Inversely obtained hydrologic parameters are always uncertain (nonunique) because of errors associated with the measurements and the invoked conceptual model, among other factors. Quantification of this uncertainty in multidimensional parameter space is often difficult because of complexities in the structure of the objective function. In this study we describe parameter uncertainties using uniform distributions and fit these distributions iteratively within larger absolute intervals such that two criteria are met: (i) bracketing most of the measured data (>90%) within the 95% prediction uncertainty (95PPU) and (ii) obtaining a small ratio (<1) of the average difference between the upper and lower 95PPU and the standard deviation of the measured data. We define a model as calibrated if, upon reaching these two criteria, a significant R 2 exists between the observed and simulated results. A program, SUFI-2, was developed and tested for the calibration of two bottom ash landfills. SUFI-2 performs a combined optimization and uncertainty analysis using a global search procedure and can deal with a large number of parameters through Latin hypercube sampling. We explain the above concepts using an example in which two municipal solid waste incinerator bottom ash monofills were successfully calibrated and tested for flow, and one monofill also for transport. Because of high levels of heavy metals in the leachate, monitoring and modeling of such landfills is critical from environmental points of view.

/pdf/estimating-uncertain-flow-and-transport-parameters-using-a-zy3il4tsuc.pdf

Estimating Uncertain Flow and Transport Parameters Using a Sequential Uncertainty Fitting Procedure

Statistical methods in medical research , Statistical methods in medical research , کتابخانه دیجیتال جندی شاپور اهواز

Statistical methods in medical research

This article review methodologies used for analyzing ordered categorical (ordinal) response variables. We begin by surveying models for data with a single ordinal response variable. We also survey recently proposed strategies for modeling ordinal response variables when the data have some type of clustering or when repeated measurement occurs at various occasions for each subject, such as in longitudinal studies. Primary models in that case includemarginal models andcluster-specific (conditional) models for which effects apply conditionally at the cluster level. Related discussion refers to multi-level and transitional models. The main emphasis is on maximum likelihood inference, although we indicate certain models (e.g., marginal models, multi-level models) for which this can be computationally difficult. The Bayesian approach has also received considerable attention for categorical data in the past decade, and we survey recent Bayesian approaches to modeling ordinal response variables. Alternative, non-model-based, approaches are also available for certain types of inference.

The analysis of ordered categorical data: An overview and a survey of recent developments

of the conditional distribution speci cations. Chapters 8 and 10 extend these methods from two to more dimensions. Chapter 9 investigates estimation in conditionally speci ed models. Chapter 11 considers models speci ed by conditioning on events speci ed by one variable exceeding a value rather than equaling a value, and Chapter 12 considers models for extreme-value data. Chapter 13 extends conditional speci cation to Bayesian analysis. Chapter 14 describes the related simultaneous-equation models, and Chapter 15 ties in some additional topics. An appendix describes methods of simulation from conditionally speci ed models. Chapters 1–4, plus Chapters 9 and 13, comprise a lively overview of conditionally speci ed models. The remainder of the text constitutes a detailed catalog of results speci c to different conditional distributions. Although this catalog is certainly of value, the reader desiring a briefer and less detailed introduction to the subject might skip the remainder at  rst reading. This text is a revision of the book by Arnold, Costillo, and Sarabia (1992). The current version is of similar breadth, but with much more depth than the original. The text is clearly written and accessible with relatively few mathematical prerequisites. I found surprisingly few typographical errors; the authors are to be congratulated for this. In a few cases, regularity conditions for results are not given in full. Generally, this causes little confusion, although something does appear to be missing in the statement of Aczél’s key theorem (Theorem 1.3). Fortunately, most of the results in the sequel are derived from corollaries to this theorem, and the corollaries are stated more precisely. I noted few gaps in the material covered. The only area that I thought was insuf ciently represented was application to Markov chain Monte Carlo. Conditional speci cation is particularly important in Gibbs sampling. I believe that many practitioners would bene t from a discussion of the issues involved in these sampling schemes. Each chapter contains numerous exercises. These exercises appear to be at an appropriate level for a graduate course in statistics, and appear to provide appropriate reinforcement for the material in the preceding chapters.

Runs and Scans With Applications

Response variability is often correlated across populations of neurons, and these noise correlations may play a role in information coding. In previous studies, this possibility has been examined f...

https://www.physiology.org/doi/pdf/10.1152/jn.00919.2005

Effects of noise correlations on information encoding and decoding.

φ-divergence .statistics are obtained by either replacing both distributions involved in the argument of the φ -divergence measure by their sample estimates or replacing one distribution and considering the other as given. The sampling properties of estimated divergence-type measures are investigated. Approximate means and variances are derived and asymptotic distributions are obtained. Tests of goodness of fit of observed frequencies to expected ones and tests of equality of divergences based on two or more multinomial samples are constructed.

Divergence statistics: sampling properties and multinomial goodness of fit and divergence tests

In this paper methods are presented for obtaining parametric measures of information from the non-parametric ones and from information matrices. The properties of these measures are examined. The one-dimensional parametric measures which are derived from the non-parametric are superior to Fisher's information measure because they are free from regularity conditions. But if we impose the regularity conditions of the Fisherian theory of information, these measures become linear functions of Fisher's measure.

New parametric measures of information

This chapter presents a higher-order-logic formalization of the main concepts of information theory (Cover & Thomas, 1991), such as the Shannon entropy and mutual information, using the formalization of the foundational theories of measure, Lebesgue integration, and probability. The main results of the chapter include the formalizations of the Radon-Nikodym derivative and the Kullback-Leibler (KL) divergence (Coble, 2010). The latter provides a unified framework based on which most of the commonly used measures of information can be defined. The chapter then provides the general definitions that are valid for both discrete and continuous cases and then proves the corresponding reduced expressions where the measures considered are absolutely continuous over finite spaces.

Information, Measures of

The problem of loss of information due to the discretization of data and its estimate is studied for various measures of information. The results of Ghurye and Johnson (1981) are generalized and supplemented for the Csiszar and Renyi measures of information as well as for Fisher's information matrix.

Discrete approximations to the Csiszár, Renyi, and Fisher measures of information

The best policy for an insurance company is that which lasts for a long period of time and is less uncertain with reference to its claims. In information theory, entropy is a measure of the uncertainty associated with a random variable. It is a descriptive quantity as it belongs to the class of measures of variability, such as the variance and the standard deviation. The purpose of this paper is to investigate the effect of inflation, truncation or censoring from below (use of a deductible) and truncation or censoring from above (use of a policy limit) on the entropy of losses of insurance policies. Losses are differentiated between per-payment and per-loss (franchise deductible). In this context we study the properties of the resulting entropies such as the residual loss entropy and the past loss entropy which are the result of use of a deductible and a policy limit, respectively. Interesting relationships between these entropies are presented. The combined effect of a deductible and a policy limit is also studied. We also investigate residual and past entropies for survival models. Finally, an application is presented involving the well-known Danish data set on fire losses.

Takis Papaioannou

Papers

Divergence statistics: sampling properties and multinomial goodness of fit and divergence tests

New parametric measures of information

Information, Measures of

Discrete approximations to the Csiszár, Renyi, and Fisher measures of information

Residual and Past Entropy in Actuarial Science and Survival Models