The Perils and Pitfalls of Matching War Deaths Across Lists: Part 1

I argued in an earlier post that matching deaths across lists is a nontrivial exercise that involves a lot of judgement and that, therefore, needs to be done transparently.  Here is the promised follow up post which I do jointly with Josh Dougherty of Iraq Body Count.  In fact, we’ll make this into another multi-part series as there are many different sources and issues to explore. This is a large subject of growing importance to the conflict field, so we may also eventually convert some of this material into a journal article. Throughout this series we’ll draw heavily on Josh’s extensive experience matching violent deaths across sources for the Iraq conflict.

Today we’ll set the table with some preliminaries and offer basic findings, with more detailed exploration of the data to follow in future posts.

First, list matching for Iraq has involved a combination of event matching and victim matching.  Events are usually considered to be discrete violent incidents, such as suicide bombings, air attacks or targeted assassinations, and are typically defined by their location, date, size, type and other features.

The event matching aspect of the Iraq work means that it won’t always be directly relevant to pure victim-based matching efforts such as those underpinning the statistical work of Peru’s Truth and Reconciliation Commission (TRC), or the various efforts involving casualty lists covering the war in Syria.  We’ll talk more about pure victim-based matching in a future post.  However, matching events is ultimately still about matching deaths/victims, so the issues that arise are very similar and most of what we write here will be relevant to victim-based matching.

Second, we analyse a matching exercise from this paper by Carpenter, Fuller and Roberts (CFR) that attempts to match events from the Iraq war across two sources.  This CFR paper has been cited in some major journal articles.  In fact, Megan Price and Patrick Ball, the main author of the statistical report of the Peruvian TRC, relied heavily on CFR’s matching in some of their own papers. Yet CFR’s matching turns out to be very bad.

Third, we won’t address here the main matching exercise of 2,500 records carried out (again badly) in the CFR paper.  We cover, rather, a robustness check matching smaller samples that CFR present towards the end of their paper, and which should be more easily digestible for readers.  A proper analysis of CFR’s main matching exercise is beyond the scope of this series, but we can say here that the kind of problems affecting the robustness check generally carry over into the main matching exercise. Note, however, that CFR’s main matching is done by hand with human researchers, whereas the robustness check that we cover below is described as “computer-driven” and “non-subjective”. Still, both the human and computer approaches use essentially an algorithmic matching approach with very similar pre-determined parameters. The major difference is that in one case an algorithm is applied by hand, with more room for human judgment, while in the other it is apparently applied more strictly with the help of a machine. Indeed, CFR report that the two approaches “resulted in the same conclusions,” so they suggest that their robustness check has succeeded and that we should feel more confident in their findings.

In this exercise, CFR match samples from two sources covering events that occurred in Karbala, Iraq, between 2004 and 2009.  The sources are Iraq Body Count (IBC) and the Iraq War Logs published by WikiLeaks in 2010, also known as the official SIGACTs database of the US military.  Here are the methods of IBC.

Unfortunately, we know of no formal statement of a data collection methodology for SIGACTs, however we do know that it is compiled by the US Department of Defence from the field reports of US and Coalition soldiers, Iraqi security forces and other Iraqi sources.  We can also learn about SIGACTs by inspecting the entries.  This one, for example, describes a “search and attack” operation in which Coalition Forces killed seven “Enemy” fighters in the Diyala governorate.  The entry displays SIGACTs’ standard data-entry fields which include the date, time, GPS coordinates, event type, reporting unit and numbers killed and wounded. The casualty numbers are further divided into “Enemy”, “Friendly”, “Civilian” and “Host Nation” categories. Each record begins with a short headline and also contains a longer text description of the events. These descriptions tend to be rather jargon-filled but can be read fluently after some practice.

We will show in the next post of this series that careful reading of the detailed text descriptions is essential for matching SIGACTs-recorded deaths against other sources correctly. The CFR work runs aground already at this data inspection stage because they worked only with a summary version of the data, published by The Guardian, which omits the detailed text descriptions. Note also that the above-cited Price and Ball paper, which closely follows the CFR lead, shares CFR’s cavalier approach to the SIGACTs data, writing incorrectly of its methodology:

SIGACTSs based on daily “Significant Activity Reports” which include “…known attacks on Coalition forces, Iraqi Security Forces, the civilian population, and infrastructure. It does not include criminal activity, nor does it include attacks initiated by Coalition or Iraqi Security Forces”

This is not true of the full SIGACTs database released in 2010, and instead comes third hand from a description of some statistics on “Enemy-initiated attacks” that appeared in a 2008 US DoD report. Those data were derived from only selected portions of the SIGACTs database and their description does not apply to the full dataset. A cursory glance at the full SIGACTs dataset would have quickly revealed that it includes criminal activity and attacks initiated by Coalition or Iraqi Security Forces.

