Matches in SemOpenAlex for { <https://semopenalex.org/work/W615631462> ?p ?o ?g. }
- W615631462 abstract "In the early 20th century data analysis was constrained by computability. Calculations were performed by hand, providing real practical limits on the types of problems which were tractable. Salsburg (2002) provides a calculation showing that at least 8 months of 12-hour days would have been required for R. A. Fisher to have produced the tables in his Studies in Crop Variation I (Fisher, 1921) with the mechanical means at his disposal. It is hardly surprising that the emphasis during this period remained on linear models - problems soluble by ordinary least squares, with the tools at hand.It was not until the 1960s that nonlinear regression began to appear regularly in the literature, and no accident that this eventuates concurrently with the appearance of machines to automate iterative calculations. The heavier computational burden had previously been insurmountable. But even after the advent of early computers, great emphasis was placed on the development of algorithms which could make effcient use of limited hardware resources - processors were slow and memory limited. Research into algorithms became synonymous with effciency, and the attendant (O)-notation. The Fast Fourier Transform of Cooley and Tukey (1965) provides the archetypal example of the era. The explicit reference to speed in the title underscores the imperative.In the early 21st century, the situation has improved markedly. Computing power is cheap and relatively abundant, and software is designed with re-use of objects and systems integration in mind. There has been a co-evolution of research into modelling methods. Modelling frameworks have diversified, and are now capable of representing a much broader range of observable phenomena. Informed by Tukey's observation Far better an approximate answer to the right question, ... than an exact answer to the wrong question (Tukey, 1962), we build models which more accurately reflect our