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Abstract: In this research, two-state Markov switching models are proposed to study accident frequencies and severities. These models assume that there are two unobserved states of roadway safety, and that roadway entities (e.g., roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies or severities are generated by separate processes (e.g., Poisson, negative binomial, multinomial logit). Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for estimation of Markov switching models. To demonstrate the applicability of the approach, we conduct the following three studies. In the first study, two-state Markov switching count data models are considered as an alternative to zero-inflated models for annual accident frequencies, in order to account for preponderance of zeros typically observed in accident frequency data. In the second study, two-state Markov switching Poisson model and two-state Markov switching negative binomial model are estimated using weekly accident frequencies on selected Indiana interstate highway segments over a five-year time period. In the third study, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. One of the most important results found in each of the three studies, is that in each case the estimated Markov switching models are strongly favored by roadway safety data and result in a superior statistical fit, as compared to the corresponding standard (non-switching) models.
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Title: Comparison between CPBPV, ESC/Java, CBMC, Blast, EUREKA and Why for Bounded Program Verification
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Abstract: This report describes experimental results for a set of benchmarks on program verification. It compares the capabilities of CPBVP "Constraint Programming framework for Bounded Program Verification" [4] with the following frameworks: ESC/Java, CBMC, Blast, EUREKA and Why.
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Title: A Generalized Publication Bias Model
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Abstract: Scargle (2000) has discussed Rosenthal and Rubin's (1978) "fail-safe number" (FSN) method for estimating the number of unpublished studies in meta-analysis. He concluded that this FSN cannot possibly be correct because a central assumption the authors used conflicts with the very definition of publication bias. While this point has been made by others before (Elsahoff, 1978; Darlington, 1980; Thomas, 1985, Iyengar & Greenhouse, 1988), Scargle showed, by way of a simple 2-parameter model, how far off Rosenthal & Rubin' s estimate can be in practice. However, his results relied on the assumption that the decision variable is normally distributed with zero mean. In this case the ratio of unpublished to published papers is large only in a tiny region of the parameter plane. Building on these results, we now show that (1) Replacing densities with probability masses greatly simplifies Scargle's derivations and permits an explicit statement of the relation between the probability alpha of Type I errors and the step-size beta; (2) This result does not require any distribution assumptions; (3) The distinction between 1-sided and 2-sided rejection regions becomes immaterial; (4) This distribution-free approach leads to an immediate generalization to partitions involving more than two intervals, and thus covers more general selection functions.
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Title: Medical robotics: where we come from, where we are and where we could go
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Abstract: This short note presents a viewpoint about medical robotics.
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Title: Dynamic modeling of mean-reverting spreads for statistical arbitrage
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Abstract: Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.
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Title: Initial Results on the F-logic to OWL Bi-directional Translation on a Tabled Prolog Engine
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Abstract: In this paper, we show our results on the bi-directional data exchange between the F-logic language supported by the Flora2 system and the OWL language. Most of the TBox and ABox axioms are translated preserving the semantics between the two representations, such as: proper inclusion, individual definition, functional properties, while some axioms and restrictions require a change in the semantics, such as: numbered and qualified cardinality restrictions. For the second case, we translate the OWL definite style inference rules into F-logic style constraints. We also describe a set of reasoning examples using the above translation, including the reasoning in Flora2 of a variety of ABox queries.
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Title: Index wiki database: design and experiments
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Abstract: With the fantastic growth of Internet usage, information search in documents of a special type called a "wiki page" that is written using a simple markup language, has become an important problem. This paper describes the software architectural model for indexing wiki texts in three languages (Russian, English, and German) and the interaction between the software components (GATE, Lemmatizer, and Synarcher). The inverted file index database was designed using visual tool DBDesigner. The rules for parsing Wikipedia texts are illustrated by examples. Two index databases of Russian Wikipedia (RW) and Simple English Wikipedia (SEW) are built and compared. The size of RW is by order of magnitude higher than SEW (number of words, lexemes), though the growth rate of number of pages in SEW was found to be 14% higher than in Russian, and the rate of acquisition of new words in SEW lexicon was 7% higher during a period of five months (from September 2007 to February 2008). The Zipf's law was tested with both Russian and Simple Wikipedias. The entire source code of the indexing software and the generated index databases are freely available under GPL (GNU General Public License).
