|
Maurice Tweedie
Maurice Charles Kenneth Tweedie (30 September 1919 – 14 March 1996) was a British medical physicist and statistician from the University of Liverpool. He was known for research into the exponential family probability distributions. Education and career Tweedie read physics at the University of Reading and attained a BSc (general) and BSc (special) in physics in 1939 followed by a MSc in physics 1941. He found a career in radiation physics, but his primary interest was in mathematical statistics where his accomplishments far surpassed his academic postings. Contributions Tweedie distributions Tweedie's contributions included pioneering work with the Inverse Gaussian distribution. Arguably his major achievement rests with the definition of a family of exponential dispersion models characterized by closure under additive and reproductive convolution as well as under transformations of scale that are now known as the Tweedie exponential dispersion models. As a consequenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Reading, UK
Reading ( ) is a town and borough in Berkshire, England, and the county town of Berkshire. It is the United Kingdom's largest town, with a combined population of 355,596. Most of its built-up area lies within the Borough of Reading, although some outer suburbs are parts of neighbouring local authority areas. It is located in the Thames Valley at the confluence of the rivers Thames and Kennet. Reading is a major commercial centre, especially for information technology and insurance. It is also a regional retail centre, serving a large area of the Thames Valley with its shopping centres, including the Oracle, the Broad Street Mall, and the pedestrianised area around Broad Street. It is home to the University of Reading. Every year it hosts the Reading Festival, one of England's biggest music festivals. Reading has a professional association football team, Reading F.C., and participates in many other sports. Reading dates from the 8th century. It was a trading and ecclesiastic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Tweedie Distribution
In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models. The Tweedie distributions were named by Bent Jørgensen in after Maurice Tweedie, a statistician and medical physicist at the University of Liverpool, UK, who presented the first thorough study of these distributions in 1982 when the conference was held. Around the same time, Bar-Lev and Enis published about the same topic. Definitions The (reproductive) Tweedie distributions are defined as subfamily of (reproductive) exponential dispersion models (ED), with a special mean- var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Diffusion Model
In machine learning, diffusion models, also known as diffusion-based generative models or score-based generative models, are a class of latent variable model, latent variable generative model, generative models. A diffusion model consists of two major components: the forward diffusion process, and the reverse sampling process. The goal of diffusion models is to learn a diffusion process for a given dataset, such that the process can generate new elements that are distributed similarly as the original dataset. A diffusion model models data as generated by a diffusion process, whereby a new datum performs a Wiener process, random walk with drift through the space of all possible data. A trained diffusion model can be sampled in many ways, with different efficiency and quality. There are various equivalent formalisms, including Markov chains, denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. They are typically trained ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Empirical Bayes Method
Empirical Bayes methods are procedures for statistical inference in which the prior probability distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed before any data are observed. Despite this difference in perspective, empirical Bayes may be viewed as an approximation to a fully Bayesian treatment of a hierarchical model wherein the parameters at the highest level of the hierarchy are set to their most likely values, instead of being integrated out. Introduction Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model. In, for example, a two-stage hierarchical Bayes model, observed data y = \ are assumed to be generated from an unobserved set of parameters \theta = \ according to a probability distribution p(y\mid\theta)\,. In turn, the parameters \theta can be considered samples drawn from a population characterised b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Self-organized Criticality
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality. The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper , following an earlier paper by Jonathan Katz published in 1987 in ''Physical Review Letters'', and is considered to be one of the mechanisms by which complexity arises in nature. Its concepts have been applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology and others. SOC is typically observed in slowl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Multifractal System
A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed. Multifractal systems are common in nature. They include the length of coastlines, mountain topography, fully developed turbulence, real-world scenes, heartbeat dynamics, human gait and activity, human brain activity, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed to mathematical convergence effects related to the central limit theorem that have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models, as well as the geometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Genome Evolution
Genome evolution is the process by which a genome changes in structure (sequence) or size over time. The study of genome evolution involves multiple fields such as structural analysis of the genome, the study of genomic parasites, gene and ancient genome duplications, polyploidy, and comparative genomics. Genome evolution is a constantly changing and evolving field due to the steadily growing number of sequenced genomes, both prokaryotic and eukaryotic, available to the scientific community and the public at large. History Since the first sequenced genomes became available in the late 1970s, scientists have been using comparative genomics to study the differences and similarities between various genomes. Genome sequencing has progressed over time to include more and more complex genomes including the eventual sequencing of the entire human genome in 2001. By comparing genomes of both close relatives and distant ancestors the stark differences and similarities between species began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Metastasis
Metastasis is a pathogenic agent's spreading from an initial or primary site to a different or secondary site within the host's body; the term is typically used when referring to metastasis by a cancerous tumor. The newly pathological sites, then, are metastases (mets). It is generally distinguished from cancer invasion, which is the direct extension and penetration by cancer cells into neighboring tissues. Cancer occurs after cells are genetically altered to proliferate rapidly and indefinitely. This uncontrolled proliferation by mitosis produces a primary tumor, primary tumour heterogeneity, heterogeneic tumour. The cells which constitute the tumor eventually undergo metaplasia, followed by dysplasia then anaplasia, resulting in a Malignancy, malignant phenotype. This malignancy allows for invasion into the circulation, followed by invasion to a second site for tumorigenesis. Some cancer cells, known as circulating tumor cells (CTCs), are able to penetrate the walls of lymp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Random Matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic methods, the cavity method, or the replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors. Many physical phenomena, such as the spectrum of nuclei of heavy atoms, the thermal conductivity of a lattice, or the emergence of quantum chaos, can be modeled mathematically as problems concerning large, random matrices. Applications Physics In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pink Noise
Pink noise, noise, fractional noise or fractal noise is a signal (information theory), signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each Octave (electronics), octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems. The name arises from the pink appearance of visible light with this power spectrum. This is in contrast with white noise which has equal intensity per frequency interval. Definition Within the scientific literature, the term "1/f noise" is sometimes used loosely to refer to any noise with a power spectral density of the form S(f) \propto \frac, where is frequency, and , with exponent usually close to 1. On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Taylor's Law
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924–2007). Taylor's original name for this relationship was the law of the mean. The name ''Taylor's law'' was coined by Southwood in 1966. Definition This law was originally defined for ecological systems, specifically to assess the spatial clustering of organisms. For a population count Y with mean \mu and variance \operatorname (Y), Taylor's law is written : \operatorname (Y) = a\mu^b, where ''a'' and ''b'' are both positive constants. Taylor proposed this relationship in 1961, suggesting that the exponent ''b'' be considered a species specific index of aggregation. This power law has subsequently been confirmed for many hundreds of species. Taylor's law has also been applied to assess the time d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
