From 4eb3e44fbd107ae3dd5881ec3e30612c10fed476 Mon Sep 17 00:00:00 2001
From: Riku-Laine <28960190+Riku-Laine@users.noreply.github.com>
Date: Sat, 9 Mar 2019 20:10:49 +0200
Subject: [PATCH] =?UTF-8?q?pdf:n=20nimetty=20ja=20viitteet=20lis=C3=A4tty?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 OllinTutk.pdf => Kandi.pdf | Bin 140813 -> 179681 bytes
 Kandi.synctex.gz           | Bin 0 -> 20195 bytes
 Kandi.tex                  | 188 +++++++++++++++++++++++++++++++++++++
 OllinTutk.synctex.gz       | Bin 14311 -> 0 bytes
 OllinTutk.tex              | 174 ----------------------------------
 viitteet.bib               |   9 ++
 6 files changed, 197 insertions(+), 174 deletions(-)
 rename OllinTutk.pdf => Kandi.pdf (53%)
 create mode 100644 Kandi.synctex.gz
 create mode 100644 Kandi.tex
 delete mode 100644 OllinTutk.synctex.gz
 delete mode 100644 OllinTutk.tex
 create mode 100644 viitteet.bib

diff --git a/OllinTutk.pdf b/Kandi.pdf
similarity index 53%
rename from OllinTutk.pdf
rename to Kandi.pdf
index b49e9f2ad9058e573d8fc143cf201597b81b2e26..ad15bc2f501968801e8bbcb6d97c1a38a3cc8715 100644
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diff --git a/Kandi.tex b/Kandi.tex
new file mode 100644
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--- /dev/null
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+\documentclass[12pt,a4paper,leqno]{report}
+
+%\usepackage[ansinew]{inputenc} Vaihdettu paketti alla olevaan, jotta ääkköset toimii
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[finnish]{babel}
+\usepackage{amsthm}
+\usepackage{amsfonts}         
+\usepackage{amsmath}
+\usepackage{amssymb}
+
+\usepackage[nottoc]{tocbibind} % Löhteet sisällykseen
+%\usepackage[round,sort,comma]{natbib} % Natbib että harvard
+\usepackage[fixlanguage]{babelbib}
+\selectbiblanguage{finnish}
+
+
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\C}{\mathbb{C}}
+\newcommand{\Q}{\mathbb{Q}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\No}{\mathbb{N}_0}
+\newcommand{\Z}{\mathbb{Z}}
+\newcommand{\diam}{\operatorname{diam}}
+
+\theoremstyle{plain}
+\newtheorem{lause}[equation]{Lause}
+\newtheorem{lem}[equation]{Lemma}
+\newtheorem{prop}[equation]{Propositio}
+\newtheorem{kor}[equation]{Korollaari}
+
+\theoremstyle{definition}
+\newtheorem{maar}[equation]{Määritelmä}
+\newtheorem{konj}[equation]{Konjektuuri}
+\newtheorem{esim}[equation]{Esimerkki}
+
+\theoremstyle{remark}
+\newtheorem{huom}[equation]{Huomautus}
+
+\pagestyle{plain}
+\setcounter{page}{1}
+\addtolength{\hoffset}{-1.15cm}
+\addtolength{\textwidth}{2.3cm}
+\addtolength{\voffset}{0.45cm}
+\addtolength{\textheight}{-0.9cm}
+
+\title{Kandidaatin tutkielma\\ {\Large Kausaalipäättely ja epätäydellinen informaatio takuukäsittelyissä}} % Parempi otsikko
+\author{Riku Laine, Helsingin yliopisto}
+\date{\today}
+
+\begin{document}
+
+\maketitle
+
+\tableofcontents
+
+\chapter{Esipuhe ja kiitokset}\label{epkiit}
+
+Kiitokset Michael Mathioudakikselle ja 
+
+\chapter{Tiivistelmä}\label{tiiv}
+
+\chapter{Johdanto}\label{johd}
+
+Tämän tutkielman tavoitteena on ennustaa yhdysvaltalaisten rikollisten rikoksen uusimisriskiä kausaalipäättelyä hyödyntävällä mallilla. Onngelma mallia selective labels.
