MACHALOVÁ, J., VAJČNEROVÁ, I., RYGLOVÁ, K.: **Spatial** **modelling** of assumption of tourism development with geographic IT using. Acta univ. agric. et silvic. Mendel. Brun., 2010, LVIII, No. 6, pp. 279–294 The aim of this article is to show the possibilities of **spatial** **modelling** and analysing of assumptions of tourism development in the Czech Republic with the objective to make decision-making processes in tourism easier and more eﬃ cient (for companies, clients as well as destination managements). The development and placement of tourism depend on the factors (conditions) that inﬂ uence its ap- plication in speciﬁ c areas. These factors are usually divided into three groups: selective, localization and realization. Tourism is inseparably connected with space – countryside. The countryside can be modelled and consecutively analysed by the means of geographical information technologies. With the help of **spatial** **modelling** and following analyses the localization and realization conditions in the regions of the Czech Republic have been evaluated. The best localization conditions have been found in the Liberecký region. The capital city of Prague has negligible natural conditions; however, those social ones are on a high level. Next, the **spatial** analyses have shown that the best realization conditions are provided by the capital city of Prague. Then the Central-Bohemian, South-Moravian, Moravian-Silesian and Karlovarský regions follow. The development of tourism destination is de- pended not only on the localization and realization factors but it is basically aﬀ ected by the level of local destination management. **Spatial** **modelling** can help destination managers in decision-making processes in order to optimal use of destination potential and eﬃ cient targeting their marketing ac- tivities.

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Regionalized compositional data (in form of percentages, probabilities, proportions, frequencies, and concentrations) are common in geosciences. Geochemical and mineralogical data, proportions of material occupied the porous media in an aquifer or oil reservoir, proportions of rock types, soil types and land uses in the study area are examples of such compositional information. Most of the time regionalized compositional data are statistically and spatially related to one or more dependent categorical data such as rock types, soil types, alteration units, and continental crustal blocks. Complex statistical and **spatial** relationships between these mixed data should be honoured in the simulated and/or estimated models. Developing joint predictive models for such geospatial mixed data is necessary due to their applicability for geoscience **modelling** projects. This PhD thesis explored and introduced several approaches to **spatial** **modelling** of regionalized compositional and categorical data for different situations and applications. To this end, multiple-point geostatistical techniques have priority due to their capability for reproducing complex **spatial** patterns. However, to implement MPS techniques, large and dense compositional and categorical training images or training data are needed. For situations where such training information is not available and/or complex **spatial** patterns are not present in the study area (or such patterns are not our interest), two-point geostatistical algorithms can be implemented. Finally, several advantages of machine learning algorithms such as recognition of complex statistical patterns, internal feature selection and cross-validation can be used for the joint **modelling** of compositional and categorical data. However, care should be taken while implementing such techniques on geospatial data as they are non-**spatial** algorithms.

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A vital aspect of **spatial** heterogeneity is pattern , which can be dened as a departure from randomness (Galiano, 1982 Addicott et al., 1987). The character of the distribution of species and habitats is of fundamental ecological and sociobiological importance. The geometric shape of the constituents of an ecosystem, may, for example, aect the response to disease or para- sites. For example a complex of small habitats will provide a physical barrier to the spread of an epidemic (Jetschke, 1992) and the destruction of ne-scale vegetational mosaics by re manage- ment programs has created large patches through which res spread rapidly (Minnich, 1983). Larger patches are, however, benecial under other circumstances: predators are able to remove aphid clusters if they can move over suciently large areas, whereas a patchy environment in- hibits predator movements and leads to pest outbreaks (Kareiva & Andersen, 1988). Thus the levels of clumping or aggregation of species, resources or features in the physical environment are important for understanding the functioning of systems and the response of individuals. Many measures of aggregation have been developed in the biological and physical sciences (Leg- endre & Fortin, 1989). Biometricians have concentrated on statistical tests for distinguishing aggregated, random and regular patterns (Thomas, 1951 Diggle, 1977 Galiano, 1982 Perry, 1995). Many **spatial** models clearly produce clumped patterns, so that a statistical test to prove the presence of aggregation does not provide signicant new information. More useful is the dynamical approach to the variation in the level of clumping which is developed here for discrete **spatial** models, which is also highly relevant to other lattice-based data, such as satellite images.

