Developments in the Gulf since the beginning of this year have raised fundamental questions about the security of the region in general and Qatar in particular. How can Qatar and other Gulf Cooperation Council (GCC) states become effective, independent military powers that do not rely on external security guarantees to ensure their safety? The question for Qatar is how it can build, over the next five years, a national defence capability that would enable it to protect the state and its vital interests even in the absence of Gulf or regional support, or if the United States provides only limited assistance. The aim is to explore whether Qatar can achieve what might be described as defence autonomy, rather than isolation. In other words, Qatar should remain open to alliances and partnerships without making its security dependent on the decisions of another state.

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Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty. Learning a separate flow for every parameter configuration quickly becomes intractable, since the number of joint settings grows exponentially with the number of parameters. We introduce Factorizable Normalizing Flows (FNFs), which represent the parameter-dependent density as a fixed, high-fidelity flow for a reference configuration composed with a learnable transformation that is polynomial in the parameters and factorized over them. This structure has a practical consequence: each parameter's effect is learned in isolation, from samples in which that parameter alone is varied. The combined response of many parameters is then recovered by summation at inference, without ever sampling their combinatorially large joint space. On a controlled problem with two interpretable deformations applied jointly to the data, the learned transformation reproduces the true deformations and matches the optimal likelihood, while optional interaction terms capture residual correlations when several parameters vary strongly at once. The resulting model is interpretable, scales linearly with the number of parameters, and keeps the likelihood tractable. This provides a general tool for any inference workflow requiring continuous density morphing, and directly enables the next generation of unbinned likelihood fits in high energy physics.

Modern multivariate regression problems involve several related outcomes whose regression effects are not only nonlinear, heterogeneous, and outcome-specific, but also where the residual dependence among outcomes is scientifically meaningful. Existing multivariate Bayesian tree-based methods typically address only part of this problem: some impose substantial sharing of tree architecture across outcomes, which is overly restrictive when responses depend on distinct predictors or effect modifiers, while others accommodate residual dependence but retain simpler mean structures. This paper develops multiVCBART, a multivariate varying-coefficient Bayesian additive regression tree framework that jointly models flexible outcome-specific coefficient surfaces and a sparse residual precision matrix. Each entry of the coefficient matrix $B(x)$ is represented by an independent BART ensemble, allowing predictor effects to vary nonlinearly with modifiers $x$ across outcomes, while a Graphical Horseshoe prior on the precision matrix $Ω$ captures parsimonious residual conditional dependence. To permit efficient computation, we introduce a sampler that reduces the multivariate Gaussian likelihood to a sequence of scalar pseudo-response updates, decoupling the tree backfitting from the Graphical Horseshoe step. Theoretically, we establish the first posterior contraction rates for a multivariate BART model with jointly estimated residual dependence, proving near-minimax adaptation to underlying smoothness and structural sparsity. Empirically, multiVCBART outperforms existing multivariate tree models and Bayesian SUR competitors on sparse, high-dimensional datasets. Finally, in a re-analysis of the Genomics of Drug Sensitivity in Cancer dataset, our method identifies distinct biomarker signals and recovers a coherent residual pharmacologic network.

We propose doubly robust adaptive conformal inference (DR-ACI), which constructs prediction intervals for doubly robust pseudo-outcomes under temporal dependence. Calibration targets the pseudo-outcome ψDRt; under estimator consistency, this yields asymptotically conservative CATE containment (Corollary 6). Temporal block cross-fitting preserves switch-coefficient mixing bounds and the DML product-bias rate up to an explicit coupling remainder.

We study linear TD(0) under Markovian sampling, where data are generated along a single trajectory. We provide high-probability guarantees for a plain unprojected TD(0) algorithm with Polyak-Ruppert (PR) averaging, using a single stepsize schedule $η_t \propto \frac{1}{τ_{\mathrm{mix}}\log(t)\sqrt{t}}$ that depends on the mixing time but requires no prior knowledge of the curvature parameter $ω$. Our first result shows that such a choice of the stepsize guarantees that the TD(0) iterates are automatically and uniformly bounded with high probability, without projections and without any stability argument based on $ω$. Building on this result, we establish a simultaneous high-probability convergence guarantee for the PR average: the same stepsize yields both a robust curvature-free $\widetilde{\mathcal{O}}\!\left(\frac{τ_{\mathrm{mix}}}{\sqrt{T}}\right)$ rate and a fast curvature-dependent $\widetilde{\mathcal{O}}\!\left(\frac{τ_{\mathrm{mix}}^2}{ωT}\right)$rate, with the bound taking the minimum of the two. The core technical ingredient is a Poisson-equation toolkit for geometrically mixing Markov chains, which decomposes Markov noise into a martingale term plus a controlled remainder and enables a new self-bounding inductive argument for pathwise stability.

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these, τ-leaping samplers have become particularly popular due to their theoretical and empirical success. However, existing theoretical analyses of τ-leaping often rely on somewhat restrictive and difficult-to-verify regularity assumptions, and their convergence bounds contain quadratic dependence on the vocabulary size. In this work, we introduce a new analytical approach for discrete diffusion models that removes the need for such assumptions. For the standard τ-leaping method, we establish convergence guarantees in KL divergence that scale linearly with vocabulary size, improving upon prior results with quadratic dependence. Our approach is also more broadly applicable: it provides the first convergence guarantees for other widely used samplers, including the Euler method and Tweedie τ-leaping. Central to our approach is a novel technique based on differential inequalities, offering a more flexible alternative to the traditional Girsanov change-of-measure methods. This technique may also be of independent interest for the analysis of other stochastic processes.

Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.

We study the adversarial Stochastic Shortest Path (SSP) problem with sparse costs under full-information feedback. In the known transition setting, existing bounds based on Online Mirror Descent (OMD) with negative-entropy regularization scale with?