Yuji Nakatsukasa
Math. Comp. 89 (2020), 1843-1866.
Abstract, references and article information

Mahbub Alam and Anish Ghosh
Trans. Amer. Math. Soc. 373 (2020), 3357-3374.
Abstract, references and article information

Robert Grizzard and Jeffrey D. Vaaler
Trans. Amer. Math. Soc. 373 (2020), 3235-3259.
Abstract, references and article information

Kamen G. Ivanov and Pencho Petrushev
Trans. Amer. Math. Soc. 373 (2020), 3117-3176.
Abstract, references and article information

V. M. Radchenko and N. O. Stefans’ka
Theor. Probability and Math. Statist. 99 (2020), 229-238.
Abstract, references and article information

S. V. Bodnarchuk and O. M. Kulyk
Theor. Probability and Math. Statist. 99 (2020), 53-65.
Abstract, references and article information

Patrick L. Combettes, Christian L. Müller.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 207--238.

Abstract:
We introduce a flexible optimization model for maximum likelihood-type estimation (M-estimation) that encompasses and generalizes a large class of existing statistical models, including Huber’s concomitant M-estimator, Owen’s Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions, a construction that extends a convex function to a jointly convex one in terms of an additional scale variable. These nonsmooth functions are shown to be amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. We derive novel proximity operators for several perspective functions of interest via a geometrical approach based on duality. We then devise a new proximal splitting algorithm to solve the proposed M-estimation problem and establish the convergence of both the scale and regression iterates it produces to a solution. Numerical experiments on synthetic and real-world data illustrate the broad applicability of the proposed framework.

The horseshoe prior is frequently employed in Bayesian analysis of high-dimensional models, and has been shown to achieve minimax optimal risk properties when the truth is sparse. While optimization-based algorithms for the extremely popular Lasso and elastic net procedures can scale to dimension in the hundreds of thousands, algorithms for the horseshoe that use Markov chain Monte Carlo (MCMC) for computation are limited to problems an order of magnitude smaller. This is due to high computational cost per step and growth of the variance of time-averaging estimators as a function of dimension. We propose two new MCMC algorithms for computation in these models that have significantly improved performance compared to existing alternatives. One of the algorithms also approximates an expensive matrix product to give orders of magnitude speedup in high-dimensional applications. We prove guarantees for the accuracy of the approximate algorithm, and show that gradually decreasing the approximation error as the chain extends results in an exact algorithm. The scalability of the algorithm is illustrated in simulations with problem size as large as $N=5,000$ observations and $p=50,000$ predictors, and an application to a genome-wide association study with $N=2,267$ and $p=98,385$. The empirical results also show that the new algorithm yields estimates with lower mean squared error, intervals with better coverage, and elucidates features of the posterior that were often missed by previous algorithms in high dimensions, including bimodality of posterior marginals indicating uncertainty about which covariates belong in the model.

Andreas Anastasiou, Robert E. Gaunt.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 136--149.

Abstract:
We use the delta method and Stein’s method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic multivariate normal distribution. Our bounds apply in situations in which the MLE can be written as a function of a sum of i.i.d. $t$-dimensional random vectors. We apply our general bound to establish a bound for the multivariate normal approximation of the MLE of the normal distribution with unknown mean and variance.

George Karabatsos, Fabrizio Leisen.

Source: Statistics Surveys, Volume 12, 66--104.

Abstract:
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for describing the complexity of these datasets. These models often exhibit a likelihood function which is intractable due to the large sample size, high number of parameters, or functional complexity. Approximate Bayesian Computational (ABC) methods provides likelihood-free methods for performing statistical inferences with Bayesian models defined by intractable likelihood functions. The vastity of the literature on ABC methods created a need to review and relate all ABC approaches so that scientists can more readily understand and apply them for their own work. This article provides a unifying review, general representation, and classification of all ABC methods from the view of approximate likelihood theory. This clarifies how ABC methods can be characterized, related, combined, improved, and applied for future research. Possible future research in ABC is then outlined.

Aryeh Kontorovich, Iosif Pinelis.

Source: The Annals of Statistics, Volume 47, Number 5, 2822--2854.

