# Interviews and Forum on the Future of Science & Technology Videos

The DTCA (Defence Trade Controls Act) Forum we held on 10 April at the University of Melbourne on Defence regulation of science and technology in Australia was recorded. Here are the available video links:

# Enforcement of the DTCA 2012 is Imminent

— Kevin B Korb

In passing the Defence Trade Controls Act 2012 the Australian parliament responded to concerns that the Act would impose too great a burden on scientific and technological research in Australia by deferring its enforcement for two years and setting up a Steering Group to review and propose amendments in the meantime. That time is up, and the Steering Group has issued its proposed amendments. Below is my submission to the public review of the amendment, which is finishing at then end of January, that is, the end of this week.

# Submission in Response to the Defence Trade Controls Amendments Bill 2015 (DTCB)

The DTCB seeks to rectify some of the errors introduced with the passage of the Defence Trade Controls Act 2012 (DTCA). It goes about this by ameliorating some of the burden imposed on institutions and individuals created by DTCA in doing research on dual-use (not military) goods. In my view, the DTCB is misdirected and likely to fail to afford sufficient relief for many researchers and research projects, leading to tertiary education and research paying a very high cost for little or no benefit in the near to medium term. The correct remedy would be to rewrite the DTCA so as to include provisions closely comparable to the corresponding UK and US legislation that exempt publication, scientific research and higher education involving dual-use goods. For example, the UK Export Controls Act 2002 (section 8) explicitly exempts:

the communication of information in the ordinary course of scientific research; the making of information generally available to the public; or the communication of information that is generally available to the public

while nevertheless allowing a Ministerial override in exceptional cases. The DTCA contains no protection for ordinary scientific research and education. The Steering Group's proposal is meant to address some of the defects thereby introduced, but clearly the most direct and effective addressing of the defects would be to write a comparable clause into the act rather than try to treat all of the symptoms of illness that the lack of the clause must necessarily introduce. By the latter approach the illness will remain and any failure to see or predict a nasty symptom will only be treated retrospectively, after the damage has been done.

The Chief Scientist's Steering Group claims that part of its mandate is to see that researchers are not disadvantaged in comparison with the United States and the UK. That is an objective that simply cannot be met without adopting equivalent legislation.

Having registered my general objection to the approach of the Steering Group, I will review some of its specific proposals.

The greatest attempt at relief of the DTCB 2015 appears to be the exemption for publication and pre-publication of dual-use goods, distinguishing these from the international "supply" of goods. This will indeed enable some research to progress across many areas which otherwise, under DTCA 2012, would be impossible. It appears that the Steering Group considers this to be relief enough, but massive problems remain. In particular, electronic and other transmissions of new research in dual-use goods which are not directly related to publication or an attempt to publish would remain controlled, and unpermitted communications punishable by prison, even though these are a part of the ordinary course of scientific research. A great deal of existing friendly communications with international research collaborators, potential collaborators, students, etc. will be criminalized. Also included as "supply" are ordinary scientific conferences and meetings, if they neglect to publish proceedings. Invitations to visit and give talks at leading institutions around the world will have to routinely be turned down by researchers in controlled areas, unless they take the opportunity to never return to Australia. [It should be noted that there is a specific exemption for exclusively oral communications; however, it is typical that pdf notes are projected on host equipment, which would be a criminal act of "supply" under the legislation.]

Since our institutions are pushing hard to internationalize our research collaborations and educational activities, the treatment of them as criminal actions when outside the direct control of the Department of Defence will seriously handicap both research and education in dual-use areas. Educational institutions will no longer be able to treat their materials as proprietary and instead be forced to publish them. Pre-publication collaborative research, on the other hand, is always an iffy project, and publications, or even attempted publications, are no sure outcome. If the activities needed to generate good research are controlled, it will not much matter that its end product (publication) is uncontrolled: there won't be anything to publish.