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Note th a t the distribution is exact if b{s) is constant on A, otherwise it is an approx imation. Gamma random fields offer a means by which we can model uncertainty about both the location and the size of factors (for example, the pores in the cement) th at we believe have an influence on the formation of cracks. Wolpert and Ickstadt (1998a) introduced the idea of using Gamma random fields in their class of Bayesian hierarchical models used to analyse spatially dependent count data. As an illustra tive example, they modelled the density and **spatial** correlation of hickory trees. The incorporation of a Gamma random field and Gaussian kernel in order to model latent **spatial** covariates was also used in the analysis of the effect of traffic pollution on respiratory disorders in children (Best et al. (2000a)). It has also been used in the analysis of origin/destination trip data (Ickstadt and Wolpert (1999)).

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Because the **spatial** configuration of cervix cancer needs to be defined according to the applicator perspective, an appli- cator coordinate system needs to be defined. The applicator reconstruction [9, 10] is performed on radiotherapy plan- ning systems by importing predefined geometry structures. The applicator consists of tandem, ring and eventual ad- ditional needles, see Figure 1, which are all reconstructed independently. The ring structure, when inserted, tightly fits to the cervix anatomy, and provides a good base for defining the applicator coordinate system. Different appli- cator types may have different ring diameter, may be de- scribed with different number of contour points, however in practice the point ordering is always the same. For the illustration see Fig. 2. We propose that the applicator coor- dinate system is defined with origin in the ring center (the last point of the contour), xy plane in the ring plane, x axis in the direction towards ring contour starting point and z axis in the direction of the tandem.

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Previous approaches to quantifying geographical accessibility to healthcare have included straight-line (Euclidean) distances [19,21-26], drive times [8,27,28] and network analyses [26,29]. Euclidean distances fail to account for different patterns of service use and topo- graphy and assume utilisation rates are uniform within facility catchments and that patients always use the nearest facility [6,25,26]. Drive times have been shown to be a preferable measure in developed countries [30] where vehicular transport is widespread, but are unlikely to be useful in a developing country context where a large proportion of the population walk to the nearest facility [26]. An alternative, the cost surface based on travel times, showed closer agreement with the pattern of use in rural South Africa when modelled as a logistic function [31]. These forms of distance measurement have been used to analyse utilisation by using metrics such as number of health facilities within a certain pre- defined distance of the facility, the average distance to n number of health facilities and the gravity model [6,32]. The gravity model is a **spatial** interaction model analo- gous to Newton’s law of gravity where the force of attraction between two bodies varies proportionally to the product of their masses and inversely to distance between them [33,34]. In this form, patient interaction with healthcare is denoted by flow from patient origin to the health service while the masses are represented by various utilization effects such as cost, size of health facility or propensity of patient groups to use healthcare [15]. The other distance metrics either ignore the inter- action with other possible providers within the consid- ered region or may assume that patients always use the nearest facility [35].

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The bottom right plot in Figure 5 shows the posterior covariance function with 95% confi- dence interval. This shows that **spatial** correlation is over quite a short range, around 0-1000 metres. Plots comparing the prior to the posterior for the parameters σ and φ showed that these were well identified by the data (the identifiability of φ is a common problem in **spatial** analyses). Table 2 gives the estimated coefficients from the Weibull model for the three years under consideration, it can be seen that the coefficients are quite similar for each year. Using the **spatial** survival **modelling** framework, we can also illustrate answers to questions of substantive interest including (i) where in space is the London Fire Brigade’s target response time of 6 minutes not being met; and (ii) what have been the effects on target response times of the 2014 fire station closures?

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Perancangan bandar dan wilayah merupakan antara bidang yang terlibat secara langsung dalam menyusun strategi pengurusan sumber asli. Ia bertanggungjawab dalam menentukan hala tuju pembangunan melalui penyediaan pelan-pelan pembangunan seperti Rancangan Struktur Negeri (RSN) dan Rancangan Tempatan Daerah (RTD). Perkembangan teknologi GIS telah mencipta peluang dalam membantu aktiviti perancangan mencapai keputusan dengan lebih cepat dan tepat. Keupayaan GIS yang terpenting adalah kebolehannya menangani data **spatial** (ruangan) dan data atribut (bukan ruangan) yang berkaitan dengan sesuatu objek (Ahris, 1994). Dengan perkataan lain, GIS menyediakan kerangka bagi mengintegrasi jumlah data **spatial** dan atribut yang banyak daripada berbagai-bagai sumber dan masa tertentu. Kesudahannya, suatu proses pembuatan keputusan yang baik dapat diputuskan berdasarkan beberapa senario semasa yang dihasilkan menggunakan fungsi GIS.

