in Bayesian models of the Occamian simplicity principle) and objective probabilities (which are needed in Bayesian models of the Helmholtzian likelihood principle). Furthermore, Occamian counterparts of Bayesian priors and conditionals have led to another confusion, which seems to have been triggered by a dual role of regularity in perception. This confusion is discussed by contrasting complete and incomplete Occamian approaches to perceptual organization. [Copyright &y& Elsevier]

It is investigated how implementing the likelihood ratio (LR) framework works out in the case of camera identification based on image-sensor-specific noise patterns. Two typical case scenarios are considered, one with images of low quality andthe other with images of high quality. In both cases, it is possible to obtain statistical distributions having a good fit with the reference data both for ‘matching’ and for ‘non-matching’ comparisons, and LRs are determined. It turns out that if the reference data are well separated, in the case of ‘matching’ images/cameras, the statistical fit of the distribution for ‘non-matches’ is constantly evaluated in a range where there is a lack of reference data. Because of this extrapolation issue, the LRsthat emerge are not reliable. This is not a problem that is unique to camera identification: if the informative value of any forensic comparison is high the problem emerges. An alternative approach is presented which consists of choosing a threshold value separating ‘matches’ from ‘non-matches’ and quantifying the strength of evidence of being larger/smaller than this value. If sample sizes of reference data increase LR results will increase as well, and it is shown that this approach is stable. [ABSTRACT FROM PUBLISHER]

In forensics it is a classical problem to determine, when a suspect S shares a property Γ with a criminal C, the probability that S = C. In this article we give a detailed account of this problem in various degrees of generality. We start with the classical case where the probability of having Γ, as well as the a priori probability of being the criminal, is the same for all individuals. We then generalize the solution to deal with heterogeneous populations, biased search procedures for the suspect, Γ-correlations, uncertainty about the subpopulation of the criminal and the suspect, and uncertainty about theΓ-frequencies. We also consider the effect of the way the search for S is conducted, in particular when this is done by a database search. A returning theme is that we show that conditioning is of importance when one wants to quantify the 'weight' of the evidence by a likelihood ratio. Apart from these mathematical issues, we also discuss the practical problems in applying these issues to the legal process. The posterior probabilities of C = S are typically the same for all reasonable choices of the hypotheses, but this is not the whole story. The legal process might force one to dismiss certain hypotheses, for instance when the relevant likelihood ratio depends on prior probabilities. We discuss this and related issues as well. As such, the article is relevant both from a theoretical and from an applied point of view. [ABSTRACT FROM AUTHOR]

In human motor control, there is uncertainty in both estimation of initial sensory state and prediction of the outcome of motor commands. With practice, increasing precision can often be achieved, but such precision incurs costs in time, effort, and neural resources. Therefore, motor planning must account for variability, uncertainty, and noise, not just at the endpoint of movement but throughout the movement. The author presents a mathematical basis for understanding the time course of uncertainty during movement. He shows that it is possible to achieve accurate control of the endpoint of a movement even with highly inaccurate and variable controllers. The results provide a first step toward a theory of optimal control for variable, uncertain, and noisy systems that must nevertheless accomplish real-world tasks reliably. [ABSTRACT FROM AUTHOR]

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs. [ABSTRACT FROM AUTHOR]

Abstract: Entrepreneurship education ranks high on policy agendas in Europe and the US, but little research is available to assess its impact. To help close this gap we investigate whether entrepreneurship education affects intentions to be entrepreneurial uniformly or whether it leads to greater sorting of students. The latter can reduce the average intention to be entrepreneurial and yet be socially beneficial. This paper provides a model of learning in which entrepreneurship education generates signals to students. Drawing on the signals, students evaluate their aptitude for entrepreneurial tasks. The model is tested using data from a compulsory entrepreneurship course. Using ex-ante and ex-post-survey responses from students, we find that intentions to found decline somewhat although the course has significant positive effects on students’ self-assessed entrepreneurial skills. The empirical analysis supports the hypothesis that students receive informative signals and learn about their entrepreneurial aptitude. We outline implications for educators and public policy. [ABSTRACT FROM AUTHOR]

