Difference between revisions of "Biostatistics 615/815 Fall 2011"

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== Objective ==
 
== Objective ==
  
−
In this winter, Biostatistics 615/815 aims for providing students with a practical understanding of computational aspects in implementing statistical methods. Although C++ language will be used throughout the course, using Java programming language for homework and project will be acceptable.
+
In Fall 2011, Biostatistics 615/815 aims for providing students with a practical understanding of computational aspects in implementing statistical methods. Although C++ language will be used throughout the course, using Java programming language for homework and project will be acceptable.
  
 
== Target Audience ==
 
== Target Audience ==
Line 10: Line 10:
  
 
== Textbook ==
 
== Textbook ==
−
* Required Textbook : Cormen, Leiserson, Rivest, and Stein, "Introduction to Algorithms", Third Edition, The MIT Press, 2009 [http://mitpress.mit.edu/algorithms/ [Official Book Web Site]]
+
* Recommended Textbook : Cormen, Leiserson, Rivest, and Stein, "Introduction to Algorithms", Third Edition, The MIT Press, 2009 [http://mitpress.mit.edu/algorithms/ [Official Book Web Site]]
 
* Optional Textbook : Press, Teukolsky, Vetterling, Flannery, "Numerical Recipes", 3rd Edition, Cambridge University Press, 2007 [http://www.nr.com/ [Official Book Web Site]]
 
* Optional Textbook : Press, Teukolsky, Vetterling, Flannery, "Numerical Recipes", 3rd Edition, Cambridge University Press, 2007 [http://www.nr.com/ [Official Book Web Site]]
  
 
== Class Schedule ==
 
== Class Schedule ==
  
−
Classes are scheduled for Tuesday and Thursdays, 8:30 - 10:00 am at SPH II M4318
+
Classes are scheduled for Tuesday and Thursdays, 8:30 - 10:00 am at SPH II M4332
  
 
== Topics ==
 
== Topics ==
Line 21: Line 21:
 
The following contents are planned to be covered.  
 
The following contents are planned to be covered.  
  
−
=== Part I : Algorithms 101 ===
+
=== Part I : C++ Basics and Introductory Algorithms ===
−
* Understanding of Computational Time Complexity
+
* Computational Time Complexity
 
* Sorting
 
* Sorting
 
* Divide and Conquer Algorithms
 
* Divide and Conquer Algorithms
Line 28: Line 28:
 
* Key Data Structure
 
* Key Data Structure
 
* Dynamic Programming
 
* Dynamic Programming
 +
* Hidden Markov Models
  
−
=== Part II : Matrix Operations and Numerical Optimizations ===
+
=== Part II : Numerical Methods and Randomized Algorithms ===
−
* Matrix decomposition (LU, QR, SVD)
+
* Random Numbers
−
* Implementation of Linear Models
+
* Matrix Operations and Least Square Methods
−
* Numerical Optimizations
+
* Importance Sampling
−
 