Further background on the SIGACTs (Iraq War Logs) data can be found here and here.

CFR derives their Karbala sample, plus a separate Irbil one to which we will return later, by:

filtering the entire WL data set in the event description for the appearance of the words ‘‘Irbil’’ and ‘‘Karbala.’’

You should interpret “the entire WL data set” to mean the entire Civilian category, with at least 1 death, of the Guardian version of the SIGACTs dataset, i.e., the version that omits the detailed text descriptions of each record.  In this context, the above phrase “event description” can only refer to the headline of each record, as there is nothing else in the Guardian version of the dataset that could both approximate an “event description” and contain the word “Karbala”.

The above filtering yields a sample of 50 records containing 558 deaths.  However, strangely, CFR report only 39 records in their results table.  It would seem that CFR had an additional, unreported, filtering stage that eliminated 11 records.  Or perhaps CFR simply made a mistake.  There is no way to know at present how or why this happened because CFR do not list their 39 Karbala records or their matching interpretations for each in their paper, and have ignored or refused past data requests.  Consequently, we will simply follow CFR’s reported sampling methodology, as it appears in their paper, and proceed with matching the 50 records it produces.

CFR’s reported matching algorithm applied to this sample contains three matching requirements:

  1. Event dates must be within one calendar day of each other.
  2. The number killed cannot be more than + or – 30% apart.
  3. Weapon types must match.

CFR report one main finding on Karbala alone (again, we will return to Irbil later):

the majority of events in WL [SIGACTs] are not in IBC and vice-versa.

Indeed, CFR’s results table claims that only 1 of their 39 SIGACT records match IBC on all three of their criteria. [Note that the first version of this post said that there were 2 matches rather than the correct number which is 1] They report only event, not death, statistics, but there is an obvious implication that IBC missed a high percentage of the deaths in the Karbala sample.

The problem is that their results are very wrong. When we compare each of the records in detail, the majority of records and the vast majority of deaths in the Karbala sample match with IBC. Specifically, 95% of deaths (533 out of 558) and 66% of records (33 out of 50) match with the IBC database.

However, when we apply CFR’s matching algorithm to those same records, only 24% of deaths (132 of 558) and 22% of records (11 of 50) match on all three criteria. We should note here that applying CFR’s algorithm is not as simple or straightforward as it might seem. Their three requirements all raise some ambiguities that need to be resolved by subjective judgement in practice, and the outcomes of these choices can move the final numbers around a bit.  We will discuss these issues in our next post, but any resolution of these ambiguities will still leave an enormous distance between CFR results and the truth.

It should be stressed that the CFR approach apparently seemed reasonable and reliable to the authors, journal referees and editors, and to other researchers, like Price and Ball, who build on CFR’s work. Yet their approach ultimately gets the data all wrong, and for reasons that become pretty clear when one examines the data in detail. Indeed, we find that CFR’s conclusions reflect defects in their methodology far more than they reflect holes in IBC’s coverage of conflict deaths in Karbala.

With this in mind, let’s circle back to the Peru debate which inspired the present series on matching. In the Peru discussion Daniel Marique Vallier and Patrick Ball (MVB) argue that some of Silvio Rendon’s point estimates for numbers of people killed in the Peruvian war are “impossible” because these point estimates are below numbers obtained by merging and deduplicating deaths appearing on multiple lists. But the results we report here should shock anyone who previously thought that counts emerging from such list mergers can simply be taken at face value and treated uncritically as absolute minima. MVB’s matching is unlikely to be anywhere near as bad as CFR’s, but we still need to see the matching details before we can begin to talk seriously about minima.

Our next post will share the Karbala sample along with our case-by-case matching interpretations and dig into the details of how and why the CFR approach got things so wrong.


Important New Violent Death Estimates for the War in Peru with Implications Beyond just Peru: Part 6

This is the latest installment in a series that considers the statistical report done for the Peruvian Truth and Reconciliation Commission (TRC), Silvio Rendon’s critique of this statistical report and a reply to Rendon from Daniel Manrique Vallier and Patrick Ball (MVB) who worked on the TRC statistical report.  The present post continues to discuss the MVB reply.

