On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Class of Models for Uncorrelated Random Variables

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence

The hydraulic behaviour of sand and silt soils around the residual-state condition

Geotechnical and geo-environmental engineering problems may require the computation of near-ground-surface water balances. Evaluation of the unsaturated coefficient of permeability function is often necessary in order to undertake numerical simulations associated with the water balance evaluations. Evaporation at ground surface has the potential to reduce the water content of the soil to values less than the residual water content. However, it appears that the accuracy of commonly used methods for the determination of the permeability function around residual-state conditions is unknown. There may be lack of accuracy due to an oversimplification of the physics of water movement around the residual-state condition. Evaluation of the coefficient of permeability function around the residual-state condition requires reliable experimental data in the low water-content range. In this study, the concept of residual-state condition is reviewed, and a definition of the conditions suitable for geotechnical engineering practice is suggested. A transition zone for the soil-water content/soil-suction profile is defined for steady-state flow systems. A possible link between the limits of the transition zone and the residual-state condition is proposed. A method is developed for predicting the unsaturated coefficient of permeability, based on a new definition of the residual-state condition. The method is based on the theory of vapour-phase flow and on the soil-water characteristic curve. A series of evaporation tests were conducted in an environmentally controlled room on two different types of soil samples: sand and clayey silt. The unsaturated coefficient of permeability functions for the selected soils were established. The steady-state evaporation method used in this study proved to measure the unsaturated coefficient of permeability function in the low-water content range. The results obtained from the predictive method proposed in this thesis are compared to the experimental data and to the data predicted by the previously proposed methods. Predictions computed when using the new method appear to be more accurate than those from previously proposed methods. It was not possible to draw firm conclusions from the tests performed regarding the relationship between the residual-state condition and the upper and lower limits of the transition zone of the water-content/soil-suction profile

A unified approach to non-negative matrix factorization and probabilistic latent semantic indexing

Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two matrices, W and H, each with nonnegative entries, V ~ WH. NMF has been shown to have a unique parts-based, sparse representation of the data. The nonnegativity constraints in NMF allow only additive combinations of the data which enables it to learn parts that have distinct physical representations in reality. In the last few years, NMF has been successfully applied in a variety of areas such as natural language processing, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. We present a generalized approach to NMF based on Renyi\u27s divergence between two non-negative matrices related to the Poisson likelihood. Our approach unifies various competing models and provides a unique framework for NMF. Furthermore, we generalize the equivalence between NMF and probabilistic latent semantic indexing, a well-known method used in text mining and document clustering applications. We evaluate the performance of our method in the unsupervised setting using consensus clustering and demonstrate its applicability using real-life and simulated data

Multivariate dynamic information

AbstractThis paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall–Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables

Variants of Mixtures: Information Properties and Applications

In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function

Maksimiziranje efikasnosti rudarenja u kamenolomu, prikaz studije slučaja

Nowadays, the dimension stone industry performs a crucial role in the world economy. Accordingly, dimension stone quarries’ importance grows due to their different applications in various construction, building, and decorative industries. Some issues threaten this industry and provide a financial risk that should be taken into account to make the smallest possible risk for investment. The presence of discontinuities in the rock mass has a key function as far as it concerns the overall quality of in situ rock blocks. It impacts the feasibility of dimension stone quarries and overall mine exploitation efficiency. Therefore, it is recommended to survey discontinuities and rock blocks and estimate the average geometry of a rock block, including the shape and size, before mining the benches to maximize mining exploitation efficiency and minimize waste ore production. This investigation aims to survey the discontinuities of the limestone quarry mine located in Josheghan, Iran, to determine and calculate rock blocks’ suitable geometry and an extraction’s direction for active mine benches. For this purpose, the scanline method was applied to survey discontinuities in seven active benches. 3DEC software was used to indicate discontinuities and model the rock blocks for all active benches. It was concluded that the benches’ cutting line make a 13.14 degree with the discontinuities main’s direction. The result of this study proved that by changing the direction of mining and extraction for active mine benches, the unnecessary waste production would decrease. The production rate with the recommended extraction direction will increase by about 1.13% compared to the current extraction direction, which makes 13.14 degrees with the discontinuities main’s direction. Currently, bench seven recorded the minimum production rate, which is 97.60; by applying the new extraction’s direction, it is predicted that this bench will achieve a 99.83 production rate. Consequently, it is concluded by improving the production rate, exploitation efficiency would increase considerably.Danas industrija arhitektonsko-građevnoga kamena zauzima važno mjesto u svjetskoj ekonomiji. Time raste i važnost kamenoloma. Postoje također i rizici povezani s takvim aktivnostima, posebice financijski. Nazočnost pukotina u stijenskoj masi može biti glavni rizik među njima, jer one ruše kvalitetu kamena, a time utječu na iskoristivost kamenoloma. Stoga je vrlo važno istražiti pukotine, stijenske blokove, njihovu geometriju i dimenzije prije otkopavanja, kako bi se podigla iskoristivost i smanjila količina jalovine. Ovdje su izučene pukotine u kamenolomu vapnenca u Josheghanu, Iran. Izračunana je odgovarajuća geometrija stijenskih blokova važna za eksploataciju. Metodom Scanline predviđene su pukotine na sedam radilišta, a paketom 3DEC za cijeli kamenolom. Izračunano je kako se smjer otkopavanja treba projicirati s otklonom od 13,14 stupnjeva u odnosu na glavni smjer pružanja pukotina. Dokazano je kako se promjenom smjera rudarenja povećava i udjel jalovine. No, rudarenjem pod navedenim kutom povećat će se pridobivanje za 1,13 % u usporedbi s trenutačnim. Na radilištu broj sedam zabilježena je minimalna proizvodnja od 97,60, a primjenom ovih rezultata očekuje se dosizanje vrijednosti od 99,83. Na taj način moguće je znatno povećati proizvodnju i iskoristivost