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Title: Reconsidering the asymptotic null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models
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Abstract: Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. Here we show, by simulation and by theoretical arguments based on the geometry of the parameter space, that all aspects of the previously stated asymptotic null distribution are incorrect--both the binomial mixing probabilities and the chi-square components. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be ten times larger. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and the mixing components show severe departures from chi-square distributions. Thus, the asymptotic null distribution has complex features that raise challenges for the assessment of significance of multivariate linkage findings. We propose a method to generate an asymptotic null distribution that is much faster than other empirical methods such as gene-dropping, enabling us to obtain P values with higher precision more efficiently.
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Title: Sample size effects in multivariate fitting of correlated data
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Abstract: A common problem in analysis of experiments or in lattice QCD simulations is fitting a parameterized model to the average over a number of samples of correlated data values. If the number of samples is not infinite, estimates of the variance of the parameters ("error bars") and of the goodness of fit are affected. We illustrate these problems with numerical simulations, and calculate approximate corrections to the variance of the parameters for estimates made in the standard way from derivatives of the parameters' probability distribution as well as from jackknife and bootstrap estimates.
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Title: Higher Order Moments Generation by Mellin Transform for Compound Models of Clutter
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Abstract: The compound models of clutter statistics are found suitable to describe the nonstationary nature of radar backscattering from high-resolution observations. In this letter, we show that the properties of Mellin transform can be utilized to generate higher order moments of simple and compound models of clutter statistics in a compact manner.
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Title: Persistent Clustering and a Theorem of J. Kleinberg
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Abstract: We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorem analogous to one of J. Kleinberg, in which one obtains an existence and uniqueness theorem instead of a non-existence result. We explore further properties of this unique scheme, stability and convergence are established.
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Title: Decomposable Principal Component Analysis
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Abstract: We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem using a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We demonstrate the application of our methodology in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we propose an approximate statistical graphical model and distribute the computation of PCA.
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Title: A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data
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Abstract: We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but has changed the way we think about problems.
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Title: Investigation of the Zipf-plot of the extinct Meroitic language
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Abstract: The ancient and extinct language Meroitic is investigated using Zipf's Law. In particular, since Meroitic is still undeciphered, the Zipf law analysis allows us to assess the quality of current texts and possible avenues for future investigation using statistical techniques.
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Title: Spatial planning with constraints on translational distances between geometric objects
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Abstract: The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest constraint in which the minimum translational distance between objects is greater than zero, or more generally, than some positive value. We present a technique, based on the Minkowski operations, for generating the translational C-space maps for spatial planning with more general and more complex constraints on the relative position of geometric objects, such as constraints on various types (not only on the minimum) of the translational distances between objects. The developed technique can also be used, respectively, for spatial planning with constraints on translational distances in a given direction, and rotational distances between geometric objects, as well as for spatial planning with given dynamic geometric situation of moving objects.
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Title: Building an interpretable fuzzy rule base from data using Orthogonal Least Squares Application to a depollution problem
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Abstract: In many fields where human understanding plays a crucial role, such as bioprocesses, the capacity of extracting knowledge from data is of critical importance. Within this framework, fuzzy learning methods, if properly used, can greatly help human experts. Amongst these methods, the aim of orthogonal transformations, which have been proven to be mathematically robust, is to build rules from a set of training data and to select the most important ones by linear regression or rank revealing techniques. The OLS algorithm is a good representative of those methods. However, it was originally designed so that it only cared about numerical performance. Thus, we propose some modifications of the original method to take interpretability into account. After recalling the original algorithm, this paper presents the changes made to the original method, then discusses some results obtained from benchmark problems. Finally, the algorithm is applied to a real-world fault detection depollution problem.
