Estadística. Tema 4: contrastes de bondad de ajuste de variables continuas (curso 2014-2015)

T4. Contrastes de Bondad de Ajuste para distribuciones continuas. Método Kolmogorov-Smirnov.

MGOF: Stata module to perform goodness-of-fit tests for multinomial data

mgof computes goodness-of-fit tests for the distribution of a discrete (categorical, multinomial) variable. The default is to perform classical large sample chi-squared approximation tests based on Pearson's X2 statistic and the log likelihood ratio (G2) statistic or a statistic from the Cressie-Read family. Alternatively, mgof computes exact tests using Monte Carlo methods or exhaustive enumeration. A Kolmogorov-Smirnov test for discrete data is also provided. The moremata package, also available from SSC, is required.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

A new Stata command called -mgof- is introduced. The command is used to compute distributional tests for discrete (categorical, multinomial) variables. Apart from classic large sample $\chi^2$-approximation tests based on Pearson's $X^2$, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read 1984), large sample tests for complex survey designs and exact tests for small samples are supported. The complex survey correction is based on the approach by Rao and Scott (1981) and parallels the survey design correction used for independence tests in -svy:tabulate-. The exact tests are computed using Monte Carlo methods or exhaustive enumeration. An exact Kolmogorov-Smirnov test for discrete data is also provided.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Let S be a countable set and let Q = (q(ij), i, j is an element of S) be a conservative q-matrix over S with a single instantaneous state b. Suppose that we are given a real number mu >= 0 and a strictly positive probability measure m = (m(j), j is an element of S) such that Sigma(i is an element of S) m(i)q(ij) = -mu m(j), j 0 b. We prove that there exists a Q-process P(t) = (p(ij) (t), i, j E S) for which m is a mu-invariant measure, that is Sigma(i is an element of s) m(i)p(ij)(t) = e(-mu t)m(j), j is an element of S. We illustrate our results with reference to the Kolmogorov 'K 1' chain and a birth-death process with catastrophes and instantaneous resurrection.

BEM-ESTAR NO TRABALHO E PERCEPÇÃO DE SUCESSO NA CARREIRA COMO ANTECEDENTES DE INTENÇÃO DE ROTATIVIDADE.

O objetivo geral deste estudo foi analisar, interpretar e discutir as relações entre as percepções de sucesso na carreira, bem-estar no trabalho e a intenção de rotatividade em trabalhadores da Região Sudeste do Brasil. Participaram desta pesquisa 500 trabalhadores que atuam no estado de São Paulo em organizações não governamentais, públicas e privadas. Como instrumento para coleta de dados foi utilizado um questionário de autopreenchimento composto de cinco escalas que mediram as variáveis da pesquisa. A presente pesquisa se propôs a apresentar, interpretar e discutir as relações entre as variáveis, como também, testar as hipóteses referentes ao modelo conceitual proposto, por meio de uma pesquisa de natureza transversal com abordagem quantitativa, cujos dados coletados foram analisados por aplicação de técnicas estatísticas paramétricas (cálculos de estatísticas descritivas: médias, desvio padrão, teste t e correlações; cálculos de estatísticas multivariadas: análise de regressão linear múltipla stepwise e teste da normalidade das variáveis, por meio do teste de Kolmogorov-Smirnov). O tratamento e análise dos dados foram realizados pelo software estatístico Statistical Package for the Social Science SPSS, versão 18.0 para Windows. Os resultados obtidos demonstraram que as dimensões de bem-estar no trabalho exercem forte e significativo impacto sobre a intenção de rotatividade dos profissionais, enquanto que a percepção de sucesso na carreira contribuiu com valores baixos neste impacto, devido ao formato do modelo hipotético. A pesquisa possibilitou concluir que quanto mais a empresa se preocupa em proporcionar um ambiente de trabalho que seja animador, interessante e que cause entusiasmo, menos os profissionais pensarão em deixá-la.

A UTILIZAÇÃO DO LASER DE BAIXA INTENSIDADE NA MOVIMENTAÇÃO DENTÁRIA E NA SENSIBILIDADE DOLOROSA APÓS APLICAÇÃO DE FORÇA ORTODÔNTICA

