SLIDE 1
NTNU
Slide no.: 2
Two types of statistical models
Neyman categorises statistical models into two groups:
- Interpolating models
Used merely to capture rough effects in the data
- Explorative models
Analysis of Survival Times Using Bayesian Networks Helge Langseth - - PowerPoint PPT Presentation
Analysis of Survival Times Using Bayesian Networks Helge Langseth - - PowerPoint PPT Presentation
Analysis of Survival Times Using Bayesian Networks Helge Langseth Presented at ESREL 98 Trondheim, Norway, 16-19 June 1998 NTNU Two types of statistical models Neyman categorises statistical models into two groups: Interpolating
SLIDE 2
SLIDE 3
NTNU
Slide no.: 3
Scope
With a database as a starting point, we want to build an explorative model to pinpoint how to reduce the rate of critical failures in a system components. Our main goal is to build a model to gain understanding about how the covariates contribute to the system’s survival times.
SLIDE 4
NTNU
Slide no.: 4
The History of Graphical Models
- Graphical models in statistics can be dated back to
Wright’s notation in 1921.
- The calculation complexity did however, render
the Bayesian Networks neglected for 60 years
- In the 1980’ties, effective algorithms for exact
calculations on graphs, and later on computer intensive methods like Markov-Chain Monte- Carlo brought the Bayesian Networks back into the light, and up on the Top 5 Statistical Buzz- Word of the Week.
SLIDE 5
NTNU
Slide no.: 5
Bayesian Networks
Age Exposure To Toxic Gender Smoking Cancer Serum Calcium Lung Tumour
SLIDE 6
NTNU
Slide no.: 6
Conditional Independence
Age Exposure To Toxic Gender Smoking Cancer Serum Calcium Lung Tumour
Cancer is independent of Age and Gender given Exposure To Toxic and Smoking
SLIDE 7
NTNU
Slide no.: 7
“Fundamental Theorem”
Every multidimensional statistical distribution function can be represented by a Bayesian Network.
∏ ∏
= = −
= =
n i i n i i i n
x f x x x x f x x x f
1 1 1 2 1 2 1
) rs" predecesso All |" ( ) ,..., , | ( ) ,..., , (
1 2 3 4 n
SLIDE 8
NTNU
Slide no.: 8
Nodes are Probability Tables
Gender Smoking Age Exposure To Toxic Cancer Serum Calcium Lung Tumour Age Exposed To Toxic Material In (25,65) Not In (25, 65) True 5 % 1% False 95 % 99%
SLIDE 9
NTNU
Slide no.: 9
Where do the Networks come from?
Situation:
We want to build a model to analyse a multidimensional vector X.
Aid:
To do so, we have N i.i.d. realisations of X, x1, …, xN AND / OR a domain expert.
Unknowns:
- The network structure
- The parameters in the local node tables
SLIDE 10
NTNU
Slide no.: 10
Generating Networks:
- Initialize Network
repeat
- Propose some Change to the structure
- Fit Parameters to the new structure
- Evaluate the new network according to
some measure (like BIC, AIC, MDL)
- If the New network is Better than the
previous, then Keep the Change until Finished
SLIDE 11
NTNU
Slide no.: 11
Bayesian Networks are used in:
- In “expert systems”, mostly in medical domains
(e.g. the MUNIN system)
- In decision support systems (e.g. for NASA)
- In analysis of dynamic systems (e.g. speech
recognition, the BAT-Mobile)
- …
SLIDE 12
NTNU
Slide no.: 12
Bayesian Networks, Summary:
- An estimate of the multidimensional density
- Easy to understand for non-statisticians (e.g. a
domain expert)
- The representation is optimized for tasks like
– Prediction – Classification – Decision support
- Can incorporate prior domain knowledge:
– “Top down analysis”: Expert knowledge – “Bottom up” analysis: Data driven system verification
SLIDE 13
NTNU
Slide no.: 13
Reliability Analysis
- Data-set: 219 Gas-Turbines with 2921 failures and
300 censored survival times from the OREDA-IV database
- Each failure is described by ten covariates, e.g.,
System Type, Manufacturer, Actual/Planned PM,...
- We have special interest in Time To Fail and
Failure Severity (Critical or Degraded)
- Problem to solve: “How can we reduce the
frequency of critical failures?”
SLIDE 14
NTNU
Slide no.: 14
Generated Network
Actual PM Planned PM System Code Manufact. Operating Mode Sub unit Design Class Location
Installation Code
Environ- ment Severity Class Time to Fail
SLIDE 15
NTNU
Slide no.: 15
“Clique” Graph
Environ. Location System Subunit TTF PM Severity Location: Installation Code Location PM: Planned PM Actual PM System: System Code Operating Mode Manufacturer Environment: Installation Code Environment System Code Design Class
SLIDE 16
NTNU
Slide no.: 16
Model Verification
1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 Bayesian network Cox regression
SLIDE 17
NTNU
Slide no.: 17
Conclusions
- We have generated a Bayesian Network to analyse
a data-set from the OREDA IV database.
- The Bayesian Network enabled both Qualitative
and Quantitative analysis of the data-set.
- To verify the calculations, the numerical results