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Tutkimuksen ensimmäisen osan tarkoituksena oli selvittää erilaisia eriyttämisen tapoja ja käytänteitä, sekä eriyttämisen vaikuttavuutta. Lähteinä käytettiin aikaisempaa tutkimusta ja kirjallisuutta eriyttämisestä. Eriyttämisellä tarkoitetaan kaikkeen opetukseen kuuluvia keinoja huomioida oppilaiden ja opetusryhmien erilaiset tarpeet. Eriyttämisellä pyritään luomaan kaikille oppilaille tasa-arvoiset mahdollisuudet kehittää itseään ja oppia uutta. Opetusta voidaan eriyttää opetettavan sisällön valinnan, syvyyden ja laajuuden suhteen, opetusjärjestelyjen ja käytetyn ajan suhteen, opetusmenetelmien, työtapojen ja materiaalin suhteen, sekä arvioinnin ja palautteen antamisen muotojen suhteen. Lahjakkaiden eriyttämistä käsiteltiin myös erikseen: kuinka heidän opetustaan voi rikastuttaa luokkahuoneessa ja mitä mahdollisuuksia on lahjakkaiden koulun ulkopuoliseen eriyttämiseen. Tutkimuksen toisessa osassa tarkoituksena oli idea-tasolla antaa esimerkkejä seitsemännen luokan alun, lukuja ja laskutoimituksia jakson, opetuksen eriyttämiseen. Opetusta on hyvä muokata pienin askelin, ideat opittuaan ja omaksuttuaan eriyttämistä on helpompi soveltaa myös jatkossa. Käytäntö näyttää kullekin oppilaalle ja opetusryhmälle parhaiten toimivat eriyttämisen tavat. Eriyttämisen suunnittelussa korostuu jatkuvan arvioinnin merkitys sekä ydinasioiden tunnistaminen. Eriyttäminen on opetuksen väline, ei päätarkoitus. Opetusta eriyttämällä voidaan nostaa oppimismotivaatiota, vaikuttaa positiivisesti työrauhaan sekä suoda kaikille oppilaille oppimisen ilo. Opettajan positiivinen asenne eriyttämiseen vaikuttaa kokemukseen eriyttämisen haasteellisuudesta, myönteisellä asenteella eriyttämistä ei koeta liian haastavaksi. Opetuksen eriyttämisen tarpeen arvioimisen ja suunnittelun avuksi voi hyödyntää eriyttämisen laatukriteeristöä (Rock et al, liitteenä).