(Note that I may not resume this series until Silvio Rendon’s rejoinder is published.  Meanwhile, I’m also working with Josh Dougherty of Iraq Body Count on an offshoot post that will cover the practice and pitfalls of matching deaths across multiple lists.)

Today I’ll comment on nine figures from the MVB reply: figure 1 in the main body of the paper and figures 2-9 in the appendix.

I won’t produce any of the figures here because they are misleading and a picture is worth a thousand words.  The main features I object to are that the figures  substitute lower (preliminary) stratum-level estimates for Rendon’s main estimates and suppress the uncertainly surrounding these estimates.  Moreover, MVB portray some of these these lowered point estimates as falling within an “impossibility region,” a characterization which further assumes that MVB’s matching of deaths across sources was perfectly executed on fully accurate data.

Nevertheless, the figures do convey some interesting simulation-based information that addresses the question of when a direct estimation approach outperforms MVB’s indirect one and vice versa.  Each of the nine figures uses data from a stratum for which one can directly estimate Shining Path (SP) deaths.  (There are nine such strata before multiple imputation and two more, not covered by the figures, after multiple imputation.)

The X axis in each picture represents all the possible true values for the number of SP-caused deaths (with the true values indexed by N).  MVB perform simulations that estimate the number of SP-caused deaths many times for each stratum and for each N using both direct capture-recapture and MVB’s indirect capture-recapture methodology.  MVB then calculate the deviation of each estimate from the underlying true value, square these deviations (so that negative deviations do not cancel out positive ones) and take the mean of these squared deviations across all simulation runs for each value of N.  Finally, they graph these “mean-squared errors” for each method and each N in all nine strata.

For eight out of the nine strata the direct method outperforms (i.e., has lower mean-squared errors) the indirect method for values of N below some critical value and the the indirect method outperforms the direct one above this same critical value.  (For one stratum the reverse is true but there is never a big difference between the two methods in this stratum so this doesn’t seem to matter much.)  For three strata the critical value for which the best performing method switches from direct to indirect is inside of MVB’s “impossibility region”.

In eight out of the nine strata the indirect method outperforms the direct method when the true number of people killed by the SP is set equal to the estimate that the TRC actually made for that stratum (using the indirect method).  Essentially, this rather unsurprising result says that the indirect method performs well in simulations of cases for which the TRC’s indirect estimate  delivered a correct result.  And the indirect method also performs well when the TRC’s estimate is not spot on but still reasonably close to being correct.

The direct method tends to outperform the indirect one in simulations that start from the assumption that the direct estimate is correct.  Nevertheless,  in three out of the nine strata the indirect method actually wins this contest.

Overall, these simulation results tend to favor the indirect method over the direct one, especially when the true numbers are assumed to be rather high.

That said,  the direct method in the simulations does not match Rendon’s main method because, again, MVB omit the multiple imputation step of Rendon’s procedures.  Incorporating multiple imputation should shift the balance back towards Rendon.  And, again, I would like to see a similar exercise performed on Rendon’s alternative approach that covers the whole country with ten strata.

Here’s one last point before I sign off.  As of now, the MVB reply is still just a working paper, not yet published in Research and Politics.    The main advantage of posting a working paper before publication is that you can respond to feedback.  Thus, it would be great and appropriate for MVB to take advantage of the remaining time window by purging the misleading material about impossible point estimates without uncertainty intervals from the published version of their paper.  (See post 4 and post 5 of this series in addition to the present one for further details.)  This move would help lead us toward more fruitful future discussions.

Important New Violent Death Estimates for the War in Peru with Implications Beyond just Peru: Part 5

I’ll start this post by reacting to some interesting comments to part 4 of this series which was, you may be surprised to learn,  preceded by part 1, part 2 and part 3.  I’ll assume that readers have some familiarity with these posts but I’ll also try to go slowly and remind readers of things we’ve discussed before.

Recall that there is a statistical report done for the Peruvian Truth and Reconciliation Commission (TRC), Silvio Rendon’s critique of this statistical report and a reply to Rendon from Daniel Manrique Vallier and Patrick Ball (MVB) who worked on the TRC statistical report.

Let’s focus first on the data.

The TRC statistical report and Rendon’s critique are both based on what I’ll  call “the original data,” which consists of 3 (after some consolidation) lists containing a total of 25,000 unique (it is claimed) deaths, many appearing on multiple lists.