Abstract:
We provide an exact nonasymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-approximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized “voting” procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form $c_{infty}/sqrt{ u}$ as $ u oinfty$, where $c_{infty}=0.16997dots$ is a universal constant, $ u=m/d$, $m$ is the size of the training sample and $d$ is the Vapnik–Chervonenkis dimension of the hypothesis class. It is shown that the differences between these asymptotic and nonasymptotic bounds, as well as the differences between these two bounds and the maximum EER of any learning algorithms that minimize the empirical risk, are asymptotically negligible, and all these differences are due to ties in the mentioned “voting” procedures. A few easy to compute nonasymptotic lower bounds on the minimax EER are also obtained, which are shown to be close to the exact asymptotic lower bound $c_{infty}/sqrt{ u}$ even for rather small values of the ratio $ u=m/d$. As an application of these results, we substantially improve existing lower bounds on the tail probability of the excess risk. Among the tools used are Bayes estimation and apparently new identities and inequalities for binomial distributions.

Carolyn M. Rutter, Jonathan Ozik, Maria DeYoreo, Nicholson Collier.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2189--2212.

Abstract:
Microsimulation models (MSMs) are used to inform policy by predicting population-level outcomes under different scenarios. MSMs simulate individual-level event histories that mark the disease process (such as the development of cancer) and the effect of policy actions (such as screening) on these events. MSMs often have many unknown parameters; calibration is the process of searching the parameter space to select parameters that result in accurate MSM prediction of a wide range of targets. We develop Incremental Mixture Approximate Bayesian Computation (IMABC) for MSM calibration which results in a simulated sample from the posterior distribution of model parameters given calibration targets. IMABC begins with a rejection-based ABC step, drawing a sample of points from the prior distribution of model parameters and accepting points that result in simulated targets that are near observed targets. Next, the sample is iteratively updated by drawing additional points from a mixture of multivariate normal distributions and accepting points that result in accurate predictions. Posterior estimates are obtained by weighting the final set of accepted points to account for the adaptive sampling scheme. We demonstrate IMABC by calibrating CRC-SPIN 2.0, an updated version of a MSM for colorectal cancer (CRC) that has been used to inform national CRC screening guidelines.

Jeffrey Regier, Andrew C. Miller, David Schlegel, Ryan P. Adams, Jon D. McAuliffe, Prabhat.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1884--1926.

Abstract:
We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.

Nicolas Privault, Grzegorz Serafin.

Source: Bernoulli, Volume 26, Number 1, 587--615.

Abstract:
We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and weighted $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraph counts in the Erdős–Rényi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering recent results obtained for triangles and improving other bounds in the Wasserstein distance.

Michael V. Boutsikas, Eutichia Vaggelatou

Source: Bernoulli, Volume 16, Number 2, 301--330.

Abstract:
Let X 1 , X 2 , …, X n be a sequence of independent or locally dependent random variables taking values in ℤ + . In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the distribution of the sum ∑ i =1 n X i and an appropriate Poisson or compound Poisson distribution. These bounds include a factor which depends on the smoothness of the approximating Poisson or compound Poisson distribution. This “smoothness factor” is of order O( σ −2 ), according to a heuristic argument, where σ 2 denotes the variance of the approximating distribution. In this way, we offer sharp error estimates for a large range of values of the parameters. Finally, specific examples concerning appearances of rare runs in sequences of Bernoulli trials are presented by way of illustration.

Jeong Eun Lee, Geoff K. Nicholls, Robin J. Ryder.

Source: Bayesian Analysis, Volume 14, Number 4, 1245--1269.

Abstract:
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets, including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible set for an approximate posterior based on some approximate prior and likelihood. We estimate the realised posterior coverage achieved by the approximate credible set. This is the coverage of the unknown “true” parameter if the data are a realisation of the user’s ideal observation model conditioned on the parameter, and the parameter is a draw from the user’s ideal prior. In one approach we estimate the posterior coverage at the data by making a semi-parametric logistic regression of binary coverage outcomes on simulated data against summary statistics evaluated on simulated data. In another we use Importance Sampling from the approximate posterior, windowing simulated data to fall close to the observed data. We illustrate our methods on four examples.

Julyan Arbel, Pierpaolo De Blasi, Igor Prünster.

Source: Bayesian Analysis, Volume 14, Number 3, 753--771.