 
−
=== Part III : Advanced Statistical Methods ===
 
−
* Hidden Markov Models
 
 
* Expectation Maximization
 
* Expectation Maximization
 
* Markov-Chain Monte Carlo Methods
 
* Markov-Chain Monte Carlo Methods
 +
* Simulated Annealing
 +
* Gibbs Sampling
  
 
== Class Notes ==
 
== Class Notes ==
−
* Lecture 1 : Statistical Computing -- [[Media:Biostat615-lecture1-handout.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture1-presentation.pdf | (Presentation mode - PDF)]]
+
* Lecture 1 : Introduction to Statistical Computing -- [[Media:Biostat615-Fall2011-lecture01-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture01-presentation.pdf | (Presentation PDF)]]
−
* Lecture 2 : C++ Basics and Precisions -- [[Media:Biostat615-lecture2-handout-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture2-presentation.pdf | (Presentation mode - PDF)]]
+
* Lecture 2 : Introduction to C++ Programming -- [[Media:Biostat615-Fall2011-lecture02-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture02-presentation.pdf | (Presentation PDF)]]
−
* Lecture 3 : Implementing Fisher's Exact Test -- [[Media:Biostat615-lecture3-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture3.pdf | (Presentation mode - PDF)]]
+
* Lecture 3 : C++ Basics and Fisher's Exact Test -- [[Media:Biostat615-Fall2011-lecture03-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture03-presentation.pdf | (Presentation PDF)]]
−
* Lecture 4 : Classes and STLs -- [[Media:Biostat615-lecture4-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture4-presentation.pdf | (Presentation mode - PDF)]]
+
* Lecture 4 : Standard Template Libraries + Divide and Conquer Algorithms-- [[Media:Biostat615-Fall2011-lecture04-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture04-presentation.pdf | (Presentation PDF)]]
−
* Lecture 5 : Divide and Conquer Algorithms -- [[Media:Biostat615-lecture5-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture5.pdf | (Presentation mode - PDF)]]
+
* Lecture 5 : Sorting Algorithms -- [[Media:Biostat615-Fall2011-lecture05-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture05-presentation.pdf | (Presentation PDF)]]
−
* Lecture 6 : Linear Sorting Algorithms and Elementary Data Structures -- [[Media:Biostat615-lecture6-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture6-presentation.pdf | (Presentation mode - PDF)]]
+
* Lecture 6 : Sorting Algorithms & Arrays -- [[Media:Biostat615-Fall2011-lecture06-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture06-presentation.pdf | (Presentation PDF)]]
−
* Lecture 7 : Linear Sorting Algorithms and Elementary Data Structures -- [[Media:Biostat615-lecture7-nup.pdf | (Handout mode - PDF)]] [[Media:Biostat615-lecture7-presentation.pdf | (Presentation mode - PDF)]]
+
* Lecture 7 : List and Binary Search Trees -- [[Media:Biostat615-Fall2011-lecture07-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture07-presentation.pdf | (Presentation PDF)]]
 +
* Lecture 8 : Hash Tables -- [[Media:Biostat615-Fall2011-lecture08-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture08-presentation.pdf | (Presentation PDF)]]
 +
* Lecture 9 : Dynamic Programming -- [[Media:Biostat615-Fall2011-lecture09-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture09-presentation.pdf | (Presentation PDF)]]
 +
* Review : Dynamic Programming & Midterm Review -- [[Media:Biostat615-Fall2011-midterm-2011-winter-.pdf | (PDF)]]
 +
* Lecture 10 : Hidden Markov Model-- [[Media:Biostat615-Fall2011-lecture10-handout.pdf | (PDF)]]  '''(UPDATED on Oct 29th at 12:51PM)'''
 +
* Lecture 11 : Hidden Markov Model (cont'd) -- [[Media:Biostat615-lecture11-2011-10-20.pdf | (PDF)]] '''(UPDATED on Oct 28th at 1:42PM)'''
 +
* Lecture 12 : Boost Library & Random Numbers -- [[Media:Biostat615-lecture12-2011-10-25.pdf | (PDF)]]
 +
* Lecture 13 : Single dimensional optimization -- [[Media:Biostat615-lecture13-2011-10-27.pdf | (PDF)]]
 +
* Lecture 14 : Single and multi dimensional optimizations -- [[Media:Biostat615-fall2011-lecture14.pdf | (PDF)]] (Updated on Nov 3rd 1:25AM)
 +
* Lecture 15 : Multi dimensional optimizations -- [[Media:Biostat615-fall2011-lecture15.pdf | (PDF)]] (Updated Nov 8 10:35AM)
 +
* Lecture 16 : E-M algorithm -- [[Media:Biostat615-fall2011-lecture16.pdf | (PDF)]] (Updated Nov 8 10:35AM)
 +
* Lecture 17 : Simulated Annealing -- [[Media:Biostat615-fall2011-lecture17.pdf | (PDF)]]
 +
* Lecture 18 : Gibbs Sampling -- [[Media:Biostat615-fall2011-lecture18.pdf | (PDF)]] (Updated Nov 16 10:00PM)
 +
* Lecture 19 : Importace Sampling -- [[Media:Biostat615-fall2011-lecture19.pdf | (PDF)]]
 +
* Lecture 20 : Advanced Hidden Markov Models -- [[Media:Biostat615-fall2011-lecture20.pdf | (PDF)]]
 +
* Lecture 21 : Linear Algebra in C++ -- [[Media:Biostat615-fall2011-lecture21.pdf | (PDF)]]
 +
* Lecture 22 : More Linear Algebra in C++ -- [[Media:Biostat615-fall2011-lecture22.pdf | (PDF)]]
 +
* Lecture 23 : Interfacing between C++ and R -- [[Media:Biostat615-fall2011-lecture23.pdf | (PDF)]]
 +
* Review : Final Review -- [[Media:Biostat615-winter2011-final.pdf | (PDF)]] [[Media:Biostat615-homework-review.pdf | (Homework)]]
  