The option to emigrate, if taken, will have to be taken permanently, by the way, without any opportunity to return to visit friends or family, unless the academic is willing to face arrest for the "crime" of having pursued her or his career overseas. Indeed, it would be conceivable that Australia should seek extradition of such notorious criminal academics. It's also clear that proprietary dual-use industrial research, which is hardly ever published, must come under the control and permit regime, meaning that the Steering Group's amendments offer industry no relief at all.

The Steering Group's Guide claims that the Defence and Strategic Goods List (DSGL) is narrowly defined so as to minimize its impact on civilian research. As an example, they point out that restrictions on research on robust computers designed to deal with temperature extremes are limited to those that fall outside the wide bounds of -45C to 85C. But the DSGL in this respect suffers from the same kind of flaws as the approach taken by the Steering Group: it excludes from its onerous restrictions research which its drafters happen to know and think about, but capturing a great deal of potential civilian research that hasn't occurred to them. For an example: fault-tolerant computing is a general concept of wide civilian applicability. It is covered as dual-use in DSGL, but with exclusions of the above type. For a particular example, error detection and correction in "main storage" is excluded from the DSGL restrictions. However, it apparently did not occur to the drafters that many computers have error detection and correction outside of main storage, in particular in components involved in internal and external communications. As the DSGL currently stands, research on such fault-tolerant aspects of computing is regulated, even if that research is effectively the same as research done to improve "main memories".

When I scanned my faculty's (Monash Faculty of IT) postgraduate classes, I found about one-third them touched upon or directly treated research areas covered by DSGL's dual-use list. The DSGL is emphatically not a narrow list impinging upon only a few exotic research areas.

To be sure, the exact scope of the DSGL is unclear. A key example (for me, at any rate) is robotics: robots are explicitly controlled as a dual-use good (at least when coupled with the usual image processing). Since software connected with a controlled dual-use good is automatically controlled, and since any artificial intelligence software may be used in robots with image processing, the DSGL seems to imply that all AI research is controlled. I have, many months ago, asked DECO whether this is correct; I have received no answer. On the face of it, however, DTCA and DTCB are set to eliminate Australia as a serious player in information technology.

Under both the existing and the proposed legislation coverage of the DSGL is subject to the interpretation of the Department of Defence. Since the DSGL is both ambiguous and has an overly broad coverage of dual-use goods, as argued above, the proposed legislation will inevitably provide the Department of Defence the power to choose to enforce, or to not enforce, penalties against researchers whose projects may be interpreted as falling under DSGL controls. This will inevitably result in discouraging research in any such area and will also provide the Department of Defence apparently arbitrary powers to persecute or punish civilian researchers at will or whim.

The reassurance that the Criminal Code Act 1995 would make unlikely a successful prosecution of those who "diligently" follow compliance rules but make some mistake is very little comfort: 1) although the proposed amendments reduce the compliance costs of DTCA 2012, those costs remain very high; 2) the latitude in interpreting DSGL means that an innocent mistake may well be interpreted as an intentional violation of the law; 3) prosecutors in all legal systems around the world have on at least some occasions abused their power and prosecuted people, not to enforce the law, but for political or private purposes that may be served regardless of the outcome of the prosecution.

The Steering Group refers to the DSGL exemption for "basic scientific research" and information that is already in the "public domain", suggesting that in such cases research communications will thereby not be subject to control by the Department of Defence. The DSGL does make these exemptions and also one for patent applications. Neither the UK nor the US found those exemptions to be adequate and expanded the scope of exemptions in their further legislation, as I showed at the beginning. In my view, they have good reasons not to rely upon the DSGL alone. The Steering Group omitted mention that the DSGL restricts the exemption for basic scientific research to research which is not also intended for application. However, the ARC, universities and other funding organizations almost always demand that research be conducted with a view to its application, suggesting that the DSGL exemption will hardly ever come into force. It has also been pointed out that the administrative burden of determining what is and what is not in the public domain across hundreds of research areas by both research organizations seeking to be compliant and by the Department of Defence itself in monitoring compliance will be enormous.

