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* Lecture 9 : Dynamic Programming -- [[Media:Biostat615-Fall2011-lecture09-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture09-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)]]
 
* Review : Dynamic Programming & Midterm Review -- [[Media:Biostat615-Fall2011-midterm-2011-winter-.pdf | (PDF)]]
* Lecture 10 : Hidden Markov Model-- [[Media:Biostat615-Fall2011-lecture10-handout.pdf | (Handout PDF)]] [[Media:Biostat615-Fall2011-lecture10-presentation.pdf | (Presentation PDF)]]
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* 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 | (Handout PDF)]] [[Media:Biostat615-lecture11-2011-10-20.pdf | (Presentation PDF)]]
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* Lecture 11 : Hidden Markov Model (cont'd) -- [[Media:Biostat615-lecture11-2011-10-20.pdf | (PDF)]] '''(UPDATED on Oct 28th at 1:42PM)'''
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* Lecture 12 : Boost Library & Random Numbers -- [[Media:Biostat615-lecture12-2011-10-25.pdf | (PDF)]]
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* Lecture 13 : Single dimensional optimization -- [[Media:Biostat615-lecture13-2011-10-27.pdf | (PDF)]]
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* Lecture 14 : Single and multi dimensional optimizations -- [[Media:Biostat615-fall2011-lecture14.pdf | (PDF)]] (Updated on Nov 3rd 1:25AM)
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* Lecture 15 : Multi dimensional optimizations -- [[Media:Biostat615-fall2011-lecture15.pdf | (PDF)]] (Updated Nov 8 10:35AM)
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* Lecture 16 : E-M algorithm -- [[Media:Biostat615-fall2011-lecture16.pdf | (PDF)]] (Updated Nov 8 10:35AM)
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* Lecture 17 : Simulated Annealing -- [[Media:Biostat615-fall2011-lecture17.pdf | (PDF)]]
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* Lecture 18 : Gibbs Sampling -- [[Media:Biostat615-fall2011-lecture18.pdf | (PDF)]] (Updated Nov 16 10:00PM)
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* Lecture 19 : Importace Sampling -- [[Media:Biostat615-fall2011-lecture19.pdf | (PDF)]]
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* Lecture 20 : Advanced Hidden Markov Models -- [[Media:Biostat615-fall2011-lecture20.pdf | (PDF)]]
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* Lecture 21 : Linear Algebra in C++ -- [[Media:Biostat615-fall2011-lecture21.pdf | (PDF)]]
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* Lecture 22 : More Linear Algebra in C++ -- [[Media:Biostat615-fall2011-lecture22.pdf | (PDF)]]
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* Lecture 23 : Interfacing between C++ and R -- [[Media:Biostat615-fall2011-lecture23.pdf | (PDF)]]
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* Review : Final Review -- [[Media:Biostat615-winter2011-final.pdf | (PDF)]] [[Media:Biostat615-homework-review.pdf | (Homework)]]
    
== Problem Sets ==
 
== Problem Sets ==
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* 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 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)]]
 
* Problem Set 2 -- Due on Thursday October 6th, 2011 [[Media:Biostat615-Fall2011-homework02.pdf | (PDF)]] [[Media:Biostat615-Fall2011-homework02-solutions.pdf | (PDF-SOLUTIONS)]]
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** (Update Oct 2, 2011 : Note that the problem 1 and 3 are slightly updated for clarification)
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** (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] )
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* Problem Set 3 -- Due on Tuesday November 1st, 2011 [[Media:Biostat615-homework03.pdf | (PDF)]] (UPDATED on Oct 25th at 11:10AM)
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* Problem Set 4 -- Due on Tuesday November 15th, 2011 [[Media:Biostat615-homework04.pdf | (PDF)]]
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* Problem Set 5 -- Due on Tuesday November 29th, 2011 [[Media:Biostat615-fall2011-homework05.pdf | (PDF)]]
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* Problem Set 6 -- Due on Tuesday December 13th, 2011 [[Media:Biostat615-fall2011-homework06.pdf | (PDF)]]
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** [http://www.sph.umich.edu/csg/abecasis/class/2006/ModelFittingData.txt DOWNLOAD DATA FOR PROBLEM 1]
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** [http://dl.dropbox.com/u/1850834/zip_01.zip DOWNLOAD DATA FOR PROBLEM 3]
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=== Supplementary Data sets for Problem Sets ===
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* 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)
** (Update Oct 2, 2011 : Note that the problem 1 and 3 are slightly updated for clarification)
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* Problem Set 3
** (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] )
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** 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.
* Problem Set 3 -- Due on Tuesday November 1st, 2011 [[Media:Biostat615-homework03.pdf | (PDF)]]
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TIME TOSS P(FAIR) P(BIAS) MLSTATE
** Example output data for problem 3-2 (input is the second column)
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1 H 0.5950 0.4050 FAIR
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2 T 0.8118 0.1882 FAIR
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3 H 0.8071 0.1929 FAIR
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4 T 0.8584 0.1416 FAIR
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5 H 0.7613 0.2387 FAIR
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6 H 0.7276 0.2724 FAIR
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7 T 0.7495 0.2505 FAIR
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8 H 0.5413 0.4587 BIASED
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9 H 0.4187 0.5813 BIASED
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10 H 0.3533 0.6467 BIASED
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11 H 0.3301 0.6699 BIASED
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12 H 0.3436 0.6564 BIASED
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13 H 0.3971 0.6029 BIASED
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14 T 0.5028 0.4972 BIASED
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15 H 0.3725 0.6275 BIASED
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16 H 0.2985 0.7015 BIASED
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17 H 0.2635 0.7365 BIASED
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18 H 0.2596 0.7404 BIASED
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19 H 0.2858 0.7142 BIASED
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20 H 0.3482 0.6518 BIASED
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** 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
 