Abstract:
In this paper we consider approximations to the popular Pitman–Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the approximation error in total variation distance. We derive the asymptotic distribution of the random truncation point as the approximation error $epsilon$ goes to zero in terms of a polynomially tilted positive stable random variable. The practical usefulness and effectiveness of this theoretical result is demonstrated by devising a sampling algorithm to approximate functionals of the $epsilon$ -version of the Pitman–Yor process.

Marko Järvenpää, Michael U. Gutmann, Arijus Pleska, Aki Vehtari, Pekka Marttinen.

Source: Bayesian Analysis, Volume 14, Number 2, 595--622.

Abstract:
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.

Andreas Buja, Arun Kumar Kuchibhotla, Richard Berk, Edward George, Eric Tchetgen Tchetgen, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 606--620.

Abstract:
We respond to the discussants of our articles emphasizing the importance of inference under misspecification in the context of the reproducibility/replicability crisis. Along the way, we discuss the roles of diagnostics and model building in regression as well as connections between our well-specification framework and semiparametric theory.

Dalia Ghanem, Todd A. Kuffner.

Source: Statistical Science, Volume 34, Number 4, 604--605.

David Whitney, Ali Shojaie, Marco Carone.

Source: Statistical Science, Volume 34, Number 4, 591--598.

Anthony C. Davison, Erwan Koch, Jonathan Koh.

Source: Statistical Science, Volume 34, Number 4, 584--590.

Abstract:
This discussion focuses on areas of disagreement with the papers, particularly the target of inference and the case for using the robust ‘sandwich’ variance estimator in the presence of moderate mis-specification. We also suggest that existing procedures may be appreciably more powerful for detecting mis-specification than the authors’ RAV statistic, and comment on the use of the pairs bootstrap in balanced situations.

Roderick J. Little.

Source: Statistical Science, Volume 34, Number 4, 580--583.

Dag Tjøstheim.

Source: Statistical Science, Volume 34, Number 4, 575--579.

Nikki L. B. Freeman, Xiaotong Jiang, Owen E. Leete, Daniel J. Luckett, Teeranan Pokaprakarn, Michael R. Kosorok.

Source: Statistical Science, Volume 34, Number 4, 572--574.

Jerald F. Lawless.

Source: Statistical Science, Volume 34, Number 4, 569--571.

Abstract:
I comment on the papers Models as Approximations I and II, by A. Buja, R. Berk, L. Brown, E. George, E. Pitkin, M. Traskin, L. Zhao and K. Zhang.

Sara van de Geer.

Source: Statistical Science, Volume 34, Number 4, 566--568.

Abstract:
We discuss the papers “Models as Approximations” I & II, by A. Buja, R. Berk, L. Brown, E. George, E. Pitkin, M. Traskin, L. Zao and K. Zhang (Part I) and A. Buja, L. Brown, A. K. Kuchibhota, R. Berk, E. George and L. Zhao (Part II). We present a summary with some details for the generalized linear model.

Andreas Buja, Lawrence Brown, Arun Kumar Kuchibhotla, Richard Berk, Edward George, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 545--565.

Abstract:
We develop a model-free theory of general types of parametric regression for i.i.d. observations. The theory replaces the parameters of parametric models with statistical functionals, to be called “regression functionals,” defined on large nonparametric classes of joint ${x extrm{-}y}$ distributions, without assuming a correct model. Parametric models are reduced to heuristics to suggest plausible objective functions. An example of a regression functional is the vector of slopes of linear equations fitted by OLS to largely arbitrary ${x extrm{-}y}$ distributions, without assuming a linear model (see Part I). More generally, regression functionals can be defined by minimizing objective functions, solving estimating equations, or with ad hoc constructions. In this framework, it is possible to achieve the following: (1) define a notion of “well-specification” for regression functionals that replaces the notion of correct specification of models, (2) propose a well-specification diagnostic for regression functionals based on reweighting distributions and data, (3) decompose sampling variability of regression functionals into two sources, one due to the conditional response distribution and another due to the regressor distribution interacting with misspecification, both of order $N^{-1/2}$, (4) exhibit plug-in/sandwich estimators of standard error as limit cases of ${x extrm{-}y}$ bootstrap estimators, and (5) provide theoretical heuristics to indicate that ${x extrm{-}y}$ bootstrap standard errors may generally be preferred over sandwich estimators.

