Dismissal of the illusion of uncertainty in the assessment of a likelihood ratio

The use of the Bayes factor (BF) or likelihood ratio as a metric to assess the probative value of forensic traces is largely supported by operational standards and recommendations in different forensic disciplines. However, the progress towards more widespread consensus about foundational principles is still fragile as it raises new problems about which views differ. It is not uncommon e.g. to encounter scientists who feel the need to compute the probability distribution of a given expression of evidential value (i.e. a BF), or to place intervals or significance probabilities on such a quantity. The article here presents arguments to show that such views involve a misconception of principles and abuse of language. The conclusion of the discussion is that, in a given case at hand, forensic scientists ought to offer to a court of justice a given single value for the BF, rather than an expression based on a distribution over a range of values.

Intervals between response choices on a single-item measure of quality of life.

BACKGROUND: A single overall rating of quality of life (QoL) is a sensitive method that is often used in population surveys. However, the exact meaning of response choices is unclear. In particular, uneven spacing may affect the way QoL ratings should be analyzed and interpreted. This study aimed to determine the intervals between response choices to a single-item QoL assessment. METHODS: A secondary analysis was conducted on data from the Lc65+ cohort study and two additional, population-based, stratified random samples of older people (N = 5,300). Overall QoL was rated as excellent, very good, good, fair or poor. A QoL score (range 0-100) was derived from participants' answers to a 28-item QoL assessment tool. A transformed QoL score ranging from 1 (poor) to 5 (excellent) was calculated. The same procedure was repeated to compute seven domain-specific QoL subscores (Feeling of safety; Health and mobility; Autonomy; Close entourage; Material resources; Esteem and recognition; Social and cultural life). RESULTS: Mean (95 % confidence intervals) QoL scores were 96.23 (95.81-96.65) for excellent, 93.09 (92.74-93.45) for very good, 81.45 (80.63-82.27) for good, 65.44 (62.67-68.20) for fair and 54.52 (45.31-63.73) for poor overall QoL, corresponding to transformed QoL scores of respectively 5.00, 4.70, 3.58, 2.05, and 1.00. Ordinality of the categories excellent to poor was preserved in all seven QoL subscores. CONCLUSIONS: The excellent-to-poor rating scale provides an ordinal measure of overall QoL. The intervals between response choices are unequal, but an interval scale can be obtained after adequate recoding of excellent, very good, good, fair and poor.

Worldwide trends in diabetes since 1980: a pooled analysis of 751 population-based studies with 4.4 million participants.

One of the global targets for non-communicable diseases is to halt, by 2025, the rise in the age-standardised adult prevalence of diabetes at its 2010 levels. We aimed to estimate worldwide trends in diabetes, how likely it is for countries to achieve the global target, and how changes in prevalence, together with population growth and ageing, are affecting the number of adults with diabetes. We pooled data from population-based studies that had collected data on diabetes through measurement of its biomarkers. We used a Bayesian hierarchical model to estimate trends in diabetes prevalence-defined as fasting plasma glucose of 7.0 mmol/L or higher, or history of diagnosis with diabetes, or use of insulin or oral hypoglycaemic drugs-in 200 countries and territories in 21 regions, by sex and from 1980 to 2014. We also calculated the posterior probability of meeting the global diabetes target if post-2000 trends continue. We used data from 751 studies including 4,372,000 adults from 146 of the 200 countries we make estimates for. Global age-standardised diabetes prevalence increased from 4.3% (95% credible interval 2.4-7.0) in 1980 to 9.0% (7.2-11.1) in 2014 in men, and from 5.0% (2.9-7.9) to 7.9% (6.4-9.7) in women. The number of adults with diabetes in the world increased from 108 million in 1980 to 422 million in 2014 (28.5% due to the rise in prevalence, 39.7% due to population growth and ageing, and 31.8% due to interaction of these two factors). Age-standardised adult diabetes prevalence in 2014 was lowest in northwestern Europe, and highest in Polynesia and Micronesia, at nearly 25%, followed by Melanesia and the Middle East and north Africa. Between 1980 and 2014 there was little change in age-standardised diabetes prevalence in adult women in continental western Europe, although crude prevalence rose because of ageing of the population. By contrast, age-standardised adult prevalence rose by 15 percentage points in men and women in Polynesia and Micronesia. In 2014, American Samoa had the highest national prevalence of diabetes (>30% in both sexes), with age-standardised adult prevalence also higher than 25% in some other islands in Polynesia and Micronesia. If post-2000 trends continue, the probability of meeting the global target of halting the rise in the prevalence of diabetes by 2025 at the 2010 level worldwide is lower than 1% for men and is 1% for women. Only nine countries for men and 29 countries for women, mostly in western Europe, have a 50% or higher probability of meeting the global target. Since 1980, age-standardised diabetes prevalence in adults has increased, or at best remained unchanged, in every country. Together with population growth and ageing, this rise has led to a near quadrupling of the number of adults with diabetes worldwide. The burden of diabetes, both in terms of prevalence and number of adults affected, has increased faster in low-income and middle-income countries than in high-income countries. Wellcome Trust.