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Title: Up-and-Down and the Percentile-Finding Problem
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Abstract: Up-and-Down (U&D) is a popular sequential design for estimating threshold percentiles in binary experiments. However, U&D application practices have stagnated, and significant gaps in understanding its properties persist. The first part of my work aims to fill gaps in U&D theory. New results concerning stationary distribution properties are proven. A second focus of this study is nonparametric U&D estimation. An improvement to isotonic regression called "centered isotonic regression" (CIR), and a new averaging estimator called "auto-detect" are introduced and their properties studied. Bayesian percentile-finding designs, most notably the continual reassessment method (CRM) developed for Phase I clinical trials, are also studied. In general, CRM convergence depends upon random run-time conditions -- meaning that convergence is not always assured. Small-sample behavior is studied as well. It is shown that CRM is quite sensitive to outlier sub-sequences of thresholds, resulting in highly variable small-sample behavior between runs under identical conditions. Nonparametric CRM variants exhibit a similar sensitivity. Ideas to combine the advantages of U&D and Bayesian designs are examined. A new approach is developed, using a hybrid framework, that evaluates the evidence for overriding the U&D allocation with a Bayesian one.
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Title: Minimal average degree aberration and the state polytope for experimental designs
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Abstract: For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic method does not in general produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on "aberration" and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase.
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Title: n-ary Fuzzy Logic and Neutrosophic Logic Operators
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Abstract: We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.
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Title: Multi-Instance Multi-Label Learning
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Abstract: In this paper, we propose the MIML (Multi-Instance Multi-Label learning) framework where an example is described by multiple instances and associated with multiple class labels. Compared to traditional learning frameworks, the MIML framework is more convenient and natural for representing complicated objects which have multiple semantic meanings. To learn from MIML examples, we propose the MimlBoost and MimlSvm algorithms based on a simple degeneration strategy, and experiments show that solving problems involving complicated objects with multiple semantic meanings in the MIML framework can lead to good performance. Considering that the degeneration process may lose information, we propose the D-MimlSvm algorithm which tackles MIML problems directly in a regularization framework. Moreover, we show that even when we do not have access to the real objects and thus cannot capture more information from real objects by using the MIML representation, MIML is still useful. We propose the InsDif and SubCod algorithms. InsDif works by transforming single-instances into the MIML representation for learning, while SubCod works by transforming single-label examples into the MIML representation for learning. Experiments show that in some tasks they are able to achieve better performance than learning the single-instances or single-label examples directly.
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Title: Uncertainty quantification in complex systems using approximate solvers
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Abstract: This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling with Bayesian formulations. The key departure from existing works is the use of inexpensive, approximate computational models in a rigorous manner. Such models can readily be derived by coarsening the discretization size in the solution of the governing PDEs, increasing the time step when integration of ODEs is performed, using fewer iterations if a non-linear solver is employed or making use of lower order models. It is shown that even in cases where the inexact models provide very poor approximations of the exact response, statistics of the latter can be quantified accurately with significant reductions in the computational effort. Multiple approximate models can be used and rigorous confidence bounds of the estimates produced are provided at all stages.
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Title: On sequential Monte Carlo, partial rejection control and approximate Bayesian computation
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Abstract: We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers. We provide a study of theoretical properties of the new algorithm, and make connections with some existing algorithms. Finally, the sampler is adapted for application under the challenging "likelihood free," approximate Bayesian computation modelling framework, where we demonstrate superior performance over existing likelihood-free samplers.
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Title: Conditional probability based significance tests for sequential patterns in multi-neuronal spike trains
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Abstract: In this paper we consider the problem of detecting statistically significant sequential patterns in multi-neuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data mining scheme to efficiently discover such patterns which are frequent in the sense that the count of non-overlapping occurrences of the pattern in the data stream is above a threshold. Here we propose a method to determine the statistical significance of these repeating patterns and to set the thresholds automatically. The novelty of our approach is that we use a compound null hypothesis that includes not only models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to calculate the mean and variance of the count for any pattern. Using this we derive a test of significance for rejecting such a null hypothesis. This also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated from a non-homogeneous Poisson model with embedded dependencies.
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Title: What It Feels Like To Hear Voices: Fond Memories of Julian Jaynes
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Abstract: Julian Jaynes's profound humanitarian convictions not only prevented him from going to war, but would have prevented him from ever kicking a dog. Yet according to his theory, not only are language-less dogs unconscious, but so too were the speaking/hearing Greeks in the Bicameral Era, when they heard gods' voices telling them what to do rather than thinking for themselves. I argue that to be conscious is to be able to feel, and that all mammals (and probably lower vertebrates and invertebrates too) feel, hence are conscious. Julian Jaynes's brilliant analysis of our concepts of consciousness nevertheless keeps inspiring ever more inquiry and insights into the age-old mind/body problem and its relation to cognition and language.