 
== Problem Sets ==
 
== Problem Sets ==
−
* Problem Set 1 : Due on January 20th, 2011 -- [[Media:Biostat615-homework1.pdf | (Problem Set 1 - PDF)]]
+
* Problem Set 0 - Running screenshots of helloWorld.cpp and towerOfHanoi.cpp - Due before the submission of Problem Set 1
−
* Problem Set 2 : Due on February 2nd, 2011 -- [[Media:Biostat615-homework1.pdf | (Problem Set 2 - PDF)]]
+
* Problem Set 1 -- Due on Tuesday September 27th, 2011 [[Media:Biostat615-Fall2011-homework01.pdf | (PDF)]] [[Media:Biostat615-Fall2011-homework01-solutions.pdf | (PDF-SOLUTIONS)]]
 +
* Problem Set 2 -- Due on Thursday October 6th, 2011 [[Media:Biostat615-Fall2011-homework02.pdf | (PDF)]] [[Media:Biostat615-Fall2011-homework02-solutions.pdf | (PDF-SOLUTIONS)]]
 +
** (Update Oct 2, 2011 : Note that the problem 1 and 3 are slightly updated for clarification)
 +
** (If you can't decompress the files above properly, use this alternative link by [http://dl.dropbox.com/u/1850834/biostat615-homework02-datasets.tar.gz CLICKING HERE] )
 +
* Problem Set 3 -- Due on Tuesday November 1st, 2011 [[Media:Biostat615-homework03.pdf | (PDF)]] (UPDATED on Oct 25th at 11:10AM)
 +
* Problem Set 4 -- Due on Tuesday November 15th, 2011 [[Media:Biostat615-homework04.pdf | (PDF)]]
 +
* Problem Set 5 -- Due on Tuesday November 29th, 2011 [[Media:Biostat615-fall2011-homework05.pdf | (PDF)]]
 +
* Problem Set 6 -- Due on Tuesday December 13th, 2011 [[Media:Biostat615-fall2011-homework06.pdf | (PDF)]]  
 +
** [http://www.sph.umich.edu/csg/abecasis/class/2006/ModelFittingData.txt DOWNLOAD DATA FOR PROBLEM 1]
 +
** [http://dl.dropbox.com/u/1850834/zip_01.zip DOWNLOAD DATA FOR PROBLEM 3]
 +
 
 +
=== Supplementary Data sets for Problem Sets ===
 +
* Problem Set 2
 
** [[Media:Shuf-1M.txt.gz| (Example data - shuf-1M.txt.gz)]] 1,000,000 randomly shuffled data (gzipped)
 
** [[Media:Shuf-1M.txt.gz| (Example data - shuf-1M.txt.gz)]] 1,000,000 randomly shuffled data (gzipped)
 
** [[Media:Rand-1M-3digits.txt.gz| (Example data - Rand-1M-3digits.txt.gz)]] 1,000,000 random data from 1 to 1,000]] (gzipped)  
 