Andreas Buja, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 523--544.

Abstract:
In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x extrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x extrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

To view more press releases, please visit http://www.snl.com/irweblinkx/news.aspx?iid=1024452.

Previous studies examining developmental outcomes associated with late preterm and early term birth have shown mixed results. Many of these studies did not fully take into account the role of the social environment in child development.

Social factors, not late preterm or early term birth, were the strongest predictors of poor developmental outcomes at 2 to 3 and 4 to 5 years. The influence of mild prematurity may lose strength beyond the neonatal period. (Read the full article)

To view more press releases, please visit http://ir.wintrust.com/news.aspx?iid=1024452.

The vertebrate limb serves as an experimental paradigm to study mechanisms that regulate development of the stereotypical skeletal elements. In this study, we simultaneously inactivated Sall4 using Hoxb6Cre and Plzf in mouse embryos, and found that their combined function regulates development of the proximal-anterior skeletal elements in hindlimbs. The Sall4; Plzf double knockout exhibits severe defects in the femur, tibia, and anterior digits, distinct defects compared to other allelic series of Sall4; Plzf. We found that Sall4 regulates Plzf expression prior to hindlimb outgrowth. Further expression analysis indicated that Hox10 genes and GLI3 are severely downregulated in the Sall4; Plzf double knockout hindlimb bud. In contrast, PLZF expression is reduced but detectable in Sall4; Gli3 double knockout limb buds, and SALL4 is expressed in the Plzf; Gli3 double knockout limb buds. These results indicate that Plzf, Gli3, and Hox10 genes downstream of Sall4, regulate femur and tibia development. In the autopod, we show that Sall4 negatively regulates Hedgehog signaling, which allows for development of the most anterior digit. Collectively, our study illustrates genetic systems that regulate development of the proximal-anterior skeletal elements in hindlimbs.

BEAF (Boundary Element-Associated Factor) was originally identified as a Drosophila melanogaster chromatin domain insulator-binding protein, suggesting a role in gene regulation through chromatin organization and dynamics. Genome-wide mapping found that BEAF usually binds near transcription start sites, often of housekeeping genes, suggesting a role in promoter function. This would be a nontraditional role for an insulator-binding protein. To gain insight into molecular mechanisms of BEAF function, we identified interacting proteins using yeast two-hybrid assays. Here, we focus on the transcription factor Serendipity (Sry-). Interactions were confirmed in pull-down experiments using bacterially expressed proteins, by bimolecular fluorescence complementation, and in a genetic assay in transgenic flies. Sry- interacted with promoter-proximal BEAF both when bound to DNA adjacent to BEAF or > 2-kb upstream to activate a reporter gene in transient transfection experiments. The interaction between BEAF and Sry- was detected using both a minimal developmental promoter (y) and a housekeeping promoter (RpS12), while BEAF alone strongly activated the housekeeping promoter. These two functions for BEAF implicate it in playing a direct role in gene regulation at hundreds of BEAF-associated promoters.

Jack Nguyen and Meir M. Barak

Cortical bone remodeling is an ongoing process triggered by microdamage, where osteoclasts resorb existing bone and osteoblasts deposit new bone in the form of secondary osteons (Haversian systems). Previous studies revealed regional variance in Haversian systems structure and possibly material, between opposite cortices of the same bone. As bone mechanical properties depend on tissue structure and material, it is predicted that bone mechanical properties will vary in accordance with structural and material regional heterogeneity. To test this hypothesis, we analyzed the structure, mineral content and compressive stiffness of secondary bone from the cranial and caudal cortices of the white-tailed deer proximal humerus. We found significantly larger Haversian systems and canals in the cranial cortex but no significant difference in mineral content between the two cortices. Accordingly, we found no difference in compressive stiffness between the two cortices and thus our working hypothesis was rejected. Seeing that the deer humerus is curved and thus likely subjected to bending during habitual locomotion, we expect that similar to other curved long bones, the cranial cortex of the deer humerus is likely subjected primarily to tensile strains and the caudal cortex is likely subject primarily to compressive strains. Consequently, our results suggest that strain magnitude (larger in compression) and sign (compression vs. tension) affect differently the osteoclasts and osteoblasts in the BMU. Our results further suggest that osteoclasts are inhibited in regions of high compressive strains (creating smaller Haversian systems) while osteoblasts’ osteoid deposition and mineralization is not affected by strain magnitude and sign.

