Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .

Thermographie zur Temperaturmessung beim Laser-Sintern – ein Beitrag zur Qualitätssicherung?

Beim Laser-Sintern wird das Pulverbett durch Heizstrahler vorgeheizt, um an der Pulveroberfläche eine Temperatur knapp unterhalb des Materialschmelzpunktes zu erzielen. Dabei soll die Temperaturverteilung auf der Oberfläche möglichst homogen sein, um gleiche Bauteileigenschaften im gesamten Bauraum zu erzielen und den Bauteilverzug gering zu halten. Erfahrungen zeigen jedoch sehr inhomogene Temperaturverteilungen, weshalb oftmals die Integration von neuen oder optimierten Prozessüberwachungssystemen in die Anlagen gefordert wird. Ein potentiell einsetzbares System sind Thermographiekameras, welche die flächige Aufnahme von Oberflächentemperaturen und somit Aussagen über die Temperaturen an der Pulverbettoberfläche erlauben. Dadurch lassen sich kalte Bereiche auf der Oberfläche identifizieren und bei der Prozessvorbereitung berücksichtigen. Gleichzeitig ermöglicht die Thermografie eine Beobachtung der Temperaturen beim Lasereingriff und somit das Ableiten von Zusammenhängen zwischen Prozessparametern und Schmelzetemperaturen. Im Rahmen der durchgeführten Untersuchungen wurde ein IR-Kamerasystem erfolgreich als Festeinbau in eine Laser-Sinteranlage integriert und Lösungen für die hierbei auftretenden Probleme erarbeitet. Anschließend wurden Untersuchungen zur Temperaturverteilung auf der Pulverbettoberfläche sowie zu den Einflussfaktoren auf deren Homogenität durchgeführt. In weiteren Untersuchungen wurden die Schmelzetemperaturen in Abhängigkeit verschiedener Prozessparameter ermittelt. Auf Basis dieser Messergebnisse wurden Aussagen über erforderliche Optimierungen getroffen und die Nutzbarkeit der Thermografie beim Laser-Sintern zur Prozessüberwachung, -regelung sowie zur Anlagenwartung als erster Zwischenstand der Untersuchungen bewertet.

Corrected kriging update formulae for batch-sequential data assimilation

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the TeX already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when TeX new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Reefs shift from net accretion to net erosion along a natural environmental gradient

Coral reefs persist in an accretion-erosion balance and ocean acidification resulting from anthropogenic CO2 emissions threatens to shift this balance in favor of net reef erosion. Corals and calcifying algae, largely responsible for reef accretion, are vulnerable to environmental changes associated with ocean acidification, but the direct effects of lower pH on reef erosion has received less attention, particularly in the context of known drivers of bioerosion and natural variability. This study examines the balance between reef accretion and erosion along a well-characterized natural environmental gradient in Kane'ohe Bay, Hawai'i using experimental blocks of coral skeleton. Comparing before and after micro-computed tomography (µCT) scans to quantify net accretion and erosion, we show that, at the small spatial scale of this study (tens of meters), pH was a better predictor of the accretion-erosion balance than environmental drivers suggested by prior studies, including resource availability, temperature, distance from shore, or depth. In addition, this study highlights the fine-scale variation of pH in coastal systems and the importance of microhabitat variation for reef accretion and erosion processes. We demonstrate significant changes in both the mean and variance of pH on the order of meters, providing a local perspective on global increases in pCO2. Our findings suggest that increases in reef erosion, combined with expected decreases in calcification, will accelerate the shift of coral reefs to an erosion-dominated system in a high-CO2 world. This shift will make reefs increasingly susceptible to storm damage and sea-level rise, threatening the maintenance of the ecosystem services that coral reefs provide.

Intrinsic noise in gene regulatory networks

Cells are intrinsically noisy biochemical reactors: low reactant numbers can lead to significant statistical fluctuations in molecule numbers and reaction rates. Here we use an analytic model to investigate the emergent noise properties of genetic systems. We find for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled. The noise strength immediately following single gene induction is almost twice the final steady-state value. We find that fluctuations in the concentrations of a regulatory protein can propagate through a genetic cascade; translational noise control could explain the inefficient translation rates observed for genes encoding such regulatory proteins. For an autoregulatory protein, we demonstrate that negative feedback efficiently decreases system noise. The model can be used to predict the noise characteristics of networks of arbitrary connectivity. The general procedure is further illustrated for an autocatalytic protein and a bistable genetic switch. The analysis of intrinsic noise reveals biological roles of gene network structures and can lead to a deeper understanding of their evolutionary origin.