Recent studies on day-care staff have reported on problems in hiring qualified staff, and in increased resignations in existing staff. These problems are connected to an increase in workload and stress, and reduced wellbeing at work. When workload and challenges in day-care work increase, there can even be a risk of diminishing the pedagogical quality of education. The problems seem to occur differently and in different magnitudes in different day-care units, which indicates learning conditions’ possible segregation. In the case of schools, the socioeconomic status of nearby population has been noticed to affect children’s predisposed abilities to learn, and their support requirements in learning. This effect can be assumed to affect early childhood education similarly, which would lead to day-cares in socioeconomically disadvantaged areas to require extra resources and staff to compensate for the children’s increased support requirements. If those extra resources are not available, the staff will experience increased workload and stress, which will cause problems in the long term. The city is known to be somewhat socioeconomically segregated, and if this is mirrored in day-cares so that the backgrounds of children in day-cares get segregated, it may also start to affect the quality of education. In this case the unevenly distributed challenges would cause institutional segregation of learning conditions in early childhood education. The institutional segregation of early childhood education or schools has not been studied much in Finland. Earlier studies on Finnish schools have been able to explain differences between schools through differences in children’s backgrounds, and there has not been a reason to doubt the institutional equality of schools’ quality. The basic principle of the Finnish early childhood education and school system is to provide every child with equal conditions and opportunities to grow and learn. These equal conditions equalise segregation in the population by offering equally high-quality education in both disadvantaged and well-off areas of the city. However, if the segregation of children’s backgrounds is accompanied by the segregation of learning conditions in day-cares, there is a risk of the cumulation of both socioeconomic disadvantage and lower quality of education. In this case, the quality would decrease exactly where it would be most needed. In my thesis I study whether there is differentiation in problems related to hiring or keeping staff in the day-cares in Helsinki, through the numbers of resigned and unqualified staff in each unit. I also look at whether this segregation of day-care units is at all related to the socioeconomic segregation of the city’s population. In the study I utilize HR data from the city of Helsinki and socioeconomic population data from Statistics Finland, which I join onto spatial data of day-cares’ locations. I use this combined dataset to study the segregation of day-cares and its connections to socioeconomic segregation using quantitative statistical methods and spatial analysis methods. The results indicate that there is perceivable segregation in the staff of day-cares in Helsinki, but socioeconomic segregation is able to statistically explain the patterns only slightly. Therefore, mostly other phenomena seem to cause the differentiation in staff related problems, but these phenomena are not yet known. In terms of institutional segregation, the early childhood education system in Helsinki seems to still be quite equal. However, more knowledge about the subject is needed, because both the results in this study, as well as previous studies show some worrying signals pointing to the possibility of institutional segregation. In addition, intense public discourse around the topic of early childhood education, and a wide-ranging worker’s strike, including day-care staff, seem demonstrative of the seriousness of these challenges in day-cares.

Sijoitusten markkinariskin suuruutta tarkastellaan usein riskimittojen avulla. Riskimitta on kuvaus mahdollisia tappioita kuvaavien satunnaismuuttujien joukosta reaalilukuihin. Riski- mittojen avulla erilaisten sijotusten riskillisyyttä pystytään vertailemaan helposti. Pankki- valvojat hyödyntävät riskimittoja pankkien vakavaraisuuden valvonnassa. Pisimpään ylei- sessä käytössä on ollut VaR (Value-at-Risk) niminen riskimitta. VaR kertoo suurimman tappion, joka koetaan jollain asetetulla luottamustasolla α eli se on tappiojakauman α- kvantiili. Baselin uusimassa ohjeistuksessa (Minimum capital requirements of market risk) odotettu vaje niminen riskimitta korvaa VaR-riskimitan pääomavaateen laskennassa. Odotet- tu vaje kertoo, mikä on tappion odotusarvo silloin, kun tappio on suurempi kuin VaR- riskimitan antama luku. Riskimittaa ollaan vaihtamassa, koska VaR ei ole teoreettisilta ominaisuuksiltaan yhtä hyvä kuin odotettu vaje. Tämä johtuu siitä, että VaR ei ole sub- additiivinen, mikä tarkoittaa sitä, että positioiden yhteenlaskettu riski voi olla joissain ta- pauksissa suurempi kuin yksittäisten positioiden riskien summa. Tämä johtaa siihen, että hajauttamattoman sijoitussalkun riski voi olla pienempi kuin hajautetun. Odotettu vaje-riskimitta ei kuitenkaan ole täysin ongelmaton, koska se ei ole konsistentisti pisteytyvä, mikä tarkoittaa, että sille ei ole olemassa pisteytysfunktiota, jonka avulla voi- taisiin verrata estimoituja ja toteutuneita arvoja konsistentisti. Lisäksi se, että odotetun vajeen suuruus riippuu kaikista häntään jäävistä tappioista, tekee siitä herkän hännässä olevien tappioiden virheille. Tämä ei ole kovin hyvä ominaisuus, koska tappiojakaumien häntien estimointiin liittyy paljon epävarmuutta. Koska riskien estimointiin liittyy epävarmuutta, sääntely velvoittaa pankkeja toteumates- taamaan regulatiivisen pääomavaateen laskennassa käytettyjä riskiestimaatteja. Toteuma- testaamisella tarkoitetaan prosessia, jossa estimoituja riskilukuja verrataan toteutuneisiin tappioihin. VaR-estimaattien toteumatestaus perustuu niiden päivien lukumäärälle tes- tausjaksolla, joina tappio ylittää VaR-estimaatin antaman tappiotason. Odotetulle vajeelle ei ole vielä olemassa yhtä vakiintuneita toteumatestausmenetelmiä kuin VaR-estimaateille. Tässä tutkielmassa esitellään kolme erilaista tapaa toteumatestata odotettu vaje estimaat- teja, nämä tavat esittelivät Kratz kollegoineen, Moldenhauer ja Pitera sekä Costanzino ja Curran. Menetelmissä tarkastellaan useamman VaR-tason yhtäaikaisia ylityksiä, suojatun position eli tappion ja riskiestimaatin erotuksen positiiviseen lukuun kumuloitu- vasti summautuvien havaintojen määrää ja VaR-ylityksien keskimääräistä suuruutta. Tutkielman laskennallisessa osuudessa tutkittiin antavatko VaR- ja odotettu vaje- toteumatestit samanlaisia tuloksia ja vaikuttaako riskin estimointiin käytetyn havainto- jakson pituus estimaattien suoriutumiseen toteumatesteissä. Laskelmissa havaittiin, että odotettu vaje- ja VaR-toteumatestit antoivat samanlaisia tuloksia. Markkinadatasta eri kokoisilla estimointi-ikkunoilla lasketut estimaatit saivat toteumatestissä erikokoisia tes- tisuureiden arvoja, ja hyväksyivät väärän mallin tai hylkäsivät oikean malli eri todennä- köisyyksillä. Kun käytettiin puhtaasti simuloitua dataa, eri kokoisilla estimointi-ikkunoilla laskettujen estimaattien tuloksissa ei ollut eroja. Näin voidaan päätellä, että testitulosten erot eri mittaisilla havaintojaksoilla laskettujen estimaattien välillä eivät johdu pelkästään havaintojen määrästä vaan myös laadusta.