** [[Media:Rand-1M-3digits.txt.gz| (Example data - Rand-1M-3digits.txt.gz)]] 1,000,000 random data from 1 to 1,000]] (gzipped)  
 
** [[Media:Rand-50k.txt.gz | (Example data - Rand-50k.txt.gz)]] 50,000 random data from 1 to 1,000,000)]] (gzippd)
 
** [[Media:Rand-50k.txt.gz | (Example data - Rand-50k.txt.gz)]] 50,000 random data from 1 to 1,000,000)]] (gzippd)
−
** Source code from Problem 3  
+
* Problem Set 3
−
  #include <iostream>
+
** Example output data for problem 3-1 (input is the second column) '''(NOTE : ADDED on Oct 25 11:45PM)''' -- This is also reflected in lecture 11 class note.
−
  #include <vector>
+
  TIME TOSS P(FAIR) P(BIAS) MLSTATE
−
  #include <ctime>
+
  1 H 0.5950 0.4050 FAIR
−
  #include <fstream>
+
  2 T 0.8118 0.1882 FAIR
−
  #include <set>
+
  3 H 0.8071 0.1929 FAIR
−
  #include "mySortedArray.h"
+
  4 T 0.8584 0.1416 FAIR
−
  #include "myTree.h"
+
  5 H 0.7613 0.2387 FAIR
−
  #include "myList.h"                                           
+
  6 H 0.7276 0.2724 FAIR
−
   
+
  7 T 0.7495 0.2505 FAIR
−
  int main(int argc, char** argv) {
+
  8 H 0.5413 0.4587 BIASED
−
  int tok;
+
  9 H 0.4187 0.5813 BIASED
−
  std::vector<int> v;
+
10 H 0.3533 0.6467 BIASED
−
  if ( argc > 1 ) {
+
11 H 0.3301 0.6699 BIASED
−
    std::ifstream fin(argv[1]);
+
12 H 0.3436 0.6564 BIASED
−
    while( fin >> tok ) { v.push_back(tok); }
+
13 H 0.3971 0.6029 BIASED
−
    fin.close();
+
14 T 0.5028 0.4972 BIASED
−
  }
+
15 H 0.3725 0.6275 BIASED
−
  else {
+
16 H 0.2985 0.7015 BIASED
−
    while( std::cin >> tok ) { v.push_back(tok); }
+
17 H 0.2635 0.7365 BIASED
−
  }                                           
+
18 H 0.2596 0.7404 BIASED
−
  mySortedArray<int> c1;
+
19 H 0.2858 0.7142 BIASED
−
  myList<int> c2;
+
  20 H 0.3482 0.6518 BIASED
−
  myTree<int> c3;
+
** Example output data for problem 3-2 (input is the second column) '''(NOTE : UPDATED on Oct 25 11:23PM)'''
−
  std::set<int> s;
+
  TIME TOSS Pr(F) Pr(HB) Pr(TB) MLSTATE
−
   
+
1 T 0.8844 0.0326 0.0830 FAIR
−
  clock_t start = clock();
+
2 H 0.9012 0.0791 0.0198 FAIR
−
  for(int i=0; i < (int)v.size(); ++i) {
+
3 H 0.9075 0.0735 0.0189 FAIR
−
    c1.insert(v[i]);
+
  4 T 0.9091 0.0145 0.0764 FAIR
−
  }
+
5 T 0.9068 0.0114 0.0818 FAIR
−
  clock_t finish = clock();
+
6 H 0.9058 0.0440 0.0502 FAIR
−
  double duration = (double)(finish-start)/CLOCKS_PER_SEC; 
+
7 T 0.8834 0.0275 0.0891 FAIR
−
  std::cout << "Sorted Array (Insert) " << duration << std::endl;
+
8 H 0.8520 0.0698 0.0783 FAIR
−
   