+
+% https://julkaisut.valtioneuvosto.fi/bitstream/handle/10024/76171/omkm_2009_2.pdf
+% https://www.mass.gov/files/documents/2016/09/qx/bail-in-united-states-literature-review.pdf
+
+\section{Takuukäsittely prosessina}\label{pros}
+
+Yhdysvalloissa voi päästä vapaaksi rahaa 
+
+\section{Yhteiskunnallinen merkitys}\label{ykmerk}
+
+\section{''Kausaalipäättely uutena paradigmana''}\label{para}
+
+\chapter{Data}\label{data}
+
+\section{COMPAS}\label{compas}
+
+\section{Synteettinen}\label{synteettinen}
+
+\section{''Selective labels''}\label{sl}
+
+\chapter{Metodit}\label{metodit}
+
+
+\section{Aiemmat tutkimukset}\label{aiemmat}
+
+
+\section{Validointimetodit}\label{validointi}
+
+\section{Kausaalipäättely}\label{kausaali}
+
+\subsection{Johdanto}\label{kausaalijohd}
+
+
+\subsection{Merkinnät}\label{kausaalimerk}
+
+\subsection{Määritelmät}\label{kausaalimäär}
+
+\subsection{Mallli}\label{kausaalimalli}
+
+\chapter{Tulokset}\label{tulokset}
+
+\section{Synteettinen}\label{synttulokset}
+
+\section{Compas}\label{compastulokset}
+
+\begin{maar}\label{tngenmaar}
+Jos $X$ on diskreetti satunnaismuuttuja, joka saa
+arvokseen luonnollisia lukuja, niin $X$:n \emph{todennäkäisyysgeneroiva 
+funktio} on
+\begin{equation}\label{genf}
+G_X(t)=\sum_{k=0}^\infty P(X=k) t^k=\sum_{k=0}^\infty p_k t^k.
+\end{equation}
+\end{maar}
+
+Mikäli $X$:n arvojoukko on äärellinen ja arvojoukon jäsenten todennäkäisyydet
+ovat nollasta poikkeavia, $G_X$ on määritelty kaikilla reaaliluvuilla
+$t$. Muutoin $G_X$ on määritelty ainoastaan niille $t\in\R$, joilla $G_X$
+suppenee. Koska pistetodennäkäisyydet $p_k=P(X=k)$ ovat ei-negatiivisia ja 
+summautuvat ykkäseksi, sarja suppenee ainakin suljetulla välillä $t\in[-1, 1]$.
+
+Generoiva funktio voidaan odotusarvon avulla ilmaista muodossa
+\begin{equation}\label{genvar}
+G_X(t) = E(t^X).
+\end{equation}
+
+\begin{lause}
+Jos $X$ on diskreetti satunnaismuuttuja, joka saa arvokseen
+luonnollisia lukuja, niin $X$:n todennäkäisyysgeneroiva funktio määrää $X$:n
+jakauman yksikäsitteisesti.
+\end{lause}
+
+\begin{proof}
+Koska määritelmän mukaan $G_X$ on ainakin välillä $[-1, 1]$ suppeneva
+potenssisarja, niin sillä on kaikkien kertalukujen derivaatat ainakin
+välillä $(-1, 1)$ ja
+\[
+p_k=\frac{G_X^{(k)}(0)}{k!},\quad k\in\N. 
+\]
+Tästä näemme, että $G_X$ määrää luvut $p_k$ ja täten $X$:n 
+jakauman yksikäsitteisesti.
+\end{proof}
+
+Seuraavaksi esittelemme tutuimpien diskreettien jakaumien todennäkäisyysgeneroivat
+funktiot. Jne\ldots
+
+\chapter{Diskussio}\label{diskussio}
+
+\begin{maar}\label{mommaar}
+Jos $X$ on satunnaismuuttuja ja odotusarvo $E(e^{tX})$
+on olemassa, kun $|t| < \delta$, $\delta > 0$, niin $X$:n \emph{momenttigeneroiva 
+funktio} on
+\begin{equation}\label{momf}
+M_X(t) = E(e^{tX}).
+\end{equation}
+\end{maar}
+
+Todennäkäisyys- ja momenttigeneroivilla funktioilla on seuraava yhteys:
+
+\begin{lause}
+Jos $X$ on diskreetti satunnaismuuttuja, jonka arvojoukko sisältyy
+joukkoon $\{0,1,2,\ldots\}$, niin 
+\[
+M_X(t) = G_X(e^t)
+\]
+edellyttäen, että $G_X$ on olemassa, kun $|t| < 1 + \delta$, $\delta > 0$.