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According to Frey and Weck (1983) the size of the underground economy can be explained by the effective tax burden, the perception of the tax burden, the unemployment rate, the level of[r]

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Methods of **spatial** statistics have been widely applied in fields like biometrics and geostatis- tics after Whittle (1954) introduced the first **spatial** models. **Spatial** econometrics, however, has only been studied for the past 40 years. Paelinck and Klaassen (1979) published the first work which deals solely with this sub-discipline of econometrics. The characteristic property of **spatial** data in contrast to non-**spatial** data is that it links attributes to a geographic lo- cation (Fischer and Wang, 2011). 1 In case of a space-time data set information about time is included, too. Due to this additional information, it is possible to model dependencies between different observations which rely on geographical proximity. A similar concept in non-**spatial** **modelling** can only be found with regard to the time dimension. Hence, many concepts of **spatial** models have been inspired by the time series literature. Unfortunately, an essential property of time series does not hold in **spatial** **modelling**: Whereas time series have a natural ordering along the time line – from the oldest to the most recent observa- tion – **spatial** data form a network which does not have a defined starting and end point. Concepts like predetermination, which often facilitates estimation in the time series context, generally do not exist in **spatial** **modelling**. Tobler’s first law of geography summarizes this circumstance nicely: “everything is related to everything else, but near things are more re- lated than distant things” (Tobler, 1970, p. 236). It also highlights another key assumption of **spatial** **modelling**: While it is anticipated that everything, for example every county or census tract, is connected to the other units through the **spatial** process, it is also assumed that this connection depends on the proximity of units, i.e. is diminishing with increasing distance.

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ity intuitively measures urban processes which are defined as the set of interac- tions that measure the patterns of flow and networks of relations in a city [10]. As such, observations in our inherently **spatial** cities can be probabilistically determined by SAC: the similarity between two observations as a function of geographical proximity. Figure 1.1 is a visualisation of this concept where each point represents a **spatial** location for some simulated observation and each colour represents a value for each observation from low (blue) to high (red). Such **spatial** relationships violate the typical assumption present in non-**spatial** statistics; all observations are independent and identically distributed (i.i.d) ran- dom variables. This violation exploits the spatiotemporal dependency structure present in cities [58]. However, such dependency structures in urban data may introduce redundancy and risk an overestimation of statistical effects, it is im- portant to take account for these redundancies, especially during the validation stages of statistical **modelling**.

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It has become clear that these reaction pathways are highly spa- tially organized within the cell, with many reactions occurring only in speciﬁc regions (Srere, 2000). For example, within signal trans- duction pathways, **spatial** gradients and microdomains of signalling occur due to localised chemical species, such as phosphatases. As intracellular distances increase, active signalling messengers are more likely to become deactivated on their journey to the cell inte- rior (Meyers et al., 2006). The dose response curves of the yeast Mitogen Activated Protein Kinase (MAPK) cascade differ depend- ing upon both the geometry of the cell and the subtle change in feedback parameters (Zhao et al., 2011).

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We have demonstrated that a Bayesian framework, based on Gaussian mixture models, for **spatial** proteomics can provide whole sub-cellular proteome uncertainty quantification on the assignment of proteins to organelles and such information is invaluable. Performing MAP inference using our generative model provides fast and straightforward approach, which is vital for quality control and early data exploration. Full posterior inference using MCMC pro- vides not only point estimates of the posterior probability that a protein belongs to a particular sub-cellular niche, but uncertainty in this assignment. Then, this uncertainty can be summa- rised in several ways, including, but not limited to, equi-tailed credible intervals of the Monte- Carlo samples of posterior localisation probabilities. Posterior distributions for indivdual pro- teins can then be rigorously interrogated to shed light on their biological mechanisms; such as, transport, signalling and interactions.

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in Amazonia have to consider that transportation networks (rivers and roads) play a decisive role in governing human settlement patterns. As an illustration, Figure 1 shows the urban settlements in Amazonia, shown as white areas, and the road network in red lines. A realistic model for land use changes in the region has to take into account that the roads establish preferential directions for human occupation and land use changes, which would be impossible to be captured in isotropic neighborhoods prevalent in most **spatial** modeling techniques. The neighborhood definitions in any **spatial** model that aims at understanding the processes in an area such as Amazonia need to be based on flexible definitions of proximity that are able to capture action-at-a-distance.

