Alexei, I am saying the simulation "process" by which you generate the expected value for the difference in the expected probabilities of failure between the two states is similar regardless of whether you set X at the mean values or at the observed values. The result will differ because the Xs differ. For each state (low and high temp) your goal is to simulate the expected probability of failure, so you can take the difference between the two states. To simulate the exp. probability for each state you have to set the right X valued for each observation, multiply out the mu_i and then take the average. Think about how you would define the Xs to achieve this given that you want one variable at the mean and the other at the observed values. Hope this helps (if it seems a bit cryptic it's because I am trying not to give away the answer yet J). Jens From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Alexei Colin Sent: Monday, March 17, 2008 11:17 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Jens, So, you're saying that there is no difference between holding pressure at its observed value and at the mean pressure. This is the part that is a bit confusing. If we 'hold a variable at its observed value' what is his special 'observed value' because there are many values - one per each observation? If we fix pressure at its mean (one number), then, we can get two vectors X1 and X2 (with the entry for temp. differing). Cool! But if we want to hold pressure at observed values, how do we get down to two vectors? It seems we have two matrices: MX1 and MX2 with number of rows = number of observations, where in each corresponding pair of rows the value for temp. differs. (If we take the average of each column of MX1 and MX2, we would then be holding pressure at its mean). (?) I hope the above is intelligible. Thank you for your time! -Alexei On 03/17/2008 07:08 PM, Jens Hainmueller wrote: Jon and Jane, c) is asking for an estimate of the first difference. So you will need to use two sets of Xs (from and to) and compute the expected value of the change in the expected probability of failure when going from one to the other set of Xs. In both sets of Xs you are supposed to hold pressure at the observed values (meaning the actual values observed in the data for this variable). There is no difference between holding pressure at its observed value or some other value like let's say its sample mean. The procedure is the same. Also see Gary's slide on first differences. The same applies for d and e. Hope this helps. jens -----Original Message----- From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l- bounces at lists.fas.harvard.edu] On Behalf Of Jon Bischof Sent: Monday, March 17, 2008 5:44 PM To: gov2001-l at lists.fas.harvard.edu Subject: [gov2001-l] expected values Hi all, We still do not understand the expected values calculations in parts c-e. The problem set asks us to use observed values of pressure (all 23 of them?) while the section code sets the other Xs at their mean values. The second approach makes sense to us since we would have 1000 betas applied to each of mean values of pressure and the proposed value of temperature. However, if we use all 23 observed values, then each set of betas gets applied to each observation, and we end up with 23 probabilities for each draw of betas. The next step of what to do with these n probabilities is unclear. Can anyone clarify the next step? How does this approach differ from using the mean value of pressure? Jon and Jane _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Hi Jens, Thanks for this explanation. Just to be clear, we should have a measure of uncertainty (ie, confidence intervals) for the first difference of each observed value of pressure, yes? This would then allow us to plot a nice graph of first differences in the temperature values by each value of pressure. Thanks for confirming this. Best, Brett _____ From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Jens Hainmueller Sent: Monday, March 17, 2008 11:28 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Alexei, I am saying the simulation "process" by which you generate the expected value for the difference in the expected probabilities of failure between the two states is similar regardless of whether you set X at the mean values or at the observed values. The result will differ because the Xs differ. For each state (low and high temp) your goal is to simulate the expected probability of failure, so you can take the difference between the two states. To simulate the exp. probability for each state you have to set the right X valued for each observation, multiply out the mu_i and then take the average. Think about how you would define the Xs to achieve this given that you want one variable at the mean and the other at the observed values. Hope this helps (if it seems a bit cryptic it's because I am trying not to give away the answer yet :-)). Jens From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Alexei Colin Sent: Monday, March 17, 2008 11:17 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Jens, So, you're saying that there is no difference between holding pressure at its observed value and at the mean pressure. This is the part that is a bit confusing. If we 'hold a variable at its observed value' what is his special 'observed value' because there are many values - one per each observation? If we fix pressure at its mean (one number), then, we can get two vectors X1 and X2 (with the entry for temp. differing). Cool! But if we want to hold pressure at observed values, how do we get down to two vectors? It seems we have two matrices: MX1 and MX2 with number of rows = number of observations, where in each corresponding pair of rows the value for temp. differs. (If we take the average of each column of MX1 and MX2, we would then be holding pressure at its mean). (?) I hope the above is intelligible. Thank you for your time! -Alexei On 03/17/2008 07:08 PM, Jens Hainmueller wrote: Jon and Jane, c) is asking for an estimate of the first difference. So you will need to use two sets of Xs (from and to) and compute the expected value of the change in the expected probability of failure when going from one to the other set of Xs. In both sets of Xs you are supposed to hold pressure at the observed values (meaning the actual values observed in the data for this variable). There is no difference between holding pressure at its observed value or some other value like let's say its sample mean. The procedure is the same. Also see Gary's slide on first differences. The same applies for d and e. Hope this helps. jens -----Original Message----- From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l- bounces