In conclusion:

There is no doubt that some new legislation is needed to deal with "intangible supply" of military technology. It is also appears right that dual-use goods should come under the control of such legislation, since by definition they may be used in military applications. But nowhere has a serious case been made that the same protections for education and academic research that the UK and the US afford themselves should not be made available to Australians and Australian institutions. Without those protections not only will civilian research in dual-use goods suffer from onerous compliance costs, those research and educational areas will inevitably go into significant decline, damaging the wider economy for at least as long as it takes the society as a whole to come to grips with the issue and change the law appropriately. And there will be no guarantee that the damage that accrues in the meantime can be undone.

The proposed amendment alleviates a few of the problems introduced by DTCA 2012. It manifestly fails in its stated goal of putting Australia on an equal footing with its trading partners, the US and the UK. This failure will cause serious and long-lasting damage to Australian education and research, unless it is addressed now.

I think Australia's Chief Scientist does not deserve an F for his
efforts. He should, however, be encouraged to try a little harder and
apparently needs more time to do so.

# De-teching Australia: Australia torpedoes its own future, blowing up science, technology and education

— Kevin B Korb

The Australian government is undermining the future of Australia by attacking science and technology research and education on a massive scale, leading Australia in a unique act of self-immolation. It is not hard to see that the future economic well-being of developed countries is intimately linked to the three key supports of modern economies: science, technology and education. This government is actively attacking all three and is also actively campaigning against all three in the media, especially through its cheerleaders in the Murdoch press.

These are some of the notable attacks on science, technology and education enacted, proposed or supported by the ministers of the Abbott government:

• Attacking the Internet in Australia by cutting the fibre-optic based National Broadband Network project started by the Labor government. Instead of fibre optics, Minister for Communications Malcolm Turnbull advocates the retention of slower, older and more maintenance-intensive copper wire connections to homes and businesses. As iinet likes to advertise, Australia is behind Romania in average Internet access speeds. Turnbull's program will keep Australia well behind the OECD average for the foreseeable future. Neither Turnbull nor Abbott have a clue that the Internet has become a key enabler of current economic growth. Watch this incredible performance by the pair of them, laughing about the Internet being a "video entertainment system". Or, watch Turnbull in this whiteboard "explainer" on how the value of the NBN in 2030 should be assessed based on the values of 2014. These are the current leaders of our government!
• Cutting science research, in particular the government is cutting funding to the Australian Research Council by around $29M per year (about 5%), to CSIRO by$86M (about 6%), to DSTO by $48M (about 10%), and to the Cooperative Research Centre program by$25M (about 14%). There are hints that more cuts are to come. These programs have been the source of much of the innovation in Australia, so their winding down will kill off what was already a weak contributor to the economy.
• Cutting university and school funding. \$30 billion has been cut from school funding, by dropping the "Gonski" reforms that Abbott previously committed to implementing. University funding per student is being cut 20%. As the OECD's Education at a Glance documents year in and year out, public education is central to economic well being; these cuts will lead Australia to the bottom of the OECD not just in education but also in future economic performance.

Many university administrators have been gulled into supporting this by the lure of the deregulation of university fees. While it may be possible for universities to make up the funding cuts by raising fees to students, it is hardly obvious that it will happen, since many students may turn away from accepting life-burdening debts in return for an education. In any case, this will increase inequality of access to education and undermine education's role in driving future economic prosperity.

• Supporting the Defence Trade Controls Act (DTCA) 2012, which will soon criminalize a large swathe of ordinary research and education in medicine, science and technology, all of which have supported economic growth in Australia for many decades.

The law was amended in a minor way in 2012 to enable a "Steering Group" led by Chief Scientist Ian Chubb to review and make recommendations for changes over a two-year period. That is why the legislation is only coming into force in May, 2015. Chubb appears to be a useful idiot for the government: his enlarged opinion of his own ability to effect changes to the law has been widely accepted within academia, with the result that many or most academic leaders have reacted with supreme complacency to the DTCA. As the drop-dead day comes nearer, we can expect more and more academics to realize that they are being turned into criminals. The NTEU has recently launched an educational campaign to inform an academic community that is still mostly asleep.