+\end{lause}
+
+\begin{proof} Nyt
+\[
+M_X(t) = E(e^{tX}) = E((e^t)^X) = G_X(e^t).\qedhere
+\]
+\end{proof}
+
+Ja niin edelleen\ldots
+
+Lorem ipsum viite \cite{suomi}
+
+\nocite{*}
+
+\bibliographystyle{babplain}
+\bibliography{viitteet} 
+
+\end{document}
diff --git a/OllinTutk.synctex.gz b/OllinTutk.synctex.gz
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diff --git a/OllinTutk.tex b/OllinTutk.tex
deleted file mode 100644
index d68f2d7..0000000
--- a/OllinTutk.tex
+++ /dev/null
@@ -1,174 +0,0 @@
-\documentclass[12pt,a4paper,leqno]{report}
-
-\usepackage[ansinew]{inputenc}
-\usepackage[T1]{fontenc}
-\usepackage[finnish]{babel}
-\usepackage{amsthm}
-\usepackage{amsfonts}         
-\usepackage{amsmath}
-\usepackage{amssymb}
-
-\newcommand{\R}{\mathbb{R}}
-\newcommand{\C}{\mathbb{C}}
-\newcommand{\Q}{\mathbb{Q}}
-\newcommand{\N}{\mathbb{N}}
-\newcommand{\No}{\mathbb{N}_0}
-\newcommand{\Z}{\mathbb{Z}}
-\newcommand{\diam}{\operatorname{diam}}
-
-\theoremstyle{plain}
-\newtheorem{lause}[equation]{Lause}
-\newtheorem{lem}[equation]{Lemma}
-\newtheorem{prop}[equation]{Propositio}
-\newtheorem{kor}[equation]{Korollaari}
-
-\theoremstyle{definition}
-\newtheorem{maar}[equation]{Määritelmä}
-\newtheorem{konj}[equation]{Konjektuuri}
-\newtheorem{esim}[equation]{Esimerkki}
-
-\theoremstyle{remark}
-\newtheorem{huom}[equation]{Huomautus}
-
-\pagestyle{plain}
-\setcounter{page}{1}
-\addtolength{\hoffset}{-1.15cm}
-\addtolength{\textwidth}{2.3cm}
-\addtolength{\voffset}{0.45cm}
-\addtolength{\textheight}{-0.9cm}
-
-\title{Generoivat funktiot}
-\author{Olli Opiskelija}
-\date{}
-
-\begin{document}
-
-\maketitle
-
-\tableofcontents
-
-\chapter{Tiivistelma}\label{tiiv}
-
-\chapter{Johdanto}\label{johd}
-
-Tämän tutkielman tarkoituksena on esitellä kausaalipäättelyn socvesllysta
-lorem ipsum.
-
-\chapter{Metodit}\label{metodit}
-
-Generoiva funktio on potenssisarja, joka
-m��ritell��n seuraavasti:
-
-\begin{maar}\label{genmaar}
-\emph{Generoiva funktio} lukujonolle $(a_k)_{k=0}^\infty$ on
-\begin{equation}
-a(x)=\sum_{k=0}^\infty a_kx^k=a_0+a_1x+a_2x^2+\ldots.
-\end{equation}
-\end{maar}
-
-Todenn�k�isyysgeneroiva funktio on m��ritelty ainoastaan diskreeteille
-jakaumille, mutta momenttigeneroiva funktio on m��ritelty sek�
-diskreeteille ett� jatkuville jakaumille. Jakaumien ominaisuuksien tutkimisessa
-generoivat funktiot ovat monella tapaa hy�dyllisi�. N�in on
-esimerkiksi siksi, ett� generoiva funktio m��r�� jakauman yksik�sitteisesti.
-Generoivien funktioiden avulla voidaan laskea jakaumien tunnuslukuja,
-odotusarvot, varianssit ja momentit. Lis�ksi niit� voidaan
-k�ytt�� riippumattomien satunnaismuuttujien summan jakautumisen
-tutkimiseen.
-
-Tutkielma on rakennettu siten, ett� ensin esittelen todenn�k�isyysgeneroivan
-funktion ja todistan sen ominaisuuksia luvussa \ref{tngen}. Luvussa
-\ref{momgen} esittelen momenttigeneroivat funktiot diskreeteille ja 
-jatkuville jakaumille sek� todistan niihin liittyvi� ominaisuuksia. 
-Oletan tunnetuksi tavallisimmat todenn�k�isyyslaskentaan
-liittyv�t k�sitteet, ks.\ \cite{Tuo}.
-
-\chapter{Todenn�k�isyysgeneroiva funktio}\label{tngen}
-
-\begin{maar}\label{tngenmaar}
-Jos $X$ on diskreetti satunnaismuuttuja, joka saa
-arvokseen luonnollisia lukuja, niin $X$:n \emph{todenn�k�isyysgeneroiva 
-funktio} on
-\begin{equation}\label{genf}
-G_X(t)=\sum_{k=0}^\infty P(X=k) t^k=\sum_{k=0}^\infty p_k t^k.