+
9 T 0.7713 0.0347 0.1940 FAIR
−
  start = clock();
+
10 T 0.6927 0.0823 0.2249 FAIR
−
  for(int i=0; i < (int)v.size(); ++i) {
+
11 H 0.4730 0.4984 0.0286 HEAD-BIASED
−
    c2.insert(v[i]);
+
12 H 0.3227 0.6706 0.0066 HEAD-BIASED
−
  }
+
  13 H 0.2236 0.7726 0.0037 HEAD-BIASED
−
  finish = clock();
+
14 H 0.1589 0.8381 0.0031 HEAD-BIASED
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC;  
+
  15 H 0.1169 0.8803 0.0028 HEAD-BIASED
−
  std::cout << "List (Insert) " << duration << std::endl;
+
16 H 0.0902 0.9072 0.0026 HEAD-BIASED
−
 
+
17 H 0.0740 0.9235 0.0025 HEAD-BIASED
−
  start = clock();
+
18 H 0.0654 0.9321 0.0025 HEAD-BIASED
−
  for(int i=0; i < (int)v.size(); ++i) {
+
19 H 0.0630 0.9346 0.0025 HEAD-BIASED
−
    c3.insert(v[i]);
+
20 H 0.0661 0.9314 0.0025 HEAD-BIASED
−
  }
+
21 H 0.0755 0.9219 0.0026 HEAD-BIASED
−
  finish = clock();
+
  22 H 0.0926 0.9038 0.0036 HEAD-BIASED
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC;  
+
23 H 0.1204 0.8684 0.0113 HEAD-BIASED
−
  std::cout << "Tree (Insert) " << duration << std::endl;
+
  24 H 0.1603 0.7586 0.0811 HEAD-BIASED
−
   
+
25 T 0.1904 0.0858 0.7238 TAIL-BASED
−
  start = clock();
+
26 T 0.1819 0.0118 0.8063 TAIL-BASED
−
  for(int i=0; i < (int)v.size(); ++i) {
+
27 T 0.1797 0.0036 0.8167 TAIL-BASED
−
    s.insert(v[i]);
+
  28 T 0.1894 0.0028 0.8077 TAIL-BASED
−
  }
+
  29 T 0.2136 0.0038 0.7826 TAIL-BASED
−
  finish = clock();
+
  30 T 0.2561 0.0123 0.7317 TAIL-BASED
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC;  
+
** Example input/output data for problem 3-3 (Applying 2-state HMM in Problem 3-1): Download using [http://dl.dropbox.com/u/1850834/biostat615-homework3-3-20k-examples.zip THIS LINK]
−
  std::cout << "std::set (Insert) " << duration << std::endl;
 
−
   
 
−
  start = clock();
 
−
  for(int i=0; i < (int)v.size(); ++i) {
 
−
    c1.search(v[i]);
 
−
  }
 
−
  finish = clock();
 
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC; 
 
−
  std::cout << "Sorted Array (Search) " << duration << std::endl;
 
−
   
 
−
  start = clock();
 
−
  for(int i=0; i < (int)v.size(); ++i) {
 
−
    c2.search(v[i]);
 
−
  }
 
−
  finish = clock();
 
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC; 
 
−
  std::cout << "List (Search) " << duration << std::endl;
 
−
   
 
−
  start = clock();
 
−
  for(int i=0; i < (int)v.size(); ++i) {
 
−
    c3.search(v[i]);
 
−
  }
 
−
  finish = clock();
 
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC; 
 
−
  std::cout << "Tree (Search) " << duration << std::endl;
 
−
   
 
−
  start = clock();
 
−
  for(int i=0; i < (int)v.size(); ++i) {
 
−
    s.find(v[i]);
 
−
  }
 
−
  finish = clock();
 
−
  duration = (double)(finish-start)/CLOCKS_PER_SEC; 
 
−
  std::cout << "std::set (Search) " << duration << std::endl;
 
−
}
 
  
 
== Office Hours ==
 
== Office Hours ==
−
* Friday 9:30AM-12:30PM
+
* Friday 9:00AM-10:30PM
−
 
 
−
== Information on Biostatistics Cluster ==
 
−
* You may want to request an account to the biostatistics cluster. Refer to https://webservices.itcs.umich.edu/mediawiki/Biostatistics/index.php/Cluster for further information.
 