• Cutting funding for the ABC and SBS. The ABC has been stripped of the Australia Network, which has been handed over to Sky News Australia, partly owned by Murdoch. This is despite the fact that the Australia Network has been a very well received broadcaster to our near neighbors for decades, providing valuable good will for our diplomatic and trading interests. Furthermore, after heavy campaigning by the Murdoch press, both public broadcasters are having their funding cut, with threats continuing of larger cuts in the future. Turnbull claims "efficiency savings" are always possible. Were that true, budgets could always be cut to zero, matching his apparent IQ.

The dramatic budget cuts are explained by Joe Hockey and Tony Abbott as being "necessary" to save Australia from a budget crisis inherited from the Labor government, as well as being dictated by fairness in spreading the burden of this salvation across the community. Although many economists have publicly denounced the claim of Australia being in budgetary crisis as nonsense, it is no surprise that the Australian public have largely seemed to swallow it whole. The Big Lie worked very well for the Nazis, and it is working very well for the Coalition government. After all, the Murdoch press controls most of the print news in Australia and very clearly sets the direction of public debate. Big Lies repeated over and over begin to seem like common knowledge rather than common nonsense.

Abbott claims his government needs no minister for science. He claims to be able to represent the portfolio unassisted. However, his understanding and interests are inimical to science, technology and education and to the long-term interests of Australia. He infamously denounced the scientific consensus on global warming as "absolute crap". He seems to view science as a convenient source of opinions, when scientists happen to agree with him, and otherwise as a nuisance. The long history of science supplying the ideas and means for engineering and technological development from the beginning of western civilization means nothing to him; instead, Abbott and his ministers prefer to attribute that history of civilization to Christianity. Theirs is a view that would have been well received in the Dark Ages.

If anyone is going to lead Australia into a new Dark Age, it is Abbott and his government: the terrorism of ISIS is nothing compared to the terrorism of our own government.

# Australia's Act of Intellectual Terrorism: DTCA 2012

— Kevin B Korb

In October 2012 the Australian parliament passed the Defence Trade Controls Act. The stated purposes of the act are unobjectionable: implementing the prior Australia-United States Defense Trade Cooperation Treaty, simplifying defence-related trade between Australia, the US and the UK, and tightening the regulation of intangible transfers of military goods, reflecting the growth of the internet in communications. Unfortunately, these good intentions have led the Australian government to adopt an extraordinarily broad definition of military goods and to impose an impossibly harsh regulatory regime on activities concerning them, to the point that what is today ordinary academic research into, for example, Bayesian network technology may tomorrow become a criminal activity subject to 10 years imprisonment. It is an act that can legitimately be called intellectual vandalism. Indeed, some academics have already abandoned long-pursued research projects out of fear of the Act being used for retribution, making it a means of intellectual terrorism.

## The Defence and Strategic Goods List

One support for the act is the Defence and Strategic Goods List (DSGL). The DSGL lists goods targeted for regulation that are strictly military and also many goods which could be put to military uses, so-called dual-use goods. These latter include a huge variety of things, including: bacilli and viruses, plant pathogens, metallic alloys, carbon fibres, neural computers, optical computers, vector and other high-performance computers, optical telecommunications, signal processors, fault-tolerant systems,1 image processing, cryptography, and, of most interest to us, robotics. The DSGL explicitly incorporates all software which is designed or modified for the "development, production or use" of the goods. This means that all software that may be used to drive robots are covered by the list and by the Act using the list: all software that can be used for intelligent decision making and analysis, which clearly means all of Bayesian network technology, not to mention all of computational statistics, data mining and artificial intelligence generally.

The Act's intent is to regulate foreign access to new research in military and dual-use goods. While all of the dual-use goods could potentially be used in military applications and controlling such uses is a worthwhile objective, all of them also are used in non-military business, industry and governance, and these civilian uses are vital to the economy and prosperity of the nation. Therefore, a reasonable balance must be struck between supporting research in these areas and controlling access to the research. As the Act stands, it is clear to us that these matters are not in balance.

