bayesian project

8/8/2019 Bayesian Project

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2010

ECE500:Discrete Mathematics BAYESIAN PROJECT: Title kita Rokok?

LECTURER: HASMILA AKMAR OMAR

MEMBER MOHD FARIS BIN DOLAMAHPUL 2009717537

MEMBER MOHD AZHAR BIN ABDULLAH 2009937901

MEMBER MUHAMMAD AZRI BIN ABDUL KUDUS 2009546345

MEMBER HAIRUL HAZWAN BIN HAIRUDDIN 2009722949



INTRODUCTION

Bayesian statistics is concerned with generating the posterior distribution of the unknown

parameters given both the data and some prior density for these parameters. As such, Bayesian

statistics provides a much more complete picture of the uncertainty in the estimation of the

unknown parameters, especially after the confounding effects of nuisance parameters areremoved. Bayesian is used to determine the probability of event occurring while another event

has already occurred. It is also called Conditional Probability. The Bayesian formula given:

P(B|A) = P(A and B) / P(A)

A is the event that already occurred, while B is event that is occurring. The sample spaced has

become smaller since event A has already occurred. Therefore, event B occur base on the

sample space A.

*kena tukar In this Bayesian project, our study case is on Alarm System. The alarm is placed at home. The

function of the alarm is to tell if the house is in danger. There are 4 things that can cause the

alarm to trigger which are Burglary, Earthquake, Tsunami and Strom. By using Bayesian

method we determine how many times the alarm will be triggered in 30 days (a month). We also

calculated the probability that Burglary, Earthquake, Tsunami and Storm will happened. Below

is the connection between Alarm, Burglary, Earthquake, Tsunami and Strom:

Diagram: Show the relationship between Alarm, Burglary, Earthquake, Tsunami and Storm.

Burglary

Tsunami

Alarm

Earthquake

Storm



THE ALARM DATA

Table: The probability event occurs.

Burglary Earthquake Tsunami Storm Alarm

Yes No Yes No Yes No Yes No Yes

True 8 12 True 4 9 True 6 10 True 7 11 12 18

False 4 6 False 8 9 False 6 8 False 5 7

True 8/12 12/18 True 4/12 9/18 True 6/12 10/18 True 7/12 11/18 12/30 18/30

False 4/12 6/18 False 8/12 9/18 False 6/12 8/18 False 5/12 7/18



CALCULATION

COMPUTING THE PROBABILITY FOR ALARM = YES

P(Burglary = true|alarm= yes)= 8/12

P(Earthquake = true|alarm=yes)= 4 / 12

P(Tsunami= true|alarm=yes)= 6 / 12

P(Storm= true|alarm= yes)= 7 / 12

P(alarm=yes)= 12 / 30

P( E| alarm=yes)* P( alarm=yes) =(8 / 12)(4 / 12)(6 / 12)(7 / 12)(12 / 30)=0.0259

P( E| alarm=no)* P( alarm=no) =(12 / 18)(9 / 18)(10 / 18)(11 / 18)(18 / 30)=0.0679

0.0259<0.0679

F or the new day no is more likely than yes



CONCLUSION

bayesian project

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