Tag Archives: statistics

Two flow charts a and b with a have Full Dataset (x) having arrows to both Selection Dataset XI (text on this arrow reads use some porta a of the data for selection) and to inference dataset XII (text on this arrow reads use the remaining portion 1-a of the data for inference) and XI has an arrow to XII (text on arrow reads use any procedure to choose a model on the selection dataset and then use the inference dataset to test it b has full dataset x and two arrows connected to f(X) (text on this arrow read split data using randomization scheme) and use p(g(x)|f(X)) for inference (text on this arrow reads reveal full dataset at inference stage) and an arrow from f(x) to the other (text on this arrow reads use any procedure to choose a model from f(X))

Title:    Data Fission – Statistical Analysis through Data Point SeparationAuthors & Year:   J. Leiner, B. Duan, L. Wasserman, and A. Ramdas (2023)Journal:   Journal of the American Statistical Association[DOI:10.1080/01621459.2023.2270748]Review Prepared by David Han Why Split the Data? In statistical analysis, a common practice is to split a dataset into two (or more) parts, typically one for model development and the other for model evaluation/validation. However, a new method called data fission offers a more efficient approach. Imagine you have a single data point, and you want to divide it into two pieces that cannot be understood separately but can fully reveal the original data when combined. By adding and subtracting some random noise to create these two parts, each part contains unique information, and together they provide a complete picture. This technique is useful for making inferences after selecting a statistical model, allowing for better flexibility and accuracy compared to…

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No matter how free interactions become, tribalism remains a basic trait. The impulse to form groups based on similarities of habits – of ways of thinking, the tendency to congregate across disciplinary divides, never goes away fully regardless of how progressive our outlook gets. While that tendency to form cults is not problematic in itself (there is even something called community detection in network science that exploits – and exploits to great effects – this tendency) when it morphs into animosity, into tensions, things get especially tragic. The issue that needs to be solved gets bypassed, instead noise around these silly fights come to the fore. For example, the main task at hand could be designing a drug that is effective against a disease, but the trouble may lie in the choice of the benchmark against which this fresh drug must be pitted. In popular media, that benchmark may be the placebo – an inconsequential sugar pill, while in more objective science it could be the drug that is currently in use. There are instances everywhere of how scientists and journalists come in each other’s way (Ben Goldacre’s book Bad Science imparts crucial insights) or how even among scientists, factionalism persists: how statisticians – even to this day – prefer to be classed as frequentists or Bayesians, or how even among Bayesians, whether someone is an empirical Bayesian or not. The sad chain never stops. You may have thought of this tendency and its result. How it is promise betrayed, collaboration throttled in the moment of blossoming. While the core cause behind that scant tolerance, behind that clinging on to, may be a deep passion for what one does, the problem at hand pays little regard to that dedication. The problem’s outlook stays ultimately pragmatic: it just needs solving. By whatever tools. From whatever fields. Alarmingly, the segregations or subdivisions we sampled above and the differences they lead to – convenient though they may be – do not always remain academic: distant to the point of staying irrelevant. At times, they deliver chills much closer to the bone: whether a pure or applied mathematician will get hired or promoted, how getting published in computer science journals should be – according to many – more frequent compared to those in mainstream statistics, etc.

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As a digital detective, your mission is to decipher the preferences of your website visitors. Your primary tool? A/B testing – a method used in online controlled experiments where two versions of a webpage (version A and version B) are presented to different subsets of users under the same conditions. It’s akin to a magnifying glass, enabling you to scrutinize the minute details of user interactions across two versions of a webpage to discern their preferences. However, this case isn’t as straightforward as it seems. A recent article by Nicholas Larsen et al. in The American Statistician reveals the hidden challenges of A/B testing that can affect the results of online experiments. If these challenges aren’t tackled correctly, they can lead to misleading conclusions, affecting decisions in both online businesses and academic research.