## Australia Prepares to Eat its Brains

A key feature of the Act is that it requires prior permission to communicate new research to a foreign national in any of the nominated areas. This includes, but is hardly limited to, publishing research in academic journals. As many submissions on the bill to the Senate Committee on Foreign Affairs, Defence and Trade point out, this requirement implies that the Department of Defence (DoD) would need sufficient expertise across all of the domains listed in the DSGL to judge whether or not proposed research would require a permit. Plausibly, this is a level of expertise which the DoD does not have, nor will ever have. But the difficulties with the Act go far beyond the need to hire thousands of experts to make permit judgments upon research and education.

Obtaining prior approval for each research project and, possibly, each research communication would put an end to a very large amount of research activity in Australia, directing researchers, students and subsequent economic activity elsewhere. Permission would be required to publish across a huge range of areas under active research in the university sector. Without a clear opportunity to publish, most academics would choose not to undertake research projects in these areas, meaning that ARC and NHMRC projects would not even begin without prior approval from the Department of Defence. The Act provides no guidance as to how the DoD should make judgments about research which has yet to be conducted. Many ongoing collaborations with overseas institutions would need separate approvals or would cease. Since about half of enrolled postgraduate students are foreign nationals, for the most part without permanent residency, the requirement for prior permission to communicate new research to them would also cripple postgraduate coursework.

A minor point is that there seems to be some unclarity about whether or not foreign students can be taught anything on the DSGL without prior permission. The Chubb Steering Group's (more on them below) report on its 12 April 2013 meeting states that "the Australian export control system only regulates transfers from a person inside Australia to a person outside Australia". However, the Defence Department's Explanatory Memo for the Bill states that communications are regulated "if the supply is from an Australian person to a foreign person regardless of their geographical location" and "the provision occurs in Australia to a foreign person". Re-skimming the Act itself  (96 pages of gripping prose) unfortunately failed to reveal who's right. Still, the considerations immediately below mean this issue is well and truly dominated by other problems.

PhD and Masters theses have always been published by the institutions granting them; in consequence of the Act, either this practice would have to be abandoned, and the contents of theses in the nominated areas suppressed — which would certainly give Australian research a unique voice in the world — or prior approval for publishing as-yet uncreated new research would have to be obtained. Note that this restriction would apply to all postgraduate thesis work in dual-use domains, not just that involving foreign students.

As a crude index of how the Act unaltered will impact the activities of my own organization, the Faculty of IT at Monash University, I surveyed all masters level coursework units (5000 series units, ignoring thesis units) for topics proscribed by the Act (i.e., found in the DSGL). Note that it is an imperative that researchers who teach (which describes myself and almost all of my teaching colleagues at Monash) should incorporate new research into their own teaching. Of necessity, therefore, if a topic matches a dual-use good, it is regulated by the Act. By my count 18 out of 61 classes would come under the provisions of the Act, requiring prior permission for each international student enrolled. (The DoD Explanatory Memorandum makes it clear that individual permission is required — short of Ministerial intervention!) The main areas impacted are: security, software usable for controlling robots, telecommunications technology and high-performance computing. No doubt a similar proportion of our degree by research topics would have to be pre-approved or abandoned. The disruption to Monash FIT’s educational activities will be severe.

