Survival data and censoring
STK4900/9900 -
Lecture 9
The data in this lecture have a different form from what we
have seen earlier
Program
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The response is the time (from a well defined starting point) until
a specific event (end point) occu
Example: Emission of alpha particles
STK4900/9900 -
In an experiment from 1910 Ernest Rutherford and Hans Geiger
recorded the number of alpha-particles emitted from a polonium
source in each of 2608 eighth-minute intervals
Lecture 8
Program
1. Poisson dis
Example: Fecal fat
STK4900/9900 -
Lack of digestive enzymes in the intestine can cause bowel absorption
problems, which will be indicated by excess fat in the feces. Pancreatic
enzyme supplements can reduce the problem. The data are from a
study to determ
STK4900/9900 -
Assumptions for linear regression
Lecture 5
Model:
Program
systematic part random part (error)
1. Checking model assumptions
yi = hi + e i
Linearity
Equal variances
Normality
Influential observations
Importance of model assumptions
(1) Line
STK4900/9900 -
Lecture 1
Basic idea
Program
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8.
Introduction
Descriptive methods
Data and probability models
Normal distributions
Estimation and confidence intervals
Hypothesis testing and P-values
Robustness
Bootstrapping
The basic id
Solutions theoretical exercises for STK4900/9900.
Exercise 6
a) The average turkey weight in Virginia is YV = 12.625 with a standard deviation sV = 0.665. Correspondingly the average weight in
Wisconsin equals WV = 13.6 with a standard deviation sW = 1.44
Logistic regression with one predictor
STK4900/9900 -
We have data (x1 ,y1) , , (xn ,yn)
Lecture 7
Here yi is a binary outcome (0 or 1) for subject i and xi is
a predictor for the subject
Program
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Logistic regression with one predictor
Maxim
STK4900/9900 -
Comparing two groups
Lecture 2
In Lecture 1 we considered an example where we measured bone
mineral density (in g/cm2) for rats given isoflavone and for rats in a
control group:
Program
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Comparing two or more groups
One-way analy
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Causal effects
Confounding
Interaction
More on ANOVA
Use the HERS data,
disregarding women with
diabetes
Simple linear regression:
Sections 4.1, 4.4, (4.5), 4.6
Supplementary material on ANOVA
(Intercept)
exercise
Estimate
97.36
-1.693
80
How
STK4900/9900 -
Binary data and proportions
Lecture 6
In the first part of the course, we considered the situation
where the outcome was numerical
Program
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4.
5.
We will now consider the situation where the outcome is a
binary variable (coded as 0
STK4900/9900 -
Data structure and basic questions
Lecture 3
Data have the form:
Program
2
Data structure and basic questions
The multiple linear regression model
Categorical predictors
Planned experiments and observational studies
Section 2.5
Sections 4.1
Solutions theoretical exercises for STK4900/9900.
Exercise 1 Group 1 (Steroid) N (1 , 2 ), n1 = 8 observations.
Group 2 (Control) N (2 , 2 ), n2 = 10 observations.
90% condence interval for 1 2 is given by x1 x2 c se(1 x2 ) where
x
c = 1.746 = 95 percenti
UNIVERSITY OF OSLO
Faculty of Mathematics and Natural Sciences
Examination in
STK2130 Modeling by stochastic processes.
Day of examination: Friday, June 10, 2011.
Examination hours:
14.30 18.30.
This problem set consists of 4 pages.
Appendices:
Formulary
UNIVERSITY OF OSLO
Faculty of Mathematics and Natural Sciences
Examination in
STK2130 Modelling by Stochastic
Processes. Solution.
Day of examination: Wednesday June 11th 2014.
Examination hours:
14.30 18.30.
This problem set consists of 4 pages.
Appendic
Solution of some exercises in Mandatory Exercise # 2
Exercise 1
We look at the model
Yij = + Ai +
ij , i
= 1, . . . , I, j = 1, . . . , J
2
where Ai N (0, A ) and ij N (0, 2 ), and Ai , ij are independent for all all i = 1, . . . , I, j =
1, . . . , J.
SS
UNIVERSITETET I OSLO
Det matematisk-naturvitenskapelige fakultet
Examination in:
STK 1130 Modelling by stochastic processes.
Day of examination: Tuesday, June 13, 2006.
Examination hours:
09.0 12.00.
This examination set consists of 3 pages.
Appendices:
N
UNIVERSITETET I OSLO
Det matematisk-naturvitenskapelige fakultet
Examination in:
STK 1130 Modelling by stochastic processes.
Day of examination: Friday, June 11, 2004.
Examination hours:
14.30 17.30.
This examination set consists of 3 pages.
Appendices:
N
UNIVERSITETET I OSLO
Det matematisk-naturvitenskapelige fakultet
Examination in:
STK 1130 Modelling by stochastic processes.
Day of examination: Friday, June 10, 2005.
Examination hours:
09.0 12.00.
This examination set consists of 3 pages.
Appendices:
No