Ritzy Bay Area town torn apart after teacher's daughter, 16, was behind wheel when four friends died in high-speed crash... then she posted a TikTok video that poured fuel on the flames Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Nancy Guthrie sheriff's appalling past revealed: Beat handcuffed suspect so badly he needed intensive care, used VILE language about woman and lied in sworn statement Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal In honour of the Queen's (purple!) reign: Kate mirrors late monarch's colourful wardrobe and wears her pearl earrings and necklace US troops board second tanker as Iran is accused of breaking ceasefire'numerous times' How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger The video game where you play as JESUS: Open-world simulator lets you'follow the path' of the Messiah as he is baptized, perform miracles, fights the Devil and gets CRUCIFIED READ MORE: Rare marble artefact discovered in the'cradle of Christianity' While fans eagerly await the release of Grand Theft Auto 6, one Polish game studio has unveiled a rather unorthodox alternative. The video game, titled'I Am Jesus Christ' allows players to'walk in the footsteps of Jesus' in an immersive first-person retelling of the gospel.

'Lethal cyber-attacks are thankfully rare. But a new AI release could change that.' 'Lethal cyber-attacks are thankfully rare. But a new AI release could change that.' Anthropic's new AI tool has implications for us all - whether we can use it or not Claude Mythos's apparent superhuman hacking abilities are alarming experts as the Trump administration remains blinded by hostility I n June 2024, a cyber-attack on a pathology services company caused chaos across London's hospitals. More than 10,000 appointments were cancelled. Blood shortages followed and delays to blood tests led to a patient's death . Lethal cyber-attacks like this are thankfully rare.

Time-series analysis is often affected by missing data, a common problem across several fields, including healthcare and environmental monitoring. Multiple Imputation by Chained Equations (MICE) has been prominent for imputing missing values through "fully conditional specification". We extend MICE using the Bayesian framework (tBayes-MICE), utilising Bayesian inference to impute missing values via Markov Chain Monte Carlo (MCMC) sampling to account for uncertainty in MICE model parameters and imputed values. We also include temporally informed initialisation and time-lagged features in the model to respect the sequential nature of time-series data. We evaluate the tBayes-MICE method using two real-world datasets (AirQuality and PhysioNet), and using both the Random Walk Metropolis (RWM) and the Metropolis-Adjusted Langevin Algorithm (MALA) samplers. Our results demonstrate that tBayes-MICE reduces imputation errors relative to the baseline methods over all variables and accounts for uncertainty in the imputation process, thereby providing a more accurate measure of imputation error. We also found that MALA mixed better than RWM across most variables, achieving comparable accuracy while providing more consistent posterior exploration. Overall, these findings suggest that the tBayes-MICE framework represents a practical and efficient approach to time-series imputation, balancing increased accuracy with meaningful quantification of uncertainty in various environmental and clinical settings.

Machine learning competitions (MLCs) play a pivotal role in advancing artificial intelligence (AI) by fostering innovation, skill development, and practical problem-solving. This study provides a comprehensive analysis of major competition platforms such as Kaggle and Zindi, examining their workflows, evaluation methodologies, and reward structures. It further assesses competition quality, participant expertise, and global reach, with particular attention to demographic trends among top-performing competitors. By exploring the motivations of competition hosts, this paper underscores the significant role of MLCs in shaping AI development, promoting collaboration, and driving impactful technological progress. Furthermore, by combining literature synthesis with platform-level data analysis and practitioner insights a comprehensive understanding of the MLC ecosystem is provided. Moreover, the paper demonstrates that MLCs function at the intersection of academic research and industrial application, fostering the exchange of knowledge, data, and practical methodologies across domains. Their strong ties to open-source communities further promote collaboration, reproducibility, and continuous innovation within the broader ML ecosystem. By shaping research priorities, informing industry standards, and enabling large-scale crowdsourced problem-solving, these competitions play a key role in the ongoing evolution of AI. The study provides insights relevant to researchers, practitioners, and competition organizers, and includes an examination of the future trajectory and sustained influence of MLCs on AI development.