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Census statistics play a pivotal role in making public policy decisions such as redrawing legislative districts and allocating federal funds as well as supporting social science research. However, given the risk of revealing individual information, many statistical agencies are considering disclosure control methods based on differential privacy, by adding noise to tabulated data and subsequently conducting postprocessing. The U.S. Census Bureau in particular has implemented a Disclosure Avoidance System (DAS) based on differential privacy technology to protect individual Census responses. This system adds random noise, guided by a privacy loss budget (denoted by ϵ), to Census tabulations, aiming to prevent the disclosure of personal information as mandated by law. The privacy loss budget value ϵ determines the level of privacy protection, with higher ϵ values allowing more noise. While the adoption of differential privacy has been controversial, this approach is crucial for maintaining data confidentiality. Other countries and organizations are also considering this technology as well. 

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Does a higher body mass index (BMI) increase the severity of COVID-19 symptoms? Mendelian randomization is one method that can be used to study this question without worrying about unmeasured variables (e.g., weight, height, or sex) that could affect the results. A recent paper published in the Annals of Statistics developed a new technique for Mendelian randomization which improves the ability to measure cause-and-effect relationships.

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By: Erin McGee  Paper title: Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans Authors and year: Cory McCartan, Kosuke Imai, 2023  Journal: Annals of Applied Statistics (Forthcoming 2023),  https://doi.org/10.48550/arXiv.2008.06131 In 2011, the Pennsylvania General Assembly was accused of drawing a redistricting plan for the state that diluted the power of Democratic voters, while strengthening the Republican vote. The case made its way to the Pennsylvania Supreme Court, where it was determined to be an unfairly drawn map.  With more complicated techniques, gerrymandering, or altering districts to purposefully amplify the voting power of some, while reducing others, becomes harder to recognize. Gerrymandered districts are usually identifiable by the ‘jigsaw’ shapes that split counties and municipalities in an attempt to pack certain voting groups into the same district, while splitting others. However, proving that a district map has been purposefully manipulated, as it was in Pennsylvania, is no easy task.…

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Title:   Assurance for Sample Size Determination in Reliability Demonstration Testing Authors & Year:   Kevin Wilson & Malcolm Farrow (2021) Journal:   Technometrics [DOI: 10.1080/00401706.2020.1867646] Why Reliability Demonstration Testing? Ensuring high reliability is critical for hardware products, especially those involved in safety-critical functions such as railway systems and nuclear power reactors. To build trust, manufacturers use reliability demonstration tests (RDT) where a sample of products is tested and failures are observed. If the test meets specific criteria, it demonstrates the product’s reliability. The RDT design varies based on the type of hardware product being tested, whether it is failure on demand or time to failure. Traditionally, sample sizes for RDT have been determined using methods that consider the power of a hypothesis test or risk criteria. Various approaches, such as Bayesian methods and risk criteria evaluation, have been developed over the decades in order to enhance the effectiveness of RDT. These measures…

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Machine learning models are excellent at discovering patterns in data to make predictions. However, their insights are limited to the input data itself. What if we could provide additional knowledge about the model features to improve learning? For example, suppose we have prior knowledge that certain features are more important than others in predicting the target variable. Researchers have developed a new method called the feature-weighted elastic net (“fwelnet”) that integrates this extra feature knowledge to train smarter models, resulting in more accurate predictions than regular techniques.

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In June 2023, astronomers and statisticans flocked to “Happy Valley’” Pennsylvania for the eighth installment of the Statistical Challenges in Modern Astronomy, a bidecadal conference. The meeting, hosted at Penn State University, marked a transition in leadership from founding members Eric Feigelson and Jogesh Babu to Hyungsuk Tak, who led the proceedings. While the astronomical applications varied widely, including modeling stars, galaxies, supernovae, X-ray observations, and gravitational waves, the methods displayed a strong Bayesian bent. Simulation based inference (SBI), which uses synthetic models to learn an approximate function for the likelihood of physical parameters given data, featured prominently in the distribution of talk topics. This article features work presented in two back-to-back talks on a probabilistic method for modeling (point) sources of light in astronomical images, for example stars or galaxies, delivered by Prof. Jeffrey Regier and Ismael Mendoza from the University of Michigan-Ann Arbor.

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One of the key goals of science is to create theoretical models that are useful at describing the world we see around us. However, no model is perfect. The inability of models to replicate observations is often called the “synthetic gap.” For example, it may be too computationally expensive to include a known effect or to vary a large number of known parameters. Or, there may be unknown instrumental effects associated with variability in conditions during the data acquisition.

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