O presente estudo objetivou avaliar a eficácia do Laser de Baixa Intensidade (LBI) na aceleração da movimentação dentária e na diminuição da dor frente à aplicação de força ortodôntica. A amostra foi composta por 19 pacientes, sendo doze do sexo feminino e sete do sexo masculino, com idade inicial média de 14,69 anos, todos com indicação para extrações de primeiros pré-molares. Destes, 66 caninos foram submetidos à retração inicial, sendo que 33 receberam aplicação de laser e 33 foram considerados controle. Utilizou-se o Laser de Baixa Intensidade de arseneto de gálio e alumínio, com comprimento de onda de 780nm, na dosimetria de 40mW;10J/cm2;10s/ponto, aplicado apenas uma vez ao mês em dez pontos, sendo cinco por vestibular e cinco por lingual/palatino. Modelos de gesso foram confeccionados durante todos os meses de retração dos caninos, que teve duração de quatro meses, sendo, posteriormente, digitalizados para se mensurar a quantidade de movimentação de um lado em relação ao outro, utilizando-se como referência as papilas incisivas. Para a avaliação da dor experimentada pelos pacientes, os mesmos foram orientados a preencher uma escala analógica visual (VAS) que variava de 0 a 10 , em que zero significava nenhuma dor e dez significava dor insuportável, nos intervalos de 12, 24, 48 e 72 horas após a aplicação da força ortodôntica. Foi mensurado o apinhamento de todas as hemiarcadas dos pacientes na fase inicial, medindo-se a distância entre os pontos de contato de cada dente. Para a verificação do padrão de normalidade, empregou-se o teste de Kolmogorov-Smirnov, sendo que para comparar o lado irradiado com o lado não irradiado foi utilizado o teste t pareado, exceto para a variável razão caninos/molares , analisada pelo teste não paramétrico de Wilcoxon (p<0,05). Os resultados mostraram que em relação ao apinhamento dentário, os lados irradiado e não irradiado apresentaram-se compatíveis. Além disso, não houve diferença estatisticamente significante entre a quantidade de retração dos caninos irradiados comparados aos não irradiados, o mesmo acontecendo com a sensibilidade dolorosa experimentada pelos pacientes. Concluiu-se assim que o LBI na dosimetria e forma como foi utilizado não foi eficiente na aceleração da movimentação dentária nem na redução da dor experimentada pelos pacientes frente às forças ortodônticas.

Outlier detection with partial information:Application to emergency mapping

This paper, addresses the problem of novelty detection in the case that the observed data is a mixture of a known 'background' process contaminated with an unknown other process, which generates the outliers, or novel observations. The framework we describe here is quite general, employing univariate classification with incomplete information, based on knowledge of the distribution (the 'probability density function', 'pdf') of the data generated by the 'background' process. The relative proportion of this 'background' component (the 'prior' 'background' 'probability), the 'pdf' and the 'prior' probabilities of all other components are all assumed unknown. The main contribution is a new classification scheme that identifies the maximum proportion of observed data following the known 'background' distribution. The method exploits the Kolmogorov-Smirnov test to estimate the proportions, and afterwards data are Bayes optimally separated. Results, demonstrated with synthetic data, show that this approach can produce more reliable results than a standard novelty detection scheme. The classification algorithm is then applied to the problem of identifying outliers in the SIC2004 data set, in order to detect the radioactive release simulated in the 'oker' data set. We propose this method as a reliable means of novelty detection in the emergency situation which can also be used to identify outliers prior to the application of a more general automatic mapping algorithm. © Springer-Verlag 2007.

Quantifying short-term dynamics of Parkinson's disease using self-reported symptom data from an internet social network

Background: Parkinson’s disease (PD) is an incurable neurological disease with approximately 0.3% prevalence. The hallmark symptom is gradual movement deterioration. Current scientific consensus about disease progression holds that symptoms will worsen smoothly over time unless treated. Accurate information about symptom dynamics is of critical importance to patients, caregivers, and the scientific community for the design of new treatments, clinical decision making, and individual disease management. Long-term studies characterize the typical time course of the disease as an early linear progression gradually reaching a plateau in later stages. However, symptom dynamics over durations of days to weeks remains unquantified. Currently, there is a scarcity of objective clinical information about symptom dynamics at intervals shorter than 3 months stretching over several years, but Internet-based patient self-report platforms may change this. Objective: To assess the clinical value of online self-reported PD symptom data recorded by users of the health-focused Internet social research platform PatientsLikeMe (PLM), in which patients quantify their symptoms on a regular basis on a subset of the Unified Parkinson’s Disease Ratings Scale (UPDRS). By analyzing this data, we aim for a scientific window on the nature of symptom dynamics for assessment intervals shorter than 3 months over durations of several years. Methods: Online self-reported data was validated against the gold standard Parkinson’s Disease Data and Organizing Center (PD-DOC) database, containing clinical symptom data at intervals greater than 3 months. The data were compared visually using quantile-quantile plots, and numerically using the Kolmogorov-Smirnov test. By using a simple piecewise linear trend estimation algorithm, the PLM data was smoothed to separate random fluctuations from continuous symptom dynamics. Subtracting the trends from the original data revealed random fluctuations in symptom severity. The average magnitude of fluctuations versus time since diagnosis was modeled by using a gamma generalized linear model. Results: Distributions of ages at diagnosis and UPDRS in the PLM and PD-DOC databases were broadly consistent. The PLM patients were systematically younger than the PD-DOC patients and showed increased symptom severity in the PD off state. The average fluctuation in symptoms (UPDRS Parts I and II) was 2.6 points at the time of diagnosis, rising to 5.9 points 16 years after diagnosis. This fluctuation exceeds the estimated minimal and moderate clinically important differences, respectively. Not all patients conformed to the current clinical picture of gradual, smooth changes: many patients had regimes where symptom severity varied in an unpredictable manner, or underwent large rapid changes in an otherwise more stable progression. Conclusions: This information about short-term PD symptom dynamics contributes new scientific understanding about the disease progression, currently very costly to obtain without self-administered Internet-based reporting. This understanding should have implications for the optimization of clinical trials into new treatments and for the choice of treatment decision timescales.