Tämän tutkielman tavoitteena on tutustuttaa lukija yksinkertaisiin stokastisiin prosesseihin esimerkkien avulla. Tämän lisäksi esitellään stokastisten prosessien perusominaisuuksia. Stokastiset prosessit ovat matematiikassa osa todennäköisyyslaskennan osa-aluetta. Tutkielman alussa käydään läpi todennäköisyyslaskennan peruskäsitteitä, jotka ovat välttämättömiä stokastisten prosessien ymmärtämisessä. Tämän jälkeen esitellään stokastisten prosessien perusominaisuuksia. Tutkielmassa esiteltävät stokastiset prosessit ovat Bernoullin prosessi, satunnaiskulku ja Poissonin prosessi. Jokaisesta prosessista esitetään esimerkkejä ja niihin käytettäviä jakaumia. Lopuksi on pohdintaa stokastisten prosessien hyödyntämisestä lukio-opetuksessa lyhyen ja pitkän matematiikan osalta. Pohdinta on käyty uuden opetussuunnitelman LOPS19 tavoitteiden ja sisällön mukaan. Pitkässä ja lyhyessä matematiikassa on molemmissa yhden moduulin sisällössä määritelty binomijakauma, jota voidaan käyttää joidenkin stokastisten prosessien tutkimisessa.