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Title: Offloading Cognition onto Cognitive Technology
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Abstract: "Cognizing" (e.g., thinking, understanding, and knowing) is a mental state. Systems without mental states, such as cognitive technology, can sometimes contribute to human cognition, but that does not make them cognizers. Cognizers can offload some of their cognitive functions onto cognitive technology, thereby extending their performance capacity beyond the limits of their own brain power. Language itself is a form of cognitive technology that allows cognizers to offload some of their cognitive functions onto the brains of other cognizers. Language also extends cognizers' individual and joint performance powers, distributing the load through interactive and collaborative cognition. Reading, writing, print, telecommunications and computing further extend cognizers' capacities. And now the web, with its network of cognizers, digital databases and software agents, all accessible anytime, anywhere, has become our 'Cognitive Commons,' in which distributed cognizers and cognitive technology can interoperate globally with a speed, scope and degree of interactivity inconceivable through local individual cognition alone. And as with language, the cognitive tool par excellence, such technological changes are not merely instrumental and quantitative: they can have profound effects on how we think and encode information, on how we communicate with one another, on our mental states, and on our very nature.
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Title: Formal and Informal Model Selection with Incomplete Data
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Abstract: Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of the fact that only an incomplete subset is observed. Direct comparison between model and data is then less than straightforward. Second, many commonly used models are more sensitive to assumptions than in the complete-data situation and some of their properties vanish when they are fitted to incomplete, unbalanced data. These and other issues are brought forward using two key examples, one of a continuous and one of a categorical nature. We argue that model assessment ought to consist of two parts: (i) assessment of a model's fit to the observed data and (ii) assessment of the sensitivity of inferences to unverifiable assumptions, that is, to how a model described the unobserved data given the observed ones.
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Title: Constructing word similarities in Meroitic as an aid to decipherment
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Abstract: Meroitic is the still undeciphered language of the ancient civilization of Kush. Over the years, various techniques for decipherment such as finding a bilingual text or cognates from modern or other ancient languages in the Sudan and surrounding areas has not been successful. Using techniques borrowed from information theory and natural language statistics, similar words are paired and attempts are made to use currently defined words to extract at least partial meaning from unknown words.
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Title: A game-theoretic version of Oakes' example for randomized forecasting
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Abstract: Using the game-theoretic framework for probability, Vovk and Shafer. have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests. This result generalizes work by other authors, who consider only tests of calbration. We complement this result with a lower bound. We show that Vovk and Shafer's result is valid only when the forecasts are computed with unrestrictedly increasing degree of accuracy. When some level of discreteness is fixed, we present a game-theoretic generalization of Oakes' example for randomized forecasting that is a test failing any given method of deferministic forecasting; originally, this example was presented for deterministic calibration.
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Title: Gibbs Sampling, Exponential Families and Orthogonal Polynomials
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Abstract: We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions.
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Title: Comment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials
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Abstract: Comment on ``Gibbs Sampling, Exponential Families and Orthogonal Polynomials'' [arXiv:0808.3852]
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Title: Comment: Gibbs Sampling, Exponential Families, and Orthogonal Polynomials
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Abstract: Comment on ``Gibbs Sampling, Exponential Families, and Orthogonal Polynomials'' [arXiv:0808.3852]
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Title: Covariate Balance in Simple, Stratified and Clustered Comparative Studies
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Abstract: In randomized experiments, treatment and control groups should be roughly the same--balanced--in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests? If so, should there be several such tests, one for each pretreatment variable, or should there be a single, omnibus test? Could such a test be engineered to give easily computed $p$-values that are reliable in samples of moderate size, or would simulation be needed for reliable calibration? What new concerns are introduced by random assignment of clusters? Which tests of balance would be optimal? To address these questions, Fisher's randomization inference is applied to the question of balance. Its application suggests the reversal of published conclusions about two studies, one clinical and the other a field experiment in political participation.
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Title: Comment: Lancaster Probabilities and Gibbs Sampling
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Abstract: Comment on ``Lancaster Probabilities and Gibbs Sampling'' [arXiv:0808.3852]
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Title: Comment: On Random Scan Gibbs Samplers
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Abstract: Comment on ``On Random Scan Gibbs Samplers'' [arXiv:0808.3852]
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