There are several issues concerning the original data:

First, only summary information from the original data is in the public domain.  The following table from the TRC statistical report shows the form of the publicly available original data:

We can see, for example, that there are 627 people recorded nationwide as killed by the State (“EST”) who appear on the list of the CVR (the TRC itself) and the DP (Defensoria del Pueblo) but not on the ODH (NGO’s) list.

There are 59 such tables, one for each geographical stratum.  Each one looks  like the above table but, of course, with smaller numbers.  Both the TRC and Rendon base their statistical work on these tables.

The problem is that these 59 tables alone do not allow us to examine the underlying matching of deaths across lists that they summarize.  Matching is a non-trivial step in the research that involves a lot of judgment.  I will examine the matching issue in an upcoming post.  Suffice to say here that until this step is opened up we are not doing open science.

To be fair, it appears possible for at least some researchers to obtain the detailed data from the Peruvian government and perform their own matching.  According to Patrick Ball:

“People with access to the detailed TRC data” is not an intrinsic category of people: it’s just people who have asked nicely and persisted (sometimes, like us, over several years), until they got access to the data. It seems to me that with sensitive data, obtaining the relevant information is incumbent upon the researcher: Rendon could have inquired of the Peruvian Ombudsman office to get the TRC data. It’s not secret, it just requires a bit of work to obtain, and he chose not to do so.

I don’t like this.  The data should simply be available for use.  Patrick may be right that, effectively, it’s open to all nice and persistent people.  But the data should also be available to mean and non-persistent people as well.

Let’s move on to a few observations on the MIMDES data, the detailed version of which is in the public domain.  (Apparently it’s not online right now but has been in the past and hard copies can be obtained.).

First, the public availability of the MIMDES data undermines excuses for forcing researchers to jump through hoops for the TRC data.  They are both detailed lists of people killed in the war.  These list are both held by the Peruvian government.  Why is it OK to circulate one list while requiring researchers to be nice and persistent for the other?

Second, I know nothing about the data collection methodology for the MIMDES data.  OK, perhaps I should obtain and study the MIMDES reports.  But the MVB reply paper introduces the MIMDES data into this whole discussion so they should describe the MIMDES data collection methodology in their paper.  (They also should have described the data collection methodologies for the lists used in the TRC’s statistical report.)  But the MIMDES methodology seems particularly important since Patrick Ball, in his comments on this blog, urges us to treat the MIMDES sample as more or less representative of all deaths in the war.  I would need to know something about how MIMDES performed its work before entertaining such a notion.

MVB have matched the MIMDES deaths against the TRC’s deaths and the resulting figures are central to their reply to Rendon’s critique.  For three reasons, however, I recommend that we take these merged TRC-MIMDES figures with a grain of salt, at least for now.  First, MVB don’t explain how they do the matching.  Second, they say their work is unfinished.  Third, it is difficult at present for anyone to match independently since the TRC data are not really open.  (Remember that you need the detailed TRC data in order to match it against the MIMDES data.)

That said, for the rest of the post I’ll take the numbers from MVB’s TRC-MIMDES merge as given just as I’ve done in my earlier posts.

Patrick and Daniel especially emphasize one point in their separate comments on post number 4 (in which they focus exclusively on Rendon’s Shining Path (SP) estimates).  Recall that Rendon’s main estimate starts with estimates from just the geographical strata that allow for direct estimation (after multiple imputation) and then uses spatial extrapolation (kriging) to extend these estimates to the whole of Peru.  But, MVD argue, the estimates in the selected strata are biased downwards because the fact that there’s rich enough data to do direct estimation already suggests that there are relatively few undocumented deaths left to discover in these strata.  Conversely, MVB  suggest, the strata where data is too sparse for direct estimation probably contain relatively many undocumented deaths.

This is a creative idea with some potential but I think that, if it exists, its effect is probably small. One of Rendon’s alternative estimates cuts Peru up into just 10 regional strata which cover the entire country rather than the 59 more localized strata in MVB’s stratification scheme.  This 10-stratum estimate is not subject to MVB’s selection bias argument.  The SP estimate in this case is around 1,000 deaths more than Rendon’s main estimate (which  requires strata selection and spatial extrapolation).  So perhaps MVB have identified a real bias although, if so, it seems to be a small one.  There are, of course, multiple changes when we move from Rendon’s main estimate to the 10-stratum one.  But MVB need their suggested bias to be huge in order to produce the 10,000 plus additional deaths required to make their TRC estimate look accurate.  The above comparison doesn’t suggest a bias effect of this order of magnitude.