Extraction of the license plate region is the challenging first step in the license plate recognition system. We propose a novel feature fusion concept for plate extraction. The image-feature extraction process is modeled as a feature-detection problem in noise. The geometric features are probabilistically modeled and detected under various detection thresholds. These detection results are then fused within the Bayesian framework to obtain the features for further processing. Along with a probabilistic model, a pixels voting algorithm is also tested through threshold variation. [ABSTRACT FROM AUTHOR]

Several illnesses like the hypertension, the dementia among others in reality contain borderline cases. These “ borderline” (alternately mentioned hazy) cases are neither labeled healthy nor diseased by the medical professionals. Consequently, the current diagnostic test methodology is inappropriate for data with the borderline cases. A new methodology is greatly needed to analyze and interpret diagnostic test data with the borderline cases. In this article, a new methodology is therefore developed, discussed, and illustrated. The medical parameters: the sensitivity, the specificity, and the disease prevalence of the sampled participants are calculated and interpreted using the new methodology with data on borderline dementia and blood pressure cases separately. [ABSTRACT FROM AUTHOR]

Showing simply how statistical thinking can help in weighing evidence and reaching decisions can be useful both as an introduction to an extended presentation of statistical theory and as an introduction to a looser discussion of the nature and value of data. [ABSTRACT FROM AUTHOR]

Abstract: A discrete time filter is considered where both the observation and signal process have non-linear dynamics with additive Gaussian noise. Using the reference probability framework a convolution type Zakai equation is obtained which updates the unnormalized conditional density. Using first order approximations this equation can be solved recursively and the extended Kalman filter can be derived. [Copyright &y& Elsevier]

We report the results of an experiment designed to replicate and extend recent findings on motivated political reasoning. In particular, we are interested in disconfirmation biases--the tendency to counter-argue or discount information with which one disagrees--in the processing of political arguments on policy issues. Our experiment examines 8 issues, including some of local relevance and some of national relevance, and manipulates the presentation format of the policy arguments. We find strong support for our basic disconfirmation hypothesis: people seem unable to ignore their prior beliefs when processing arguments or evidence. We also find that this bias is moderated by political sophistication and strength of prior attitude. We do not find, however, that argument type matters, suggesting that motivated biases are quite robust to changes in argument format. Finally, we find strong support for the polarization of attitudes as a consequence of biased processing. [ABSTRACT FROM AUTHOR]

In this note we wish to pass along an example that we have found useful when introducing the concepts of conditional probability and Bayes' Rule to undergraduate students. The advantages of this example over more contrived textbook examples are its level of difficulty (not too simple, but not too difficult), and its ability to encompass several key probability concepts into one problem while relating to everyday life. [ABSTRACT FROM AUTHOR]

Using a measure change related to Bayes' rule recursive estimates are obtained for an approximate conditional density where a state process has deterministic dynamics and it is observed in additive Gaussian noise. [ABSTRACT FROM AUTHOR]

Abstract: Experimental research found contradictory results regarding the occurrence of informational cascades. Whereas Anderson and Holt [Anderson, L.R., Holt, C.A., 1997. Information cascades in the laboratory. The American Economic Review 87, 847–862] confirmed the model of Banerjee [Banerjee, A.V., 1992. A simple model of herd behavior. The Quarterly Journal of Economics 107, 797–817], and Bikhchandani et al. [Bikhchandani, S., Hishleifer, D., Welch, I., 1992. A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy 100, 992–1026] through lab tests, Huck and Oechssler [Huck, S., Oechssler, J., 2000. Informational cascades in the laboratory: do they occur for the right reasons? Journal of Economic Psychology 21, 661–671] came to contradictory results on crucial issues. This article presents experimental evidence supporting further doubts concerning “Bayesian” informational cascades: just under two thirds of all decisions are characterized by an excessive orientation towards the private signal, and only a small number of the subjects (<6 percent) make rational decisions systematically and consistently. [Copyright &y& Elsevier]