One of the most important purposes of urban planning is to create good living environments for city residents. However, there are several conflicting interests that city planners should be able to reconcile in urban planning. For example, city planners should be able to accommodate a variety of functions and modes of transport in a limited street area. In addition to the different modes of transport, accessibility should also be taken into account in urban planning. Urban planning can have a strong influence on the accessibility of physical urban space, and to create accessible urban areas special focus has to be given to accessibility. In this master's thesis, urban planning is researched from the point of view of accessibility. The aim in this thesis is to find out how to coordinate accessibility and different modes of transport (pedestrian, cycling and trams) in urban planning. The thesis sought answers to the following research questions: How accessibility of urban space appeared in planning legislation, guidelines and regulations? What are the biggest challenges of combining accessibility and different modes of transport in same street areas? And how can these challenges be solved? The methods used in this thesis are literature analysis and interview surveys. The aim of literature analysis was to find out, what accessibility is and what is the relationship between accessibility and different modes of transport. Expert interviews were performed to find out, what are the challenges of combining accessibility and different modes of transport in street areas. City of Helsinki was used as a case example in this thesis. Based on this study, it seems that accessibility is taken quite well into consideration in urban planning of Helsinki. The challenges of combining accessibility and different modes of transport in same street, are caused by the lack of available street space, and the conflicts of interest related to the division of street space. These challenges can be avoided if accessibility is taken into account at the beginning of the planning process. However, best results require that accessibility is taken into account in all stages of urban planning.

Above-ground biomass (AGB) estimation is an important tool for predicting carbon flux and the effects of global warming. This study describes a novel application of remote-sensing based AGB estimation in the hemi-boreal vegetation zone of Finland, using Sentinel-1, Sentinel-2, ALOS-2 PALSAR-2, and the Multi-Source National Forest Inventory by Natural Resources Institute Finland as sources of data. A novel method of extracting data from the features of the surrounding observations is proposed, and the method’s effectiveness was evaluated. The findings showed that the method showed promising results, with the model trained using the extracted features achieving the highest evaluation scores in the study. In addition, the viability of using free and highly available satellite datasets for AGB estimation in the hemi-boreal Finland was analyzed, with the results suggesting that the free Synthetic Aperture Radar (SAR) based products had a low performance. The features extracted from the optical data of Sentinel-2 produced well-performing models, although the accuracy might still be too low to be feasible.

The Finnish Customs collects and maintains the statistics of the Finnish intra-EU trade with the Intrastat system. Companies with significant intra-EU trade are obligated to give monthly Intrastat declarations, and the statistics of the Finnish intra-EU trade are compiled based on the information collected with the declarations. In case of a company not giving the declaration in time, there needs to exist an estimation method for the missing values. In this thesis we propose an automatic multivariate time series forecasting process for the estimation of the missing Intrastat import and export values. The forecasting is done separately for each company with missing values. For forecasting we use two dimensional time series models, where the other component is the import or export value of the company to be forecasted, and the other component is the import or export value of the industrial group of the company. To complement the time series forecasting we use forecast combining. Combined forecasts, for example the averages of the obtained forecasts, have been found to perform well in terms of forecast accuracy compared to the forecasts created by individual methods. In the forecasting process we use two multivariate time series models, the Vector Autoregressive (VAR) model, and a specific VAR model called the Vector Error Correction (VEC) model. The choice of the model is based on the stationary properties of the time series to be modelled. An alternative option for the VEC model is the so-called augmented VAR model, which is an over-fitted VAR model. We use the VEC model and the augmented VAR model together by using the average of the forecasts created with them as the forecast for the missing value. When the usual VAR model is used, only the forecast created by the single model is used. The forecasting process is created as automatic and as fast as possible, therefore the estimation of a time series model for a single company is made as simple as possible. Thus, only statistical tests which can be applied automatically are used in the model building. We compare the forecast accuracy of the forecasts created with the automatic forecasting process to the forecast accuracy of forecasts created with two simple forecasting methods. In the non-stationary-deemed time series the Naïve forecast performs well in terms of forecast accuracy compared to the time series model based forecasts. On the other hand, in the stationary-deemed time series the average over the past 12 months performs well as a forecast in terms of forecast accuracy compared to the time series model based forecasts. We also consider forecast combinations where the forecast combinations are created by calculating the average of the time series model based forecasts and the simple forecasts. In line with the literature, the forecast combinations perform overall better in terms of the forecast accuracy than the forecasts based on the individual models.