  
 
== Standards of Academic Conduct ==
 
== Standards of Academic Conduct ==
Line 160: Line 153:
  
 
== Course History ==
 
== Course History ==
−
 
+
* Winter 2011 Course Web Site [[Biostatistics_615/815_Winter_2011]]
−
Goncalo Abecasis taught it in several academic years previously. For previous course notes, see [[http://www.sph.umich.edu/csg/abecasis/class Goncalo's older class notes]].
+
* Goncalo Abecasis taught it in several academic years previously. For previous course notes, see [[http://www.sph.umich.edu/csg/abecasis/class Goncalo's older class notes]].

Latest revision as of 17:35, 31 August 2012

Objective

In Fall 2011, Biostatistics 615/815 aims for providing students with a practical understanding of computational aspects in implementing statistical methods. Although C++ language will be used throughout the course, using Java programming language for homework and project will be acceptable.

Target Audience

Students in Biostatistics 615 should be comfortable with simple algebra and basic statistics including probability distribution, linear model, and hypothesis testing. Previous experience in programming is not required, but those who do not have previous programming experience should expect to spend additional time studying and learning to be familiar with a programming language during the coursework. Most students registering for the course are Masters or Doctoral students in Biostatistics, Statistics, Bioinformatics or Human Genetics.

Students in Biostatistics 815 should be familiar with programming languages so that they can complete the class project tackling an advanced statistical problem during the semester. Project will be carried out in teams of 2. The details of the possible projects will be announced soon.

Textbook

  • Recommended Textbook : Cormen, Leiserson, Rivest, and Stein, "Introduction to Algorithms", Third Edition, The MIT Press, 2009 [Official Book Web Site]
  • Optional Textbook : Press, Teukolsky, Vetterling, Flannery, "Numerical Recipes", 3rd Edition, Cambridge University Press, 2007 [Official Book Web Site]

Class Schedule

Classes are scheduled for Tuesday and Thursdays, 8:30 - 10:00 am at SPH II M4332

Topics

The following contents are planned to be covered.

Part I : C++ Basics and Introductory Algorithms

  • Computational Time Complexity
  • Sorting
  • Divide and Conquer Algorithms
  • Searching
  • Key Data Structure
  • Dynamic Programming
  • Hidden Markov Models

Part II : Numerical Methods and Randomized Algorithms

  • Random Numbers
  • Matrix Operations and Least Square Methods
  • Importance Sampling
  • Expectation Maximization
  • Markov-Chain Monte Carlo Methods
  • Simulated Annealing
  • Gibbs Sampling

Class Notes

Problem Sets

  • Problem Set 0 - Running screenshots of helloWorld.cpp and towerOfHanoi.cpp - Due before the submission of Problem Set 1
  • Problem Set 1 -- Due on Tuesday September 27th, 2011 (PDF) (PDF-SOLUTIONS)
  • Problem Set 2 -- Due on Thursday October 6th, 2011 (PDF) (PDF-SOLUTIONS)
    • (Update Oct 2, 2011 : Note that the problem 1 and 3 are slightly updated for clarification)
    • (If you can't decompress the files above properly, use this alternative link by CLICKING HERE )
  • Problem Set 3 -- Due on Tuesday November 1st, 2011 (PDF) (UPDATED on Oct 25th at 11:10AM)
  • Problem Set 4 -- Due on Tuesday November 15th, 2011 (PDF)
  • Problem Set 5 -- Due on Tuesday November 29th, 2011 (PDF)
  • Problem Set 6 -- Due on Tuesday December 13th, 2011 (PDF)