at lists.fas.harvard.edu] On Behalf Of Jon Bischof Sent: Monday, March 17, 2008 5:44 PM To: gov2001-l at lists.fas.harvard.edu Subject: [gov2001-l] expected values Hi all, We still do not understand the expected values calculations in parts c-e. The problem set asks us to use observed values of pressure (all 23 of them?) while the section code sets the other Xs at their mean values. The second approach makes sense to us since we would have 1000 betas applied to each of mean values of pressure and the proposed value of temperature. However, if we use all 23 observed values, then each set of betas gets applied to each observation, and we end up with 23 probabilities for each draw of betas. The next step of what to do with these n probabilities is unclear. Can anyone clarify the next step? How does this approach differ from using the mean value of pressure? Jon and Jane _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Brett, this sounds a bit like as if still have the wrong intuition. Let me be more explicit: for c you would want to report not four but just a single estimate (plus its standard error). the estimate we are looking for is the estimate of the difference in the expected probability of O-ring failure when going from 53_F to 31_F, holding Pressure at its observed values. Take this expression step by step and you will see why this comes down to a single estimate: 1. temp at 53 and observed values for pressure is our first state of the world. 2. temp at 31 and observed values for pressure is our second state of the world. 3. in both states of the world there is a single expected probability of failure 4. what you want is the expected value of the difference in the expected probability of failure between these two states. Hope this helps, jens From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Brett Logan Carter Sent: Wednesday, March 19, 2008 10:19 AM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Or if not a graph (there are only four observed values of pressure), at least a decent looking table. ________________________________________ From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Brett Logan Carter Sent: Wednesday, March 19, 2008 10:16 AM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Hi Jens, Thanks for this explanation. Just to be clear, we should have a measure of uncertainty (ie, confidence intervals) for the first difference of each observed value of pressure, yes? This would then allow us to plot a nice graph of first differences in the temperature values by each value of pressure. Thanks for confirming this. Best, Brett ________________________________________ From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Jens Hainmueller Sent: Monday, March 17, 2008 11:28 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Alexei, I am saying the simulation ?process? by which you generate the expected value for the difference in the expected probabilities of failure between the two states is similar regardless of whether you set X at the mean values or at the observed values. The result will differ because the Xs differ. For each state (low and high temp) your goal is to simulate the expected probability of failure, so you can take the difference between the two states. To simulate the exp. probability for each state you have to set the right X valued for each observation, multiply out the mu_i and then take the average. Think about how you would define the Xs to achieve this given that you want one variable at the mean and the other at the observed values. Hope this helps (if it seems a bit cryptic it?s because I am trying not to give away the answer yet ?). Jens From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Alexei Colin Sent: Monday, March 17, 2008 11:17 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] expected values Jens, So, you're saying that there is no difference between holding pressure at its observed value and at the mean pressure. This is the part that is a bit confusing. If we 'hold a variable at its observed value' what is his special 'observed value' because there are many values - one per each observation? If we fix pressure at its mean (one number), then, we can get two vectors X1 and X2 (with the entry for temp. differing). Cool! But if we want to hold pressure at observed values, how do we get down to two vectors? It seems we have two matrices: MX1 and MX2 with number of rows = number of observations, where in each corresponding pair of rows the value for temp. differs. (If we take the average of each column of MX1 and MX2, we would then be holding pressure at its mean). (?) I hope the above is intelligible. Thank you for your time! -Alexei On 03/17/2008 07:08 PM, Jens Hainmueller wrote: Jon and Jane, c) is asking for an estimate of the first difference. So you will need to use two sets of Xs (from and to) and compute the expected value of the change in the expected probability of failure when going from one to the other set of Xs. In both sets of Xs you are supposed to hold pressure at the observed values (meaning the actual values observed in the data for this variable). There is no difference between holding pressure at its observed value or some other value like let's say its sample mean. The procedure is the same. Also see Gary's slide on first differences. The same applies for d and e. Hope this helps. jens -----Original Message----- From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l- bounces at lists.fas.harvard.edu] On Behalf Of Jon Bischof Sent: Monday, March 17, 2008 5:44 PM To: gov2001-l at lists.fas.harvard.edu Subject: [gov2001-l] expected values Hi all, We still do not understand the expected values calculations in parts c-e. The problem set asks us to use observed values of pressure (all 23 of them?) while the section code sets the other Xs at their mean values. The second approach makes sense to us since we would have 1000 betas applied to each of mean values of pressure and the proposed value of temperature. However, if we use all 23 observed values, then each set of betas gets applied to each observation, and we end up with 23 probabilities for each draw of betas. The next step of what to do with these n probabilities is unclear. Can anyone clarify the next step? How does this approach differ from using the mean value of pressure? Jon and Jane _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Keith, The first difference is the expected difference in the expected probability of failure between the two states. I am not sure if that is what you describe below. Please see my earlier emails on this over the list where I tried to give a detailed explanation for how to do this part. Jens