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that point. Taking a percentile-based threshold is convenient when dealing with a **spatial** array of data. In Clancy et al. (2015), the 97th percentile was used. Caires and Sterl (2005) examined both the 93rd and 97th percentile and found the higher to be more appropriate in general. Vanem (2015) tested thresholds based on even higher percentiles and found, in some cases, a value around the

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O ther approaches to the same problem have involved introducing different cell types into the model. Cowpertwait (1994) explored a single-site model in which one cell type is of high intensity and short duration (‘heavy cells’) and the other has a lower intensity but a longer duration (‘light cells’). Each storm has a proportion of each type of cell and the random variables for the intensity and duration of each cell type are conditionally independent given the cell type. As long as the fitted values for the respective intensity and duration param eters of the cell types reflect the ‘heavy’ and ‘light’ properties above, a negative correlation will have been induced between the intensity and duration of the rain cells. Cowpertwait (1996) extends this model structure to a **spatial**-temporal model in which the param eter for the area of the rain cells also varies between cell types. The model formulation allows for any num ber of cell types to be specified although for every cell type introduced the num ber of param eters of the model increases by 4. Allowing the variables for intensity, duration and area to be stochastically dependent is thus a m ethod of introducing correlation which is potentially less expensive in term s of the number of model param eters to be estimated.

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NOC analysis allows us to calculate the ﬁeld components only at location p. In order to compute the ﬁeld at an arbi- trary position in the region, a **spatial** model is required. In this study, the SCH technique was chosen. The SCH mod- elling is devoted to potential and ﬁeld representation in a spherical cap. Although the method poses many difﬁculties (Hwang and Chen, 1997; Thebault et al., 2004), it has been widely employed in deriving regional geomagnetic models, for example, for Canada, Africa and China regions (Haines, 1985; Kotze, 2003; An, 2003).

Gaussian dispersion models assume an emission transport from continuous pollution sources in homogenous wind field without **spatial** limits. The transport itself is in the model provided by the convection by wind and via turbulence diffusion which is described statistically by Gaussian distribution. **Spatial** limitations, mainly the terrain, are included into model by correction coefficients. Gaussian dispersion models are commonly used for long term (f.e. annual) average concentrations **modelling**. The dispersion is calculated for a set of standard meteorological conditions and summed, weighted by probability of occurrence of such conditions. The most commonly used Gaussian dispersion models are CALINE3 (Benson, 1979) and ADMS-Urban [1]. The SYMOS’97 model [18] is a reference pollution dispersion model in the Czech Republic. It is a Gaussian model which calculates pollution dispersion of both gaseous and particulate pollutants from point, linear and area pollution sources. The model takes into account both dry and wet deposition as well as chemical reactions during transport.

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Further work might determine whether the results obtained in this investigation apply to other model formulations. The present investigation has obtained illustrative examples of how rainfall variability, as filtered by using different spa- tial aggregation lengths, feeds through to variability in mod- elled runoff response at the catchment scale. More exten- sive investigations would strengthen this understanding and provide additional guidance on the design of radar/raingauge networks for flow forecasting and the **spatial** resolution re- quirements for rainfall at different catchment scales. Acknowledgements. The writers wish to thank three anonymous reviewers for the discussions and insight provided. This work was supported by the European Community’s Sixth Framework Programme through the grant to the budget of the Integrated Project FLOODsite, Contract GOCE-CT-2004-505420 and in part by the STREP Project HYDRATE, Contract GOCE 037024. The Regional Meteorological Observatory of Friuli-Venezia-Giulia is thanked for making the radar dataset available and for the assistance in data analysis.

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The above experiment shows that this simple sensitivity test is effective for controlling the **spatial** discretisation in trajectory sub-**modelling**. For the same trajectory model, the appropriate size of grid cell may need to be varied according to geographic location (shape of bathymetry and shore line, tidal conditions) or oil spill scenario. Such tests should often be undertaken to assure the quality of model output. The suggested method is obviously practical for such purposes. Of course, this preliminary study relies heavily on qualitative analysis and professional judgement but is sufficient for illustrating the necessity for such analyses of discretisation in environmental **modelling**. More quantitative analyses can be planned and carried using more complex designs of sensitivity analysis.

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