## The Strengthened Export Controls Steering Group to the Rescue

Amendments to the Bill were proposed by the Senate Foreign Affairs, Defence and Trade Committee in October 2012 which would appear to be sufficient protection for the ongoing research and educational activities of the tertiary sector. Alternative amendments might be derived from the UK Export Controls Act, which again protect public research and education. The corresponding US International Traffic in Arms Regulations also contain a corresponding exclusion, Section 120.11. The Australian Act contains no such protection (despite the extraordinary gobbledygook produced by the US Ambassador to Australia on the subject; see item 8 on the Committee's submission page). The accompanying Explanatory Memorandum does list some exemptions, relying upon the DSGL. The DSGL exempts technology that is in the public domain, required for patents or is basic scientific research. The Department of Defence reckons that this is sufficient protection for tertiary education and research: "With the exemptions ... Defence anticipates that these controls will apply only to very specialised and high-end research" (Explanatory Memo). There are a few substantial problems with this thinking, however. The administrative burden of deciding what is already public and what is not, covering individual research publications over something like 1/3 of Australia's engineering and IT work, would probably suck up a significant percentage of Australian GDP forever. Actual scientific research, while building upon what is in the public domain lives and grows according to what it adds that is new, and so it will not generally be public domain. However, according to the Defence Explanatory Memo (footnote 16), basic scientific research excludes research "directed towards a specific practical aim or objective." So, presumably university research is in the clear. What perhaps eludes Defence experts is that a very large amount of research at universities does have a practical aim or objective. Indeed, the endless waves of "Excellence of Research in Australia"-like programs that regularly inundate academic life here are always trying to pump out information about the wider impact of research on the community. Academics are constantly being badgered to prove that their research has near-term practical impacts and objectives. I suppose an unintended salutary effect of the Bill could be to discourage academics from focusing too much on the immediate benefits of their work! Be that as it may, probably most university research comes with intended applications, and so is covered by the legislation.

In consequence researchers right now must reckon with the possibility that the communication of their efforts, whether in teaching, supervision or publication, may result in 10 years in prison.

Many parties to the discussions, such as Universities Australia and the National Tertiary Education Union, have noted the disparity in protections offered by the UK and the US compared with that on offer in the DTCA for Australians. The consequence of their raising their concerns has been a suspension of enforcement of the Act for two years and the founding of the Strengthened Export Controls Steering Group, headed by Australia's Chief Scientist Ian Chubb, to investigate and test the consequences of the Act with pilot studies. The Steering Group has roughly equal representation from Defence (and Defence industry) and academia. They are empowered to make recommendations. Some people appear to think this answers all of the concerns raised above about the legislation. But until concrete recommendations are made, and rather more importantly, acted upon by Parliament, the university sector is operating in the dark. We do not know which of our research and pedagogical activities will in the near future be prosecuted as criminal. Given that now simply posting classified information on the internet in the public interest is being trumpeted as "assisting the enemy" (Julian Assange, Edward Snowden), it is not much of a stretch to imagine the publication of research on ordinary, but dual-use, technology soon being called assisting the enemy as well.

Three outcomes seem now to be possible: (1) the law may be revised to accord with the corresponding legislation in the US and the UK; (2) the law may be left as is, but its provisions not enforced with regard to most research of a non-military nature; (3) the law may be left as it is, and its provisions enforced in a wide-ranging way. If the first option is realized, then the research and teaching environment will remain much as it has been, and the Australian nation may get on about its business. If option (3) is realized, a large portion of Australian research will simply stop. The tertiary education sector will be massively disrupted and its international reputation will collapse, outside of fields which would appear to be free of the regulations implied by the Act, such as the Arts. Much of engineering, the physical and medical sciences, and information technology would be finished in Australia. Option (2) implies less immediate impact. However, the continuing possibility and threat that an administration has only to change its mind about enforcement would have a significant chilling effect on many researchers. The choice of research area would have to weigh the opportunity for administrative interference and the ultimate potential for criminal sanctions should a researcher or her or his research rub the DoD or the government of the day in the wrong way. Over the long term, research and education in Australia would be severely crippled.

Bayesian Intelligence finds that the unamended Defence Trade Controls Act 2012:

• Fails to provide the same safeguards for research and educational activity to be found in the corresponding legislation enacted in the UK and the USA

• Will handicap research and tertiary educational activities across a wide range of domains in engineering, information technology, science and medicine

• Is likely to lead to a diversion of world-class researchers, students and projects outside of Australia

The introduction of a two-year transition period in the final Act defers, but leaves unaltered, these bad consequences. In view of these probable deleterious effects, Bayesian Intelligence, as a company dependent upon new research in a dual-use technology, strongly urges that the legislation be amended as soon as possible to incorporate similar protections to those in the corresponding legislation of the UK and the US.