  TIME TOSS Pr(F) Pr(HB) Pr(TB) MLSTATE
  1 T 0.9758 0.0068 0.0174 FAIR
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  1 T 0.8844 0.0326 0.0830 FAIR
  2 H 0.9640 0.0312 0.0048 FAIR
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  2 H 0.9012 0.0791 0.0198 FAIR
  3 H 0.9584 0.0341 0.0075 FAIR
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  3 H 0.9075 0.0735 0.0189 FAIR
  4 T 0.9504 0.0091 0.0406 FAIR
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  4 T 0.9091 0.0145 0.0764 FAIR
  5 T 0.9444 0.0118 0.0438 FAIR
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  5 T 0.9068 0.0114 0.0818 FAIR
  6 H 0.9313 0.0582 0.0105 FAIR
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  6 H 0.9058 0.0440 0.0502 FAIR
  7 H 0.9216 0.0663 0.0121 FAIR
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  7 T 0.8834 0.0275 0.0891 FAIR
  8 T 0.9068 0.0358 0.0574 FAIR
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  8 H 0.8520 0.0698 0.0783 FAIR
  9 H 0.8794 0.0672 0.0534 FAIR
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  9 T 0.7713 0.0347 0.1940 FAIR
  10 T 0.8124 0.0316 0.1560 FAIR
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  10 T 0.6927 0.0823 0.2249 FAIR
  11 T 0.7474 0.0699 0.1827 FAIR
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  11 H 0.4730 0.4984 0.0286 HEAD-BIASED
  12 H 0.5663 0.4101 0.0236 HEAD-BIASED
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  12 H 0.3227 0.6706 0.0066 HEAD-BIASED
  13 H 0.4432 0.5512 0.0056 HEAD-BIASED
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  13 H 0.2236 0.7726 0.0037 HEAD-BIASED
  14 H 0.3642 0.6325 0.0032 HEAD-BIASED
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  14 H 0.1589 0.8381 0.0031 HEAD-BIASED
  15 H 0.3164 0.6809 0.0027 HEAD-BIASED
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  15 H 0.1169 0.8803 0.0028 HEAD-BIASED
  16 H 0.2911 0.7063 0.0026 HEAD-BIASED
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  16 H 0.0902 0.9072 0.0026 HEAD-BIASED
  17 H 0.2840 0.7134 0.0026 HEAD-BIASED
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  17 H 0.0740 0.9235 0.0025 HEAD-BIASED
  18 H 0.2937 0.7033 0.0031 HEAD-BIASED
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  18 H 0.0654 0.9321 0.0025 HEAD-BIASED
  19 H 0.3215 0.6714 0.0071 HEAD-BIASED
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  19 H 0.0630 0.9346 0.0025 HEAD-BIASED
  20 H 0.3699 0.5879 0.0422 HEAD-BIASED
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  20 H 0.0661 0.9314 0.0025 HEAD-BIASED
  21 T 0.4269 0.2127 0.3604 TAIL-BASED
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  21 H 0.0755 0.9219 0.0026 HEAD-BIASED
  22 T 0.4257 0.2133 0.3610 TAIL-BASED
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  22 H 0.0926 0.9038 0.0036 HEAD-BIASED
  23 H 0.3642 0.5936 0.0422 HEAD-BIASED
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  23 H 0.1204 0.8684 0.0113 HEAD-BIASED
  24 H 0.3129 0.6800 0.0071 HEAD-BIASED
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  24 H 0.1603 0.7586 0.0811 HEAD-BIASED
  25 H 0.2828 0.7141 0.0031 HEAD-BIASED
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  25 T 0.1904 0.0858 0.7238 TAIL-BASED
  26 H 0.2709 0.7263 0.0028 HEAD-BIASED
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  26 T 0.1819 0.0118 0.8063 TAIL-BASED
  27 H 0.2751 0.7203 0.0046 HEAD-BIASED
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  27 T 0.1797 0.0036 0.8167 TAIL-BASED
  28 H 0.2947 0.6840 0.0213 HEAD-BIASED
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  28 T 0.1894 0.0028 0.8077 TAIL-BASED
  29 T 0.3214 0.5070 0.1716 HEAD-BIASED
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  29 T 0.2136 0.0038 0.7826 TAIL-BASED
  30 H 0.2823 0.6290 0.0887 HEAD-BIASED
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  30 T 0.2561 0.0123 0.7317 TAIL-BASED
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** 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]
    
== Office Hours ==
 
== Office Hours ==

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