# jinghung - Final Exam IsyE 8843 Ying Hung 901984034 Problem...

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Final Exam IsyE 8843 Ying Hung 901984034 Problem 1 There are many application of baysian wavelet in speech data analysis. The testing speech data include one clean speech utterance and three levels of noisy utterance. Here, the clean data is recorded by myself when I was saying ”Two”. Noisy data were made by integrated artificial white noise onto the clean data according to different S/N ratio. For the denoise part, I use filter ”Vaidyanathan”. When I apply Bayesian Shrinkage to this problem, the likelihood of a detail wavelet coefficient is ( 2 N, ) θσ , and that the prior on θ is also ( ) 2 N0 , τ . The Bayes rule is: () 22 2 d ττ σ + . Take and . 2 0.01 = 2 0.1 = Figure 1 : clean speech data pronouncing “Two”.

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Figure 2: Noisy data by adding white noise (S/N ratio=0.05/0.11) Figure 3: denoised data We can look at the performance of these three data by looking at the waveform. (a) clean data (b) noisy data (c) denoised data Figure 4: waveform performance We can see that after apply Bayes shinkage, the denoised data is much clear and close to the original clean data.
Problem 2 (1) By exact calculation, we have () E,A 1 P J1,M 1 B1 P B1,J1,M1,E,A PB 1 = ()( ) 1 PAB 1 ,E PB 1 PE PM1A PJ 1A 1 =⋅ () ( ) AE 1 1 ,E PE 1 PM1A PJ1A 1  ⋅⋅   ∑∑ P AB1 ,E P E P M1A P J1A And we can calculate ( ) ( ) ( ) ( ) P A1B1 ,E0 P E0 ,E1 P E1 =+ 0.998 0.94 0.002 0.95 0.94002 =×+×= ( ) ( ) ( ) ( ) PA 0B 1 1 ,E 0PE 0 1 1PE 1 0.998 0.06 0.002 0.05 0.05998 So, P J1,M1 B1 0.05998 0.01 0.05 0.94002 0.7 0.9 × × 0.5922426 = (2) By using Kevin Murphy’s BNT, The following is plot of the relation in BNT 1 2 3 4 5

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And the conditional probability is: ( ) PM1B 1 () PJ1M1 ,B 1 =0.8992 =0.6586 ( ) P J1,M1 B1 0.5922 = (3) Using BUGS we have: 1 1 ( ) 1 ( PJ1M ) =0.898 =0.655 So, ( ) ( ) P J1,M 1 B1 P J1 M 1,B1 P M 1 B1 =⋅ = 0.898*0.655 = 0.5882
Problem 3 From the data during the period 1851 to 1962, we plot the minedata Y against year, 0 2 04 06 08 01 0 0 0 12345 6 minedata against year year y From this plot we can see that there is a change point located around year 1890, it is the 40 th year in the period. After assume themodel, we can calculate the full

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## This note was uploaded on 10/23/2011 for the course ISYE 8843 taught by Professor Vidakovic during the Spring '11 term at Georgia Institute of Technology.

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jinghung - Final Exam IsyE 8843 Ying Hung 901984034 Problem...

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