1 CORRECTION: Originally, I had the following parenthesis here: "(including computers with error-detecting memories, which long ago became nearly universal)". However, I have in the meantime noticed that the DSGL has an explicit exclusion for this case, in Note a of 4A003.a on p. 165. My apology for not noticing this in the first place.

# Sally Clark is Wrongly Convicted of Murdering Her Children

— Kevin B Korb

Sally Clark, in an infamous miscarriage of justice, was convicted of murdering her two sons in the UK in 1999 after a prosecution which employed primarily statistical reasoning in a way that has become notorious as the "prosecutor's fallacy". Here I will briefly review the arguments and the statistical reasoning from a Bayesian perspective. I don't propose the details of this analysis (i.e., the exact probabilities) be taken too seriously. They are taken from fairly cursory searches on the Internet and applied in a fairly crude way. Regardless, they are far more serious than anything produced during the trial itself!

Sally Clark was arrested after her second baby died a few months old, apparently of sudden infant death syndrome (SIDS), exactly as her first child had died a year earlier. According to prosecution testimony (by a pediatrician, Sir Roy Meadow), about 1 in 8543 babies die of SIDS. They argued that there is only a probability of $\lgroup \frac{1}{8543} \rgroup^2$ $\approx 1/73000000$ that two such deaths would happen in the same family by chance alone (after controlling for tobacco smoke and a few social factors). According to the prosecution, the woman was guilty beyond a reasonable doubt. The jury returned a guilty verdict, even though there was no substantial evidence of guilt presented beyond this argument.

Let h = Clark is guilty, e1 = the evidence of the first son's death, e2 = the evidence of the second son's death. Note that the latter two are meant to establish the appearance of SIDS deaths. Then the prosecutor's argument was:

1. $P(e1|\neg h) = P(e2|\neg h) = \dfrac{1}{8543}$
2. So, $P(e1 \wedge e2|\neg h) \approx P(e1|\neg h) \times P(e2|\neg h) \approx 1/73000000$
3. So, $P(h|e1 \wedge e2) = 1 - 1/73000000 \approx 1$

There are a lot of problems with this argument. Here I will discuss the two most basic errors, which probably have the most impact and which anyone involved with assessing evidence should be capable of recognizing. First, the combination of the evidence in (2), simply by multiplication, requires the two pieces of evidence to be independent of each other. The general form of such a combination is $P(e1 \wedge e2|\neg h) = P(e1|\neg h) \times P(e2|e1,\neg h)$, which further reduces to (2) only if $P(e2|\neg h) = P(e2|e1,\neg h)$, that is, only if the two items of evidence are independent given innocence. However, risk factors for SIDS are very likely to be common to multiple children within a family, including not the just tobacco smoke and the social factors controlled for, but also poor prenatal care, low birth weights, alcohol consumption and sleeping practices (and, to be sure, physical abuse by parents). In any case, one SIDS death is well known to raise the probability of another in the family; therefore, the combined evidence of two deaths must have a higher probability than their simple multiplication. One study reported a relative risk of recurrence of SIDS of 5 times the background rate, a rate found to be comparable to other recurrent mortality risks in siblings. This yields $P(e1 \wedge e2|\neg h) = P(e1|\neg h) \times P(e2|e1,\neg h) = 1/14.7M$, instead of $1/73M$.

The second failure in the prosecution argument is the complete neglect of prior probabilities. Bayes' rule says:

• $P(h|e1 \wedge e2) = \dfrac{P(e1 \wedge e2|h)P(h)}{P(e1 \wedge e2)}$
• $P(h|e1 \wedge e2) = \dfrac{P(e1 \wedge e2|h)P(h)}{P(e1 \wedge e2|h)P(h) + P(e1 \wedge e2|\neg h)P(\neg h)}$
For simplicity, I will assume that $P(e1 \wedge e2|h) = 1$, i.e., that guilt would surely produce the evidence found. But, so far, the posterior probability of guilt can still be anything at all: we need the prior probability in order nail down the posterior probability. The prosecutor's fallacy blithely assumes instead that P(h|e) = P(e|h). This may arise because conditional probabilities are often read as "if-then" conditional statements, and these are tricky and easily misread as their reversals. (See, for example, Kahneman and Tversky's work on "base rate neglect".)
Rather than ignore the prior here, however, we should estimate it. The question is something like: how often do mothers murder their first two children within their first year of life? We can answer a more general question, namely how often do mothers kill one or more of their children, of any age. Using this, of course, means we will be overestimating the prior probability by some unknown, but likely large, amount, implying that we are only finding an upper bound to the probability of interest. A news report suggests there are about 100 cases a year in the United States, estimated from surveys of prison populations. Since there are about 120 million adult women in the United States, and about half of them have children, that yields 1 in 600000 murdering their children in any given year. The homicide rate in the US is about 4 times higher than that in the UK (judging by this table), so that gives us 1 in 2.4 million. Of course, a mother may murder her children over the course of many years, but she cannot do so in a way that resembles SIDS beyond the child's first year. She might well get caught over the course of a few years, but using the annual figure alone is almost certainly not as big a factor for underestimating the probability of guilt as counting all cases of mothers killing their children works in favor of overestimating that probability. This way of getting a prior probability is admittedly crude, but it is nevertheless far better than that used by the prosecution, namely ignoring the issue of the prior altogether! Using our assumptions above we have enough to work Bayes' theorem:

• $P(h|e1 \wedge e2) = \dfrac{P(e1 \wedge e2|h)P(h)}{P(e1 \wedge e2|h)P(h) + P(e1 \wedge e2|\neg h)P(\neg h)}$
• $P(h|e1 \wedge e2) = \dfrac{1 \times 1/2.4M}{(1 \times 1/2.4M) + (1/14.7M \times (1 - 1/2.4M))} \approx 0.86$
This is a fairly high probability of guilt. However, if we were to routinely incarcerate people with a 14% chance of being innocent, we would be doing a lot of damage to society; "beyond a reasonable doubt" surely means that a higher standard is demanded. Some people (especially, some judges) think that the higher standard means certainty and that therefore probabilistic reasoning has no place in the courts. But ignoring probabilities is hardly the same as achieving certainty: it is simply a direct path to foolish decision making, such as that exemplified in the case of Sally Clark. Her case deserved a more serious treatment, including treatment of the relevant probabilistic facts. What actually happened was that an appeals court, despite being apprised of the probabilistic errors committed during the first trial, refused to overturn her conviction. Sally Clark was eventually found innocent after it came out that the prosecution had suppressed evidence showing that her second son died of natural causes. She subsequently died of alcohol poisoning.

Contrary to a widespread view in the legal community that statistical, and especially Bayesian, reasoning should not be considered in court proceedings, it is crucial in many cases that such reasoning be used — but, of course, used correctly. Many people find correct statistical reasoning difficult, but there are ways and means of improving it, some of which we will discuss in this blog. Meanwhile, if you are interested in Bayes and the Law, you might want to take a look at Norman Fenton's project.

† I thank Professor Philip Dawid for bringing this case to my attention and for helpful comments on it. His testimony to the appellate court on this case can be read here.

‡ This is so despite the widespread counselling of parents to the contrary and claims by various studies indicating no increased risk to siblings of SIDS victims! These studies all take pains to control for the kinds of risk factors I've identified above. What is relevant here is the increased risk of SIDS regardless of the cause (excepting those that Meadows actually did control for), and so the risk without controlling for alcohol, etc. is what is of interest. That risk, of course, is increased by the occurrence of a SIDS case in the family (observing an effect of a cause raises the probability of another effect being present!). The contrary claim, by the way, is probably put to parents as a means of reassurance; however, it could easily lead to complacency and to a neglect to deal with the risk factors in place in a family — in other words, made without qualification, the advice is both wrong and irresponsible.