Cell type-specific transcriptional programs that drive differentiation of specialized cell types are key players in development and tissue regeneration. One of the most dramatic changes in the transcription program in Drosophila occurs with the transition from proliferating spermatogonia to differentiating spermatocytes, with >3000 genes either newly expressed or expressed from new alternative promoters in spermatocytes. Here we show that opening of these promoters from their closed state in precursor cells requires function of the spermatocyte-specific tMAC complex, localized at the promoters. The spermatocyte-specific promoters lack the previously identified canonical core promoter elements except for the Inr. Instead, these promoters are enriched for the binding site for the TALE-class homeodomain transcription factors Achi/Vis and for a motif originally identified under tMAC ChIP-seq peaks. The tMAC motif resembles part of the previously identified 14-bp β2UE1 element critical for spermatocyte-specific expression. Analysis of downstream sequences relative to transcription start site usage suggested that ACA and CNAAATT motifs at specific positions can help promote efficient transcription initiation. Our results reveal how promoter-proximal sequence elements that recruit and are acted upon by cell type-specific chromatin binding complexes help establish a robust, cell type-specific transcription program for terminal differentiation.

No going out to buy ingredients you don't already have, though. Crumpets are treats.

Proxima Centauri b, a planet orbiting our nearest stellar neighbour, is being blasted with cosmic rays and solar flares – which could make it warm enough to host life

“This important settlement resolves lengthy litigation on very favorable terms,” said Ignacia S. Moreno, Assistant Attorney General for the Justice Department’s Environment and Natural Resources Division.

Westar Energy has agreed to spend approximately $500 million to significantly reduce harmful air pollution from a Kansas power plant and pay a $3 million civil penalty, under a settlement to resolve violations of the Clean Air Act.

429 individuals in 16 states were arrested as part of Project Deliverance, which targeted the transportation infrastructure of Mexican drug trafficking organizations in the United States, especially along the Southwest border.

The United States, 14 states and the Saint Regis Mohawk Tribe have entered into a settlement agreement with Chapter 11 debtor Motors Liquidation Companyformerly known as General Motors Corporation, to settle certain environmental liabilities under the Comprehensive Environmental Response, Compensation and Liability Act, the Resource Conservation and Recovery Act and state environmental laws.

Two Miami health care companies and four owners and senior managers of the companies were indicted today for their alleged participation in a fraud scheme involving approximately $200 million in Medicare billing for purported mental health services.

Twenty individuals, including three doctors, were charged today in the Southern District of Florida for various health care fraud, kickback and money laundering charges related to their alleged participation in a fraud scheme involving approximately $200 million in Medicare billing for purported mental health services.

Maxim Healthcare Services Inc., one of the nation’s leading providers of home healthcare services, has entered into a settlement to resolve criminal and civil charges relating to a nationwide scheme to defraud Medicaid programs and the Veterans Affairs program of more than $61 million.

Curtis Morris, 43, of Elizabeth, Colo., and Richard Kellogg Armstrong, 77, of Prescott, Ariz., were found guilty on April 30, 2012, by a jury for mail fraud, filing false claims against the United States and conspiracy to file false claims against the United States, announced the Justice Department’s Tax Division, the U.S. Attorney’s Office for the District of Colorado and IRS-Criminal Investigation. In addition to these counts, Armstrong was also found guilty of engaging in monetary transactions in property derived from the mail fraud. The guilty verdicts were the result of a three week trial before U.S. District Court Judge Robert E. Blackburn. Morris and Armstrong are scheduled to be sentenced on Aug. 10, 2012.

Attorney General Eric Holder and Health and Human Services (HHS) Secretary Kathleen Sebelius announced today that a nationwide takedown by Medicare Fraud Strike Force operations in seven cities has resulted in charges against 107 individuals, including doctors, nurses and other licensed medical professionals, for their alleged participation in Medicare fraud schemes involving approximately $452 million in false billing.

Medicare Fraud Strike Force operations in seven cities have led to charges against 91 individuals – including doctors, nurses and other licensed medical professionals – for their alleged participation in Medicare fraud schemes involving approximately $429.2 million in false billing.