intro-inference.tex

% This file is a LaTex file for the "beamer" package to create slides for a talk or presentation


% MODIFIED by Pablo Gomez 5/20/2015

\documentclass{beamer}


\mode<presentation>
{
  \usetheme{Warsaw}
  % or ...
  \setbeamercovered{transparent}
  % or whatever (possibly just delete it)
}


\usepackage[english]{babel}
% or whatever

\usepackage[utf8]{inputenc}
% or whatever

\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.


\title[BF vs NHST] % (optional, use only with long paper titles)
{Statistical Inference}

\subtitle
{Contrasting null hypothesis testing and Bayes factors} % (optional)

\author[Greeson, Gomez] % (optional, use only with lots of authors)
{M.~Greeson\inst{1} \and P.~Gomez\inst{2}}
% - Use the \inst{?} command only if the authors have different
%   affiliation.

\institute[DePaul University] % (optional, but mostly needed)
{
  \inst{1}%
 Clinical Program\\
  DPU
  \and
  \inst{2}%
  P.S. program\\
  DPU}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.

\date[Short Occasion] % (optional)
{\today / For fun}

\subject{Talks}

\begin{document}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{Statistical Inference}

 A comparison\dots


    \begin{itemize}
       	\uncover<1->{\item [NHST] We use samples to study populations}
       	\uncover<2->{\item [Bayes] We use samples to quantify evidence for hypotheses}
  \end{itemize}
\end{frame}


\begin{frame}{Sample data I}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST] Sampling error occurs--meaning we expect our sample stats to not be perfect reflection of our population}
	\uncover<2->{\item [Bayes]  The data \emph{is what it is}}
   \end{itemize}
\end{frame}


\begin{frame}{Sample data II}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST]  We don't know how right or wrong our sample stats are due to sampling error}
	\uncover<2->{\item [Bayes] The data \emph{is what it is}}
   \end{itemize}
\end{frame}


\begin{frame}{Hypotheses I}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST]  We establish one hypothesis: the null hypothesis}
	\uncover<2->{\item [Bayes] We establish several competing hypothesis or models (for example a null and an alternative hypothesis). These hypotheses represent our \emph{prior} beliefs}
   \end{itemize}
\end{frame}
	


\begin{frame}{Hypotheses II}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST] We make assumptions about the behavior (i.e. distribution) of the population of scores under the null hypothesis}
	\uncover<2->{\item [Bayes] We make assumptions about the behavior (i.e. distribution) of the population of scores under the competing hypothesis or models (for example a null and an alternative hypothesis)}
   \end{itemize}
\end{frame}



\begin{frame}{Hypotheses III}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST] We estimate the probability of getting various sample stats from a random sample taken from that population  if the assumptions under the null hypothesis were true}
	\uncover<2->{\item [Bayes] We estimate the probabilities of getting various sample stats from a random sample if the assumptions under the different models were true}

  \end{itemize}
\end{frame}


\begin{frame}{Data collection}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST]  We then collect data from a random sample and calculate sample stats}
	\uncover<2->{\item [Bayes]  We then collect data from a random sample and calculate sample stats}
  \end{itemize}
\end{frame}




\begin{frame}{Inference I}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST]  We estimate the probability of getting our data if the assumptions about the null hypothesis were true p(data|Null) }
	\uncover<2->{\item [Bayes] Given the data that we have, we estimate the probability of our data coming from the Null and the Alternative models:  p(Null| data) \& p(Alt|data)}

    \end{itemize}

\end{frame}



\begin{frame}{Inference II}

 A comparison\dots

    \begin{itemize}
	\uncover<1->{\item [NHST] There is a decision rule. If the probability of getting our data if the assumptions about the null hypothesis were true is low enough, we reject that null hypothesis}
	\uncover<2->{\item  [Bayes]  There is no decision rule. We compute the ratio for the p(null|data) /  p(alt|data) to quantify the evidece that we have for one model over the other}
\end{itemize}
\end{frame}


\end{document}