New Jersey man's chilling'cancer map' fuels fears of poisoned neighborhood with 41 cases and counting Three stocks are high as a kite after Trump's wild executive order as investors rush to cash in New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Papa John's under fire for an outrageous message now printed on all pizza boxes Iran vows to put'new cards on the battlefield' after Trump breaks ceasefire as Vance travels to Pakistan for peace talks before deadline ends TODAY NASA's return of humans to the Moon in 2028 faces alarming setback California coffee farmers nearly escaped death before'tragic accident' as autopsy reveals disturbing new details How to lose weight when perimenopause sabotages your metabolism: I'm a PT but when I hit 46, I piled on the pounds overnight. Australia has spoken: Report reveals what everyone is thinking about Prince Harry and Meghan Markle's Australia tour Humiliating moment runner celebrates winning marathon... only to be pipped at the line by rival in brutal finish How prophet of extreme Mormon cult who had 20 wives - some aged just 10 - is now spreading evil from prison, as woman who bravely exposed him reveals new threat Netflix doc missed and'sister brides' still under his thrall Even Cameron Diaz admits she's a dirty mess. I'll get hate for saying it, but we're all thinking the same thing about THAT wrinkled forehead: CAROLINE BULLOCK Two high school sweethearts survived the Columbine High School massacre. Months later, they were gunned down in a Subway on Valentine's Day in a crime that remains unsolved AI-pocalypse: Anthropic sparks fears after developing a bot that's'too dangerous to release to the public' Anthropic has sparked fears after revealing that it has developed an AI bot deemed too dangerous to release to the public.

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned blockwise dependence, with distinct patterns within and across blocks. In this paper, we introduce a new class of time series Gaussian chain graph models that represent contemporaneous and lagged causal relations via directed edges across blocks, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation induces a cross-frequency shared group sparse plus group low-rank decomposition of the inverse spectral density matrices, which we exploit to establish identifiability of the time series chain graph structure. Building on this, we then propose a three-stage learning procedure for estimating the undirected and directed edge sets, which involves optimizing a regularized Whittle likelihood with a group lasso penalty to encourage group sparsity and a novel tensor-unfolding nuclear norm penalty to enforce group low-rank structure. We investigate the asymptotic properties of the proposed method, ensuring its consistency for exact recovery of the chain graph structure. The superior empirical performance of the proposed method is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.

Bayesian filtering and smoothing for high-dimensional nonlinear dynamical systems are fundamental yet challenging problems in many areas of science and engineering. In this work, we propose AFSF, a unified amortized framework for filtering and smoothing with conditional normalizing flows. The core idea is to encode each observation history into a fixed-dimensional summary statistic and use this shared representation to learn both a forward flow for the filtering distribution and a backward flow for the backward transition kernel. Specifically, a recurrent encoder maps each observation history to a fixed-dimensional summary statistic whose dimension does not depend on the length of the time series. Conditioned on this shared summary statistic, the forward flow approximates the filtering distribution, while the backward flow approximates the backward transition kernel. The smoothing distribution over an entire trajectory is then recovered by combining the terminal filtering distribution with the learned backward flow through the standard backward recursion. By learning the underlying temporal evolution structure, AFSF also supports extrapolation beyond the training horizon. Moreover, by coupling the two flows through shared summary statistics, AFSF induces an implicit regularization across latent state trajectories and improves trajectory-level smoothing. In addition, we develop a flow-based particle filtering variant that provides an alternative filtering procedure and enables ESS-based diagnostics when explicit model factors are available. Numerical experiments demonstrate that AFSF provides accurate approximations of both filtering distributions and smoothing paths.

Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a sufficient basis for a conclusion. Across jurisdictions, current standards and practice manuals acknowledge such extensions, while the statistical design of sequential audit procedures has not been fully explored. This study formulates audit sampling with additional, sequentially collected items as a sequential testing problem for a finite population under sampling without replacement. We define null and alternative hypotheses in terms of a tolerable deviation rate, specify stopping and decision rules, and formulate exact sequential boundary conditions in terms of finite-population error probabilities. For practical implementation, we calibrate those boundaries by Monte Carlo simulation at least-favorable deviation rates. The exact design yields ex ante control of decision error probabilities, and the simulation-based implementation approximates that design while allowing the computation of expected stopping times. The framework is most naturally suited to attribute auditing and deviation-rate auditing, especially tests of controls, and it can be extended to one-sided, two-stage, and truncated designs.

I don't see images in my head. Can training give me a mind's eye? Training programmes for people with aphantasia - the inability to create mental images - are challenging neuroscientists' understanding of how we create thoughts What do you see when you try to picture an apple? Last December, I closed my eyes and tried to visualise a potoo. This tropical bird has a "round, kind of pill-shaped head", my mental imagery coach described to me, and is covered with brown feathers. Its cartoonishly large mouth opens like a gaping smile to reveal a pink, fleshy colour, and its large irises can make its eyes seem entirely black.

He told Mission Control that they saw'an island of terrain completely surrounded by darkness.' 'Up to the north, there is a very nice double crater. It looks like a snowman just sitting there,' he continued. 'On the southern edge, there is a hole.