Applying A Normalized Compression Metric To The Measurement Of Dialect Distance

The paper discusses the application of a similarity metric based on compression to the measurement of the distance among Bulgarian dia- lects. The similarity metric is de ned on the basis of the notion of Kolmo- gorov complexity of a le (or binary string). The application of Kolmogorov complexity in practice is not possible because its calculation over a le is an undecidable problem. Thus, the actual similarity metric is based on a real life compressor which only approximates the Kolmogorov complexity. To use the metric for distance measurement of Bulgarian dialects we rst represent the dialectological data in such a way that the metric is applicable. We propose two such representations which are compared to a baseline distance between dialects. Then we conclude the paper with an outline of our future work.

A potentially scalable method for the harvesting of hMSCs from microcarriers

The use of hMSCs for allogeneic therapies requiring lot sizes of billions of cells will necessitate large-scale culture techniques such as the expansion of cells on microcarriers in bioreactors. Whilst much research investigating hMSC culture on microcarriers has focused on growth, much less involves their harvesting for passaging or as a step towards cryopreservation and storage. A successful new harvesting method has recently been outlined for cells grown on SoloHill microcarriers in a 5L bioreactor [1]. Here, this new method is set out in detail, harvesting being defined as a two-step process involving cell 'detachment' from the microcarriers' surface followed by the 'separation' of the two entities. The new detachment method is based on theoretical concepts originally developed for secondary nucleation due to agitation. Based on this theory, it is suggested that a short period (here 7min) of intense agitation in the presence of a suitable enzyme should detach the cells from the relatively large microcarriers. In addition, once detached, the cells should not be damaged because they are smaller than the Kolmogorov microscale. Detachment was then successfully achieved for hMSCs from two different donors using microcarrier/cell suspensions up to 100mL in a spinner flask. In both cases, harvesting was completed by separating cells from microcarriers using a Steriflip® vacuum filter. The overall harvesting efficiency was >95% and after harvesting, the cells maintained all the attributes expected of hMSC cells. The underlying theoretical concepts suggest that the method is scalable and this aspect is discussed too. © 2014 The Authors.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Agitation conditions for the culture and detachment of hMSCs from microcarriers in multiple bioreactor platforms

In our recent work in different bioreactors up to 2.5L in scale, we have successfully cultured hMSCs using the minimum agitator speed required for complete microcarrier suspension, N JS. In addition, we also reported a scaleable protocol for the detachment from microcarriers in spinner flasks of hMSCs from two donors. The essence of the protocol is the use of a short period of intense agitation in the presence of enzymes such that the cells are detached; but once detachment is achieved, the cells are smaller than the Kolmogorov scale of turbulence and hence not damaged. Here, the same approach has been effective for culture at N JS and detachment in-situ in 15mL ambr™ bioreactors, 100mL spinner flasks and 250mL Dasgip bioreactors. In these experiments, cells from four different donors were used along with two types of microcarrier with and without surface coatings (two types), four different enzymes and three different growth media (with and without serum), a total of 22 different combinations. In all cases after detachment, the cells were shown to retain their desired quality attributes and were able to proliferate. This agitation strategy with respect to culture and harvest therefore offers a sound basis for a wide range of scales of operation.

Five Turning Points in the Historical Progress of Statistics - My Personal Vision

Statistics has penetrated almost all branches of science and all areas of human endeavor. At the same time, statistics is not only misunderstood, misused and abused to a frightening extent, but it is also often much disliked by students in colleges and universities. This lecture discusses/covers/addresses the historical development of statistics, aiming at identifying the most important turning points that led to the present state of statistics and at answering the questions “What went wrong with statistics?” and “What to do next?”. ACM Computing Classification System (1998): A.0, A.m, G.3, K.3.2.