MOREMATA: Stata module (Mata) to provide various functions

This package includes various Mata functions. kern(): various kernel functions; kint(): kernel integral functions; kdel0(): canonical bandwidth of kernel; quantile(): quantile function; median(): median; iqrange(): inter-quartile range; ecdf(): cumulative distribution function; relrank(): grade transformation; ranks(): ranks/cumulative frequencies; freq(): compute frequency counts; histogram(): produce histogram data; mgof(): multinomial goodness-of-fit tests; collapse(): summary statistics by subgroups; _collapse(): summary statistics by subgroups; gini(): Gini coefficient; sample(): draw random sample; srswr(): SRS with replacement; srswor(): SRS without replacement; upswr(): UPS with replacement; upswor(): UPS without replacement; bs(): bootstrap estimation; bs2(): bootstrap estimation; bs_report(): report bootstrap results; jk(): jackknife estimation; jk_report(): report jackknife results; subset(): obtain subsets, one at a time; composition(): obtain compositions, one by one; ncompositions(): determine number of compositions; partition(): obtain partitions, one at a time; npartitionss(): determine number of partitions; rsubset(): draw random subset; rcomposition(): draw random composition; colvar(): variance, by column; meancolvar(): mean and variance, by column; variance0(): population variance; meanvariance0(): mean and population variance; mse(): mean squared error; colmse(): mean squared error, by column; sse(): sum of squared errors; colsse(): sum of squared errors, by column; benford(): Benford distribution; cauchy(): cumulative Cauchy-Lorentz dist.; cauchyden(): Cauchy-Lorentz density; cauchytail(): reverse cumulative Cauchy-Lorentz; invcauchy(): inverse cumulative Cauchy-Lorentz; rbinomial(): generate binomial random numbers; cebinomial(): cond. expect. of binomial r.v.; root(): Brent's univariate zero finder; nrroot(): Newton-Raphson zero finder; finvert(): univariate function inverter; integrate_sr(): univariate function integration (Simpson's rule); integrate_38(): univariate function integration (Simpson's 3/8 rule); ipolate(): linear interpolation; polint(): polynomial inter-/extrapolation; plot(): Draw twoway plot; _plot(): Draw twoway plot; panels(): identify nested panel structure; _panels(): identify panel sizes; npanels(): identify number of panels; nunique(): count number of distinct values; nuniqrows(): count number of unique rows; isconstant(): whether matrix is constant; nobs(): number of observations; colrunsum(): running sum of each column; linbin(): linear binning; fastlinbin(): fast linear binning; exactbin(): exact binning; makegrid(): equally spaced grid points; cut(): categorize data vector; posof(): find element in vector; which(): positions of nonzero elements; locate(): search an ordered vector; hunt(): consecutive search; cond(): matrix conditional operator; expand(): duplicate single rows/columns; _expand(): duplicate rows/columns in place; repeat(): duplicate contents as a whole; _repeat(): duplicate contents in place; unorder2(): stable version of unorder(); jumble2(): stable version of jumble(); _jumble2(): stable version of _jumble(); pieces(): break string into pieces; npieces(): count number of pieces; _npieces(): count number of pieces; invtokens(): reverse of tokens(); realofstr(): convert string into real; strexpand(): expand string argument; matlist(): display a (real) matrix; insheet(): read spreadsheet file; infile(): read free-format file; outsheet(): write spreadsheet file; callf(): pass optional args to function; callf_setup(): setup for mm_callf().

A generalisation of the Delogne-Kasa method for fitting hyperspheres

In this paper, we examine the problem of fitting a hypersphere to a set of noisy measurements of points on its surface. Our work generalises an estimator of Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972,117-123) which he proposed for circles and which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. We also generalise Chan's 'circular functional relationship' to describe the distribution of points. We derive the Cramer-Rao lower bound (CRLB) under this model and we derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We perform a statistical analysis of the estimate of the hypersphere's centre. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than M + 1, where M is the dimension of the hypersphere. The variance exists when the number of sample points is greater than M + 2. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRLB. We provide simulation results to support our findings.

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented.

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented.

UncertML: an XML schema for exchanging uncertainty

Authors from Burrough (1992) to Heuvelink et al. (2007) have highlighted the importance of GIS frameworks which can handle incomplete knowledge in data inputs, in decision rules and in the geometries and attributes modelled. It is particularly important for this uncertainty to be characterised and quantified when GI data is used for spatial decision making. Despite a substantial and valuable literature on means of representing and encoding uncertainty and its propagation in GI (e.g.,Hunter and Goodchild 1993; Duckham et al. 2001; Couclelis 2003), no framework yet exists to describe and communicate uncertainty in an interoperable way. This limits the usability of Internet resources of geospatial data, which are ever-increasing, based on specifications that provide frameworks for the ‘GeoWeb’ (Botts and Robin 2007; Cox 2006). In this paper we present UncertML, an XML schema which provides a framework for describing uncertainty as it propagates through many applications, including online risk management chains. This uncertainty description ranges from simple summary statistics (e.g., mean and variance) to complex representations such as parametric, multivariate distributions at each point of a regular grid. The philosophy adopted in UncertML is that all data values are inherently uncertain, (i.e., they are random variables, rather than values with defined quality metadata).

Income distribution dependence of poverty measure:a theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the 'global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy. © 2006 Elsevier B.V. All rights reserved.

Fixed vs. variable noise in 2AFC contrast discrimination: lessons from psychometric functions.

Recent discussion regarding whether the noise that limits 2AFC discrimination performance is fixed or variable has focused either on describing experimental methods that presumably dissociate the effects of response mean and variance or on reanalyzing a published data set with the aim of determining how to solve the question through goodness-of-fit statistics. This paper illustrates that the question cannot be solved by fitting models to data and assessing goodness-of-fit because data on detection and discrimination performance can be indistinguishably fitted by models that assume either type of noise when each is coupled with a convenient form for the transducer function. Thus, success or failure at fitting a transducer model merely illustrates the capability (or lack thereof) of some particular combination of transducer function and variance function to account for the data, but it cannot disclose the nature of the noise. We also comment on some of the issues that have been raised in recent exchange on the topic, namely, the existence of additional constraints for the models, the presence of asymmetric asymptotes, the likelihood of history-dependent noise, and the potential of certain experimental methods to dissociate the effects of response mean and variance.

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.

Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.