Strings of congruent primes in short intervals

Soit $p_1 = 2, p_2 = 3, p_3 = 5,\ldots$ la suite des nombres premiers, et soient $q \ge 3$ et $a$ des entiers premiers entre eux. R\'ecemment, Daniel Shiu a d\'emontr\'e une ancienne conjecture de Sarvadaman Chowla. Ce dernier a conjectur\'e qu'il existe une infinit\'e de couples $p_n,p_{n+1}$ de premiers cons\'ecutifs tels que $p_n \equiv p_{n+1} \equiv a \bmod q$. Fixons $\epsilon > 0$. Une r\'ecente perc\'ee majeure, de Daniel Goldston, J\`anos Pintz et Cem Y{\i}ld{\i}r{\i}m, a \'et\'e de d\'emontrer qu'il existe une suite de nombres r\'eels $x$ tendant vers l'infini, tels que l'intervalle $(x,x+\epsilon\log x]$ contienne au moins deux nombres premiers $\equiv a \bmod q$. \'Etant donn\'e un couple de nombres premiers $\equiv a \bmod q$ dans un tel intervalle, il pourrait exister un nombre premier compris entre les deux qui n'est pas $\equiv a \bmod q$. On peut d\'eduire que soit il existe une suite de r\'eels $x$ tendant vers l'infini, telle que $(x,x+\epsilon\log x]$ contienne un triplet $p_n,p_{n+1},p_{n+2}$ de nombres premiers cons\'ecutifs, soit il existe une suite de r\'eels $x$, tendant vers l'infini telle que l'intervalle $(x,x+\epsilon\log x]$ contienne un couple $p_n,p_{n+1}$ de nombres premiers tel que $p_n \equiv p_{n+1} \equiv a \bmod q$. On pense que les deux \'enonc\'es sont vrais, toutefois on peut seulement d\'eduire que l'un d'entre eux est vrai, sans savoir lequel. Dans la premi\`ere partie de cette th\`ese, nous d\'emontrons que le deuxi\`eme \'enonc\'e est vrai, ce qui fournit une nouvelle d\'emonstration de la conjecture de Chowla. La preuve combine des id\'ees de Shiu et de Goldston-Pintz-Y{\i}ld{\i}r{\i}m, donc on peut consid\'erer que ce r\'esultat est une application de leurs m\'thodes. Ensuite, nous fournirons des bornes inf\'erieures pour le nombre de couples $p_n,p_{n+1}$ tels que $p_n \equiv p_{n+1} \equiv a \bmod q$, $p_{n+1} - p_n < \epsilon\log p_n$, avec $p_{n+1} \le Y$. Sous l'hypoth\`ese que $\theta$, le \og niveau de distribution \fg{} des nombres premiers, est plus grand que $1/2$, Goldston-Pintz-Y{\i}ld{\i}r{\i}m ont r\'eussi \`a d\'emontrer que $p_{n+1} - p_n \ll_{\theta} 1$ pour une infinit\'e de couples $p_n,p_{n+1}$. Sous la meme hypoth\`ese, nous d\'emontrerons que $p_{n+1} - p_n \ll_{q,\theta} 1$ et $p_n \equiv p_{n+1} \equiv a \bmod q$ pour une infinit\'e de couples $p_n,p_{n+1}$, et nous prouverons \'egalement un r\'esultat quantitatif. Dans la deuxi\`eme partie, nous allons utiliser les techniques de Goldston-Pintz-Y{\i}ld{\i}r{\i}m pour d\'emontrer qu'il existe une infinit\'e de couples de nombres premiers $p,p'$ tels que $(p-1)(p'-1)$ est une carr\'e parfait. Ce resultat est une version approximative d'une ancienne conjecture qui stipule qu'il existe une infinit\'e de nombres premiers $p$ tels que $p-1$ est une carr\'e parfait. En effet, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n \le Y$ tels que $n = \ell_1\cdots \ell_r$, avec $\ell_1,\ldots,\ell_r$ des premiers distincts, et tels que $(\ell_1-1)\cdots (\ell_r-1)$ est une puissance $r$-i\`eme, avec $r \ge 2$ quelconque. \'Egalement, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n = \ell_1\cdots \ell_r \le Y$ tels que $(\ell_1+1)\cdots (\ell_r+1)$ est une puissance $r$-i\`eme. Finalement, \'etant donn\'e $A$ un ensemble fini d'entiers non-nuls, nous d\'emontrerons une borne inf\'erieure sur le nombre d'entiers naturels $n \le Y$ tels que $\prod_{p \mid n} (p+a)$ est une puissance $r$-i\`eme, simultan\'ement pour chaque $a \in A$.

Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

COMBINED FEATURE EXTRACTION TECHNIQUES AND NAIVE BAYES CLASSIFIER FOR SPEECH RECOGNITION

Speech processing and consequent recognition are important areas of Digital Signal Processing since speech allows people to communicate more natu-rally and efficiently. In this work, a speech recognition system is developed for re-cognizing digits in Malayalam. For recognizing speech, features are to be ex-tracted from speech and hence feature extraction method plays an important role in speech recognition. Here, front end processing for extracting the features is per-formed using two wavelet based methods namely Discrete Wavelet Transforms (DWT) and Wavelet Packet Decomposition (WPD). Naive Bayes classifier is used for classification purpose. After classification using Naive Bayes classifier, DWT produced a recognition accuracy of 83.5% and WPD produced an accuracy of 80.7%. This paper is intended to devise a new feature extraction method which produces improvements in the recognition accuracy. So, a new method called Dis-crete Wavelet Packet Decomposition (DWPD) is introduced which utilizes the hy-brid features of both DWT and WPD. The performance of this new approach is evaluated and it produced an improved recognition accuracy of 86.2% along with Naive Bayes classifier.

FEATURE SELECTION AND COMPARISON OF TWO NAÏVE BAYES CLASSIFICATION METHODS IN THE CONTEXT OF SPAM FILTERING

Treating e-mail filtering as a binary text classification problem, researchers have applied several statistical learning algorithms to email corpora with promising results. This paper examines the performance of a Naive Bayes classifier using different approaches to feature selection and tokenization on different email corpora

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Improving Multi-class Text Classification with Naive Bayes

There are numerous text documents available in electronic form. More and more are becoming available every day. Such documents represent a massive amount of information that is easily accessible. Seeking value in this huge collection requires organization; much of the work of organizing documents can be automated through text classification. The accuracy and our understanding of such systems greatly influences their usefulness. In this paper, we seek 1) to advance the understanding of commonly used text classification techniques, and 2) through that understanding, improve the tools that are available for text classification. We begin by clarifying the assumptions made in the derivation of Naive Bayes, noting basic properties and proposing ways for its extension and improvement. Next, we investigate the quality of Naive Bayes parameter estimates and their impact on classification. Our analysis leads to a theorem which gives an explanation for the improvements that can be found in multiclass classification with Naive Bayes using Error-Correcting Output Codes. We use experimental evidence on two commonly-used data sets to exhibit an application of the theorem. Finally, we show fundamental flaws in a commonly-used feature selection algorithm and develop a statistics-based framework for text feature selection. Greater understanding of Naive Bayes and the properties of text allows us to make better use of it in text classification.

Una aplicaci??n de la estimaci??n Bayes emp??rica para incrementar la fiabilidad de las puntuaciones parciales

Resumen tomado de la publicaci??n

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

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