The frailty of MVB’s statum-bias critique is exposed by the games they play to portray Rendon’s direct stratum estimates for the SP as systematically lower than the SP numbers in their merged TRC-MIMDES dataset.

They begin by deleting the multiple imputation step of Rendon’s procedures.  Daniel Marique Vallier explains:

Thus, showing that the application of capture-recapture to those strata leads to contradictions, automatically invalidates all the rest of the analysis. This is because those more complex estimates depend on (and amplify) whatever happens with the original 9; you can’t extrapolate from strata that are themselves inadequate. That’s what we have shown. Specifically, we have shown that the application of capture-recapture to those 9 strata (Rendon’s necessary condition) results in estimates smaller than observed counts (contradiction). This means that the basic premise, that you can use those strata as the basis for a full blown estimation, is faulty (modus tollens). Anything that depends on this, i.e. all the rest of the conclusions, is thus similarly faulty (contradiction principle).

This makes no sense.  Applying multiple imputation before capture recapture increases the estimate in every stratum.  These higher estimates then feed through the spatial extrapolation to increase the national estimates.  Deleting the multiple imputation step decreases the estimates at both the stratum and national levels.  Manrique Vallier argues, in effect, that doing something to increase Rendon’s estimates can only compound the problem of his estimates being too low.  This is like saying that drinking a lot of alcohol makes it dangerous to drive so (modus tollens) sobering up can only make it more dangerous to drive.

Next MVB try to dismiss all of Rendon’s work based on their claim that some of Rendon’s point estimates (which they have lowered) are below their merged TRC-MIMDES numbers.  Simultaneously, MVB apply a far more lenient standard to evaluate Patrick Ball’s Kosovo work (see MVB’s comments on post 4).  For Kosovo, they argue, it’s not a problem for most estimates to be below documented numbers as long as the tops of Ball’s uncertainty intervals exceed these numbers.  Moreover, it’s even OK for this criterion to fail sometimes as long as Ball’s broad patterns are correct.  I actually agree with these standards but consistency requires applying them to Rendon’s Peru work as well.

That said, Patrick Ball’s last comment makes a good point about the serious challenges to data collection in Peru.  By contrast, it’s easier to collect war-death data in Kosovo and lots of resources were devoted to doing just this..  So the true numbers in Peru might be substantially larger than MVB’s TRC-MIMDES ones.  I agree that this is possible but I would want to know a lot more about the various data collection projects in Peru before taking a strong stand on this point.

Finally, I return to Rendon’s ten strata estimate which appears immune to all the criticism contained in MVB’s reply.  The central estimate is about 2,000 deaths above MVB’s TRC-MIMDES national count for SP deaths, leaving considerable room to accommodate the discovery of more deaths, especially in light of the uncertainty interval.  That said, it would be interesting to see stratum by stratum comparisons with TRC-MIMDES to see whether there are any substantial discrepancies.

To summarize, perhaps Rendon’s SP estimates are somewhat low.  But MVB’s reply does little to undermine Rendon’s critique.beyond this minor observation.











Important New Violent Death Estimates for the War in Peru with Implications Beyond just Peru: Part 4

This is the fourth post in a series on the statistical report of the Peruvian Truth and Reconciliation Commission (TRC) , the critique of that report published by Sylvio Rendon, the reply to Rendon from two authors of the statistical report and, eventually, Rendon’s rejoinder which has not yet been published.  My earlier posts are here, here and here.

Note – I just noticed that in my last post I reversed the order of the authors on the reply paper.  I will fix this.  From now on the order will be  Daniel Manrique-Vallier and Patrick Ball (MVB).

In their abstract MVB write:

We first show that his most important result, an alternative estimate of the mortality due to the Maoist guerrillas of Shining Path is lower than existing observed data and is therefore impossible.

MVB elaborate in the introduction that:

There are three bases for our rejection of Rendon’s methods and findings: first, his estimates are inconsistent with observed data. By combining the data used by the TRC with data published by the Peruvian government between 2004 and 2006 (MIMDES 2004, 2006), we see that Rendon’s estimates for SLU [the Spanish acronym for Shining Path] are, in most strata and in the aggregate lower than the number of observed SLU victims-without considering victims who continue to be undocumented.

In short, MVB integrate new data onto the lists of documented deaths that they used in their original TRC report and that Rendon used in his critique.  MVB claim that these new integrated accounts exceed Rendon’s aggregate Shining Path (SP) estimate as well as his estimates in most of the strata for which he did direct estimates.  There is some merit from this line of argument but, as presented, it is weak and even disingenuous.