Supplementary Data sets for Problem Sets

TIME	TOSS	P(FAIR)	P(BIAS)	MLSTATE
1	H	0.5950	0.4050	FAIR
2	T	0.8118	0.1882	FAIR
3	H	0.8071	0.1929	FAIR
4	T	0.8584	0.1416	FAIR
5	H	0.7613	0.2387	FAIR
6	H	0.7276	0.2724	FAIR
7	T	0.7495	0.2505	FAIR
8	H	0.5413	0.4587	BIASED
9	H	0.4187	0.5813	BIASED
10	H	0.3533	0.6467	BIASED
11	H	0.3301	0.6699	BIASED
12	H	0.3436	0.6564	BIASED
13	H	0.3971	0.6029	BIASED
14	T	0.5028	0.4972	BIASED
15	H	0.3725	0.6275	BIASED
16	H	0.2985	0.7015	BIASED
17	H	0.2635	0.7365	BIASED
18	H	0.2596	0.7404	BIASED
19	H	0.2858	0.7142	BIASED
20	H	0.3482	0.6518	BIASED
    • Example output data for problem 3-2 (input is the second column) (NOTE : UPDATED on Oct 25 11:23PM)
TIME	TOSS	Pr(F)	Pr(HB)	Pr(TB)	MLSTATE
1	T	0.8844	0.0326	0.0830	FAIR
2	H	0.9012	0.0791	0.0198	FAIR
3	H	0.9075	0.0735	0.0189	FAIR
4	T	0.9091	0.0145	0.0764	FAIR
5	T	0.9068	0.0114	0.0818	FAIR
6	H	0.9058	0.0440	0.0502	FAIR
7	T	0.8834	0.0275	0.0891	FAIR
8	H	0.8520	0.0698	0.0783	FAIR
9	T	0.7713	0.0347	0.1940	FAIR
10	T	0.6927	0.0823	0.2249	FAIR
11	H	0.4730	0.4984	0.0286	HEAD-BIASED
12	H	0.3227	0.6706	0.0066	HEAD-BIASED
13	H	0.2236	0.7726	0.0037	HEAD-BIASED
14	H	0.1589	0.8381	0.0031	HEAD-BIASED
15	H	0.1169	0.8803	0.0028	HEAD-BIASED
16	H	0.0902	0.9072	0.0026	HEAD-BIASED
17	H	0.0740	0.9235	0.0025	HEAD-BIASED
18	H	0.0654	0.9321	0.0025	HEAD-BIASED
19	H	0.0630	0.9346	0.0025	HEAD-BIASED
20	H	0.0661	0.9314	0.0025	HEAD-BIASED
21	H	0.0755	0.9219	0.0026	HEAD-BIASED
22	H	0.0926	0.9038	0.0036	HEAD-BIASED
23	H	0.1204	0.8684	0.0113	HEAD-BIASED
24	H	0.1603	0.7586	0.0811	HEAD-BIASED
25	T	0.1904	0.0858	0.7238	TAIL-BASED
26	T	0.1819	0.0118	0.8063	TAIL-BASED
27	T	0.1797	0.0036	0.8167	TAIL-BASED
28	T	0.1894	0.0028	0.8077	TAIL-BASED
29	T	0.2136	0.0038	0.7826	TAIL-BASED
30	T	0.2561	0.0123	0.7317	TAIL-BASED
    • Example input/output data for problem 3-3 (Applying 2-state HMM in Problem 3-1): Download using THIS LINK

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The following is an extract from the School of Public Health's Student Code of Conduct [1]:

Student academic misconduct includes behavior involving plagiarism, cheating, fabrication, falsification of records or official documents, intentional misuse of equipment or materials, and aiding and abetting the perpetration of such acts. The preparation of reports, papers, and examinations, assigned on an individual basis, must represent each student’s own effort. Reference sources should be indicated clearly. The use of assistance from other students or aids of any kind during a written examination, except when the use of books or notes has been approved by an instructor, is a violation of the standard of academic conduct.

In the context of this course, any work you hand-in should be your own.

Course History

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