# Difference between revisions of "Eleisha's Segment 15: The Towne Family - Again"

(Created page with " <b>To Calculate: </b> 1. In slide 4, we used "posterior predictive p-value" to get the respective p-values 1.0e-13, .01, .12, and .0013. What if we had mistakenly just used ...") |
|||

Line 3: | Line 3: | ||

1. In slide 4, we used "posterior predictive p-value" to get the respective p-values 1.0e-13, .01, .12, and .0013. What if we had mistakenly just used the maximum likelihood estimate r=0.003, instead of integrating over r? What p-values would we have obtained? | 1. In slide 4, we used "posterior predictive p-value" to get the respective p-values 1.0e-13, .01, .12, and .0013. What if we had mistakenly just used the maximum likelihood estimate r=0.003, instead of integrating over r? What p-values would we have obtained? | ||

+ | You can easily use python to calculate the p-value for each of the Townes using the PDF of a binomial distribution. Below are the p-values | ||

+ | <pre> | ||

+ | P-value for T2: 7.82096716379e-23 | ||

+ | P-value for T11: 0.00357596170111 | ||

+ | P-value for T13: 0.000504346838529 | ||

+ | </pre> | ||

+ | |||

+ | This output was generated using the following python code: | ||

+ | |||

+ | <pre> | ||

+ | import math, scipy.stats | ||

+ | import numpy as np | ||

+ | |||

+ | mut_rate= 0.003 #Mutation Rate | ||

+ | |||

+ | n_2 = 10*37 | ||

+ | n_11 = 9*37 | ||

+ | n_13 = 10*12 | ||

+ | |||

+ | k_2 = 23 | ||

+ | k_11 = 5 | ||

+ | k_13 = 4 | ||

+ | |||

+ | def get_p_value(k, n, r): | ||

+ | p_value = 0.0 | ||

+ | for i in xrange(k, 38): | ||

+ | binom = scipy.stats.binom.pmf(i,n,r) | ||

+ | p_value = p_value + binom | ||

+ | return p_value | ||

+ | |||

+ | print "P-value for T2: " + str(get_p_value(k_2, n_2, mut_rate)) | ||

+ | print "P-value for T11: " + str(get_p_value(k_11, n_11, mut_rate)) | ||

+ | print "P-value for T13: " + str(get_p_value(k_13, n_13, mut_rate)) | ||

+ | </pre> | ||

<b> To Think About: </b> | <b> To Think About: </b> |

## Revision as of 23:12, 24 February 2014

**To Calculate: **

1. In slide 4, we used "posterior predictive p-value" to get the respective p-values 1.0e-13, .01, .12, and .0013. What if we had mistakenly just used the maximum likelihood estimate r=0.003, instead of integrating over r? What p-values would we have obtained? You can easily use python to calculate the p-value for each of the Townes using the PDF of a binomial distribution. Below are the p-values

P-value for T2: 7.82096716379e-23 P-value for T11: 0.00357596170111 P-value for T13: 0.000504346838529

This output was generated using the following python code:

import math, scipy.stats import numpy as np mut_rate= 0.003 #Mutation Rate n_2 = 10*37 n_11 = 9*37 n_13 = 10*12 k_2 = 23 k_11 = 5 k_13 = 4 def get_p_value(k, n, r): p_value = 0.0 for i in xrange(k, 38): binom = scipy.stats.binom.pmf(i,n,r) p_value = p_value + binom return p_value print "P-value for T2: " + str(get_p_value(k_2, n_2, mut_rate)) print "P-value for T11: " + str(get_p_value(k_11, n_11, mut_rate)) print "P-value for T13: " + str(get_p_value(k_13, n_13, mut_rate))

** To Think About: **

1. Can you think of a unified way to handle the Towne family problem (estimating r and deciding which family members are likely "non-paternal") without trimming the data? We'll show one such method in a later segment, but there is likely more than one possible good answer.

** Class Activity **

For the class activity on Monday February 24th, I was in group two. Our solutions can be found over at: Group Two: The Towne Family - Again, Class Activity

** Back To: Eleisha Jackson**