QuestionQuestion

In this assignment, you will find a dataset, preferably a public one, and analyse the data by using the Bayesian analysis methods covered in Applied Bayesian Statistics course in this semester, and prepare a comprehensive analysis report including descriptive analysis, proper visualisations, model specification, model implementation and diagnostic checking in JAGS. The dataset you will focus on should include one dependent variable and a number of predictor variables. The dependent variable that you will model can be either continuous or binary. The predictors can be both qualitative or quantitative.
The quality of data will be assessed in terms of originality of study and difficulty of modeling. Therefore, the length and characteristics of the dataset you will choose for the project is just up to you.

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```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(rjags)
library(coda)
library(lattice)
library(caret)
```

## Introduction

In this report, bayesian logistic regression is fitted on the bank-note authentication dataset. This data set has 1372 samples of bank notes each having 4 features and 1 dependent variable (deciding if note is authentic or not).

This data were extracted from images that were taken from genuine and forged banknote-like specimens [1]. For digitization, an industrial camera usually used for print inspection was used. The final images have 400x 400 pixels. Due to the object lens and distance to the investigated object gray-scale pictures with a resolution of about 660 dpi were gained. Wavelet Transform tool were used to extract features from images.

The feature set is:

1. variance of Wavelet Transformed image (continuous)
2. skewness of Wavelet Transformed image (continuous)
3. curtosis of Wavelet Transformed image (continuous)
4. entropy of image (continuous)
5. class (integer)

## Data Preparation

```{r}
dat <- read.csv("data_banknote_authentication.txt", header = FALSE)
names(dat) <- c("Variance", "Skewness", "Curtosis", "Entropy", "Class")
sum(is.na(dat))
dat$Variance <- (dat$Variance - mean(dat$Variance))/sd(dat$Variance)
dat$Skewness <- (dat$Skewness - mean(dat$Skewness))/sd(dat$Skewness)
dat$Curtosis <- (dat$Curtosis - mean(dat$Curtosis))/sd(dat$Curtosis)
dat$Entropy <- (dat$Entropy - mean(dat$Entropy))/sd(dat$Entropy)
```

Data doesn't have any missing data. Each numeric predictor is
normalized to zero mean and unit variance.

```{r}
pairs(dat)
```

Skewness and Curtosis are negatively correlated. Variance and Entropy looks
positive correlated. Coorelated features may be capturing the same information and may not be the best feature for predictive model....

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