Often in spatial statistics the modelled domain contains physical barriers that can have impact on how the modelled phenomena behaves. This barrier can be, for example, land in case of modelling a fish population, or road for different animal populations. Common model that is used in spatial statistics is a stationary Gaussian model, because of its computational requirements, relatively easy interpretation of results. The physical barrier does not have an effect on this type of models unless the barrier is transformed into variable, but this can cause issues in the polygon selection. In this thesis I discuss how the non-stationary Gaussian model can be deployed in cases where spatial domain contains physical barriers. This non-stationary model reduces spatial correlation continuously towards zero in areas that are considered as a physical barrier. When the correlation is selected to reduce smoothly to zero, the model is more likely to results similar output with slightly different polygons. The advantage of the barrier model is that it is as fast to train as the stationary model because both models can be trained using finite equation method (FEM). With FEM we can solve stochastic partial differential equations (SPDE). This method interprets continuous random field as a discrete mesh, and the computational requirements increases as the number of nodes in mesh increases. In order to create stationary and non-stationary models, I have described the required methods such as Bayesian statistics, stochastic process, and covariance function in the second chapter. I use these methods to define spatial random effect model, and one commonly used spatial model is the Gaussian latent variable model. At the end of second chapter, I describe how the barrier model is created, and what types of requirements this model has. The barrier model is based on a Matern model that is a Gaussian random field, and it can be represented by using Matern covariance function. The second chapter ends with description of how to create a mesh mentioned above, and how the FEM is used to solve SPDE. The performance of stationary and non-stationary Gaussian models are first tested by training both models with simulated data. This simulated data is a random sample from polygon of Helsinki where the coastline is interpreted as a physical barrier. The results show that the barrier model estimates the true parameters better than the stationary model. The last chapter contains data analysis of the rat populations in Helsinki. The data contains number of rat observations in each zip code, and a set of covariates. Both models, stationary and non-stationary, are trained with and without covariates, and the best model out of these four models was the stationary model with covariates.

Efficient estimation and forecasting of the cash flow is an interest of pension insurance companies. At the turn of the year 2019 Finnish national Incomes Register was introduced and the payment cycle of TyEL (Employees Pensions Act) changed substantially. TyEL payments are calculated and paid monthly by all of the employers insured under TyEL after January 1st 2019. Vector autoregressive (VAR) models are one of the most used and successful multivariate time series models. They are widely used with economic and financial data due to the good forecasting abilities and the possibility of analysing dynamic structures between the variables of the model. The aim of this thesis is to determine whether a VAR model offers a good fit for predicting the incoming TyEL cash flow of a pension insurance company. With the monthly payment cycle arises a question of seasonality of the incoming TyEL cash flow, and thus the focus is on forecasting with seasonally varying data. The essential theory of VAR models is given. The forecast abilities are tested by building a VAR model for monthly, seasonally varying time series similar than the pension insurance companies would have and could use for the particular prediction problem.

One of the biggest hurdles in cancer patient care is the lack of response to treatment. With the support of high-throughput drug screening, it is nowadays feasible to conduct vast amounts of drug sensitivity assays, aiding in the identification of sensitive and resistant samples to chemical perturbations. In an oncology setting, drug screening is the process by which patient cells are examined experimentally for response and activity to distinct drugs and analysed via dose-response curve fitting. However, the ability to reproduce and replicate with high confidence drug screening outcomes proved to be a challenge that needs to be addressed. Inefficient experimental designs, lack of standard protocols to control both biological and technical factors in such cell-based assays are at the core of a steep influx of experimental biases. Hence, additional endeavour has to be carried out to provide less biased estimations of drug effects. This thesis work focuses on reducing erroneous inferences (i.e., bias) from dose-response data in the curve fitting step, thereby improving the reproducibility of drug sensitivity screening through efficient dose selection. A novel two-step experimental design is introduced which significantly improves the estimation of dose-response curves while keeping the amount of cellular and chemical materials feasible.