Recall that Rendon’s main aggregate SP estimate is roughly 18,000 with a 95% uncertainty interval of about 15,500 to 21,000.  For convenience I repeat Rendon’s main table here:

MVB’s new number for documented SP-caused deaths, integrating the new data, is 17,687.  Here is MVB’s main table:

So Rendon’s main estimate is actually higher than 17,687 the new number of observed SP victims (according to MVB), not lower as MVB claim.  Moreover, the top of Rendon’s uncertainty interval is nearly 20% above 17,687, leaving much room for more SP-caused deaths to be discovered without really creating problems for Rendon’s estimate.

At this point I’m sure you’re wondering what the heck is going on here?  The answer is that MVB’s table does cite an actual Rendon SP estimate, just not his main one.  Recall that Rendon’s main estimate is based on three methodological elements: multiple imputation to assign perpetrators when these are listed as “unknown” in the TRC databases, direct estimation in the strata that allow it after multiple imputation and kriging to extend the estimate to the remaining strata.  MVB cite an estimate that used just direct estimation and kriging, not a full estimate with multiple imputation prior to direct estimation and kriging.

It’s fine for MVB to cite the direct-kriging estimate and it’s interesting to compare this one with their new figure for documented deaths.  The problem is that MVB stop at just the direct-kriging estimate and then hinge their case against Rendon on the fact that this incomplete estimate is below a cut-off value.  But multiple imputation is part of Rendon’s methodology and the complete estimate, including this step, exceeds the cut-off value..

Analogously, it’s fine to point out that Watford needed a late goal to beat Leicester City in a game that might well have ended a draw.  But it’s not OK to just ignore that late goal and claim that the game was drawn.

Alert readers may remember that Rendon offered two other SP estimates that also incorporated multiple imputation.  First, there is a fixed effects SP estimate that comes out to around 17,500.  MVB could argue, in their terms, that this estimate is “impossible” although it’s only below their new documented number by around 150 deaths.  Moreover, this estimate is surrounded by an uncertainty interval of around plus or minus 4,000 deaths and it hardly seems appropriate to focus all attention on the central estimate.  Still, it’s true this estimate does include multiple imputation and is below the new documented SP count. .

The other Rendon SP estimate comes from dividing Peru into only ten strata so that direct capture-recapture estimates can be performed for each perpetrator in each stratum.  This SP estimate is around 19,500 plus or minus 6,000, well above the new documented figure even before we factor in the uncertainty interval.

In short, there is no basis to dismiss Rendon’s methods based on the idea that they lead to impossible aggregate findings for the SP.

What about stratum by stratum estimates?  MVB’s table (above) gives figures for one stratum that place Rendon’s central estimate nearly 500 deaths below MVB’s new figure, a deficit of more than 40%.  This is interesting and I would  like to know more about this stratum but this observation has limited importance.  First of all, it is only one stratum, just a small piece of Rendon’s aggregate estimate.  Second, this stratum appears to be the most favorable one for MVB, although they characterize it as merely illustrative.  Third, MVB do not incorporate multiple imputation into the numbers they place in the table although doing so would increase the Rendon numbers. Still, I agree that Rendon’s estimate is probably below the true number for this stratum, although I am not shocked to see a statistical estimate that turns out to be below a true value.

MVB further claim in the second quote above that most of Rendon’s direct stratum estimates for SP are below their new figures for documented deaths.  Maybe this is true, but I will reserve judgment on this claim until I see stratum by stratum comparisons that incorporate multiple imputation and uncertainty intervals.

Here is one final point for today.  A few years ago I worked with Patrick Ball on an evaluation of the database of Kosovo Memory Book (KMB).  I produced a report in which I argued that there is great consistency between KMB’s list of documented deaths for the war in Kosovo and two separate statistical estimates of the same thing (covering somewhat different time periods).  One set of the statistical estimates were capture-recapture ones done by Patrick Ball and co-authors.  In many strata these estimates are below KMB’s numbers for documented deaths.  This happens in the West (see the table below) and for all time periods for which the black curve is above the blue one in figure 2 below.  I have never viewed these differences as a problem and,

indeed, I consider this work to be quite a success for Ball, KMB and the method of capture-recapture.  Yet the logic of the MVB reply seems to require that we reject Ball’s methods and findings on Kosovo.  After all, some of his central estimates are impossible.

OK, I still haven’t covered the whole reply yet but that’s enough for today.