ON ROBUST ANALYSIS OF PAYCHECK: CASE STUDY

On robust analysis of paycheck: case study. Acta univ. agric. e

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models

Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations (survey)

Analysis and Stochastic

Entropy based statistical inference for methane emissions released from wetland

We concentrate on the paradigm question how much stochasticity and how much chaos are present in the methane emission model. In particular we analyze the residua from the process of methane emissions from wetlands in the sedge-grass marsh, in South Bohemia, Czech Republic. Relation to entropy and a specific version of Kullback–Leibler divergence will be given. A graphical tool to assess the amount of entropy in the system is developed and illustrated on real data from the sedge-grass marsh methane emission

COMPARATIVE SIMULATION STUDY OF LIKELIHOOD RATIO TESTS FOR HOMOGENEITY OF THE EXPONENTIAL DISTRIBUTION

Abstract STŘELEC, L., STEHLÍK, M.: Comparative simulation study of likelihood ratio tests for homogeneity of the exponential distribution. Acta univ. agric. et silvic. Mendel. Brun., 2012, LX, No. 7, pp. 307-314 The aim of this paper is to present and discuss the power of the exact likelihood ratio homogeneity testing procedure of the number of components k in the exponential mixture. First we present the likelihood ratio test for homogeneity (ELR), the likelihood ratio test for homogeneity against twocomponent exponential mixture (ELR2), and fi nally the likelihood ratio test for homogeneity against three-component exponential mixture (ELR3). Comparative power study of mentioned homogeneity tests against three-component subpopulation alternative is provided. Therein we concentrate on various setups of the scales and weights, which allow us to make conclusions for generic settings. The natural property is observed, namely increase of the power of exact likelihood ratio ELR, ELR2 and ELR3 tests with scale parameters considered in the alternative. We can state that the diff erences in power of ELR, ELR2 and ELR3 tests are small -therefore using of the computationally simpler ELR2 test is recommended for broad usage rather than computationally more expensive ELR3 test in the cases when unobserved heterogeneity is modelled. Anyhow caution should be taken before automatic usage of ELR3 in more informative settings, since the application of automatic methods hoping that the data will enforce its true structure is deceptive. Application of obtained results in reliability, fi nance or social sciences is straightforward. exponential distribution, homogeneity testing, likelihood ratio, mixture models, Monte Carlo simulations, power study Currently, many homogeneity tests exist -see Stehlík and Wagner (2012) and references therein

Influence of organic and inorganic fertilization on soil properties and water infiltration

ArticleSoil aggregate stability (SAS) belongs to the most important parameters determining the quality of soil and fertilizer influence on soil aggregation. We evaluated the relationship between SAS, hydro–physical soil properties and infiltration rates in three long–term field experiments founded in 1956 on different soils. Soil properties under three fertilization regimes– no fertilization, farmyard manure, farmyard manure and mineral fertilization–were evaluated at silty loam Chernozem, silty loam Phaeozem and sandy loam–loam Cambisol. A significant impact of fertilization on SAS was found, even though the differences in SAS were rather low. The lowest SAS was recorded at plots with manure and mineral fertilization (25.1%) compared with plots without fertilization (28.7%) and plots with manure–only fertilization (28.2%). The highest SAS (36.5%) and the highest semi–capillary porosity (SP; 11%) were observed at sandy loam–loam soil. Hydro–physical soil properties were more favourable at fertilized plots (SP 9.6% and bulk density ρb 1.31 g cm-3 ) compared with unfertilized ones (SP 8.8% and ρb 1.35 g cm-3 ). The lowest SP (8.32%) and the highest ρb (1.37 g cm-3 ) were recorded at Phaeozem, which corresponded with the lowest SAS (19.4%). Chernozem had similar soil texture to Phaeozem, but SAS (24.7%), SP (9%) and ρb (1.27 g cm-3 ) were more favourable. Despite the low level of statistical significance due to the large variation of infiltration measurements, a higher infiltration rate was recorded at fertilized plots (45 mm hour-1 ) compared to unfertilized ones (35 mm hour-1 )

Cosmic-ray fluctuations and interplanetary magnetic fields

The relations of cosmic-ray fluctuations to those of interplanetary magnetic fields (IMF) and the possible consequences of the magnetic helicity of IMF for the acceleration of cosmic rays are examined using experimental data from two neutron monitors and data on IMF in interplanetary space. The spectral tensor of IMF at two different distances from the Sun is determined for several selected intervals of 10-15 hours duration. Data from IMP-8 and Helios-1 are used. Cross correlations of IMF with cosmic rays measured by the Lomnický Štít neutron monitor, based on 5 min data, are estimated. A comparison of spectral slopes of the power spectrum density at the Lomnický Štít and Calgary neutron monitors demonstrates the possibility of using a single neutron monitor data point as a representative of the CR fluctuation power spectrum slope. It is shown that the data are not in all cases consistent with model of 3D turbulence in interplanetary space as the cause of the cosmic-ray fluctuation spectrum. Magnetic helicity, kinetic fluctuation energy, and the correlation length of the magnetic field are deduced from the limited amount of data and compared with values obtained by Matthaeus and Goldstein (1982). Based on the theoretical approach by Fedorov et al. (1992) the efficiency of acceleration of cosmic rays due to the presence of anisotropic reflective non-invariant IMF at various heliospheric distances is estimated. © 1993 Kluwer Academic Publishers