-\end{equation}
-\end{maar}
-
-Mik�li $X$:n arvojoukko on ��rellinen ja arvojoukon j�senten todenn�k�isyydet
-ovat nollasta poikkeavia, $G_X$ on m��ritelty kaikilla reaaliluvuilla
-$t$. Muutoin $G_X$ on m��ritelty ainoastaan niille $t\in\R$, joilla $G_X$
-suppenee. Koska pistetodenn�k�isyydet $p_k=P(X=k)$ ovat ei-negatiivisia ja 
-summautuvat ykk�seksi, sarja suppenee ainakin suljetulla v�lill� $t\in[-1, 1]$.
-
-Generoiva funktio voidaan odotusarvon avulla ilmaista muodossa
-\begin{equation}\label{genvar}
-G_X(t) = E(t^X).
-\end{equation}
-
-\begin{lause}
-Jos $X$ on diskreetti satunnaismuuttuja, joka saa arvokseen
-luonnollisia lukuja, niin $X$:n todenn�k�isyysgeneroiva funktio m��r�� $X$:n
-jakauman yksik�sitteisesti.
-\end{lause}
-
-\begin{proof}
-Koska m��ritelm�n mukaan $G_X$ on ainakin v�lill� $[-1, 1]$ suppeneva
-potenssisarja, niin sill� on kaikkien kertalukujen derivaatat ainakin
-v�lill� $(-1, 1)$ ja
-\[
-p_k=\frac{G_X^{(k)}(0)}{k!},\quad k\in\N. 
-\]
-T�st� n�emme, ett� $G_X$ m��r�� luvut $p_k$ ja t�ten $X$:n 
-jakauman yksik�sitteisesti.
-\end{proof}
-
-Seuraavaksi esittelemme tutuimpien diskreettien jakaumien todenn�k�isyysgeneroivat
-funktiot. Jne\ldots
-
-\chapter{Momenttigeneroiva funktio}\label{momgen}
-
-\begin{maar}\label{mommaar}
-Jos $X$ on satunnaismuuttuja ja odotusarvo $E(e^{tX})$
-on olemassa, kun $|t| < \delta$, $\delta > 0$, niin $X$:n \emph{momenttigeneroiva 
-funktio} on
-\begin{equation}\label{momf}
-M_X(t) = E(e^{tX}).
-\end{equation}
-\end{maar}
-
-Todenn�k�isyys- ja momenttigeneroivilla funktioilla on seuraava yhteys:
-
-\begin{lause}
-Jos $X$ on diskreetti satunnaismuuttuja, jonka arvojoukko sis�ltyy
-joukkoon $\{0,1,2,\ldots\}$, niin 
-\[
-M_X(t) = G_X(e^t)
-\]
-edellytt�en, ett� $G_X$ on olemassa, kun $|t| < 1 + \delta$, $\delta > 0$.
-\end{lause}
-
-\begin{proof} Nyt
-\[
-M_X(t) = E(e^{tX}) = E((e^t)^X) = G_X(e^t).\qedhere
-\]
-\end{proof}
-
-Ja niin edelleen\ldots
-
-\begin{thebibliography}{9}
-
-\bibitem{ET}
-Gustav Elfving ja Pekka Tuominen: Todenn�k�isyyslaskenta II, 2.\ painos, Limes ry, 1990.
-
-\bibitem{Hol}
-Ilkka Holopainen: Mitta ja integraali, luentomoniste, Helsingin yliopisto, 2004.
-
-\bibitem{Ros}
-Sheldon Ross: A First Course in Probability, 5th edition, Prentice-Hall, 1998.
-
-\bibitem{Tuo}
-Pekka Tuominen: Todenn�k�isyyslaskenta I, 5.\ painos, Limes ry, 2000.
-
-\end{thebibliography}
-
-\end{document}
diff --git a/viitteet.bib b/viitteet.bib
new file mode 100644
index 0000000..343701c
--- /dev/null
+++ b/viitteet.bib
@@ -0,0 +1,9 @@
+@article{suomi,
+  author = "Michel Goossens and Frank Mittelbach and Alexander Samarin",
+  year = "2003",
+  title = "Peruna ipsum",
+  journal = "Soveltava peruna",
+  pages = "7499--7506",
+  language = {finnish}
+}
+
-- 
GitLab