Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome \(Y\in\{0,1\}\) is inferred from an observed history of market-implied probabilities and traded volumes. We introduce a mechanism-agnostic observation model in log-odds space in which price increments conditional on volume arise from a latent mixture of trader types. The resulting likelihood class encompasses informed and uninformed trading, heavy-tailed microstructure noise, and adversarial or manipulative flow, while requiring only price and volume as observables. Within this framework we define posterior uncertainty quantification for \(Y\), provide identifiability and well-posedness criteria in terms of Kullback--Leibler separation between outcome-conditional increment laws, and derive posterior concentration statements and finite-sample error bounds under general regularity assumptions. We further study stability of posterior odds to perturbations of the observed price--volume path and define realized and expected information gain via the posterior-vs-prior KL divergence and mutual information. The inverse-problem formulation yields explicit diagnostics for regimes in which market histories are informative and stable versus regimes in which inference is ill-posed due to type-composition confounding or outcome--nuisance symmetries. Extensive experiments on synthetic data validate our theoretical predictions regarding posterior concentration rates and identifiability thresholds.

A border patrol agent scans the face of a driver in Minneapolis on 13 January 2026. A border patrol agent scans the face of a driver in Minneapolis on 13 January 2026. Immigration enforcement agents across the US are increasingly relying on a new smartphone app with facial recognition technology. The app is named Mobile Fortify. Simply pointing a phone's camera at their intended target and scanning the person's face allows Mobile Fortify to pull data on an individual from multiple federal and state databases, some of which federal courts have deemed too inaccurate for arrest warrants.

The government is consulting on a social media ban for under-16s, which would have a big impact on Meta's Instagram platform. The government is consulting on a social media ban for under-16s, which would have a big impact on Meta's Instagram platform. Campaigners decry ties with'Trump-supporting' tech firms after funding is accepted to develop state AI systems Ministers have accepted $1m (£728,000) from Meta, the US tech and social media company, to build AI systems for defence, national security and transport, sparking warnings about the UK government's "alarmingly close relationship with Trump-supporting US tech giants". The money from Mark Zuckerberg's company will be used to pay experts to "develop cutting-edge AI solutions to support national security and defence teams", the Department for Science, Innovation and Technology (DSIT) announced on Tuesday. The money will pay for four British AI experts, coordinated by the government-funded Alan Turing Institute, to "play a pivotal role in rewiring our healthcare, police, transport systems and more", said Ian Murray, the minister for data and digital government.

A technician works at an Amazon Web Services AI datacenter in New Carlisle, Indiana, on 2 October 2025. A technician works at an Amazon Web Services AI datacenter in New Carlisle, Indiana, on 2 October 2025. At Davos, tech CEOs laid out their vision for AI's world domination Tech chiefs waxed poetic about AI to delegates at Davos. Plus, the'human' drama of AI startups and why Tesla is thriving in Texas This week's edition is a team effort: my colleague Heather Stewart reports on the plans for AI's world domination at Davos; I examine how huge investments have followed AI companies with little to their names but drama and dreams; and Nick Robins-Early spotlights how lax regulation of autonomous driving in Texas allowed Tesla to thrive. When they weren't discussing Donald Trump, delegates at the World Economic Forum last week were being dazzled by the prospects for artificial intelligence.

'Wake up to the risks of AI, they are almost here,' Anthropic boss warns Dario Amodei questions if human systems are ready to handle the'almost unimaginable power' that is'potentially imminent' Humanity is entering a phase of artificial intelligence development that will "test who we are as a species", the boss of the AI startup Anthropic has said, arguing that the world needs to "wake up" to the risks. Dario Amodei, a co-founder and the chief executive of the company behind the hit chatbot Claude, voiced his fears in a 19,000-word essay titled "The adolescence of technology". Describing the arrival of highly powerful AI systems as potentially imminent, he wrote: "I believe we are entering a rite of passage, both turbulent and inevitable, which will test who we are as a species." Amodei added: "Humanity is about to be handed almost unimaginable power, and it is deeply unclear whether our social, political, and technological systems possess the maturity to wield it." The tech entrepreneur, whose company is reportedly worth $350bn (£255bn), said his essay was an attempt to "jolt people awake" because the world needed to "wake up" to the need for action on AI safety.

Russia has been exploiting Ukraine's harshest winter in years to pummel energy infrastructure across the country. Repeated strikes have crippled the power supply to major Ukrainian cities, leaving millions without heating or light as temperatures hover around -15C (5F) for the third week in a row. Electrical companies carry out round-the-clock repairs - only for their work to be undone at night, when Russian drone and missiles again damage power stations. In Kyiv, people were initially able to keep the cold at bay by using electric heaters or wrapping up warm. But the freezing temperatures have lasted weeks now, with no end in sight.

'Minecraft was my way in' The Traitors 2026 finalist Jade. 'Minecraft was my way in' The Traitors 2026 finalist Jade. 'I didn't have anything to prove': what Traitors finalist Jade Scott learned about survival from video games T he latest series of The Traitors, which ended last week on a nail-biting finale, featured some of the usual characters - from guileless extroverts to wannabe Columbos endlessly observing fellow contestants for the slightest flicker of treachery. But one faithful stood out for her quiet determination, despite a ceaseless onslaught of suspicion and accusation. That person was Jade Scott, and I wasn't at all surprised when, quite early on in the series, she revealed she was a keen gamer.

Much of modern warfare is shaped by for-profit, commercial AI tech firms. This gives them an unprecedented, non-state influence over geopolitical conflict. X to block Grok AI's undressing feature

Erosion victim warns'trauma tourists' to stay away A woman who lost her home at the start of the year due to coastal erosion has warned visitors to stay away and don't gloat. Shelley Cowlin, whose home of 48 years in Thorpeness, Suffolk, was demolished in January, said tourists turning up to witness other people's suffering and even steal items from their gardens were sick. Now living in a holiday let, which she said did not feel like home, the 89-year-old called on so-called trauma tourists to leave villagers in peace. We don't want people relishing in glee at the tragedy of other people, she said. Following the demolition, Cowlin said there had been incidents of people claiming they were her gardener, or even her grandchildren, and pinching things.

Researchers are urging beachgoers to report the endangered, tagged sea snails. Breakthroughs, discoveries, and DIY tips sent six days a week. The black abalone mollusk () is a delicacy in many regions of the world, with fancy restaurant diners doling out as much as $40 per 6 to 8 ounce serving . Although the sea snails are often grown in oyster farms, they are now considered critically endangered due to overdemand and black market harvesting. But while a woman's recent abalone discovery along a beach in Australia is attracting worldwide attention, it's not due to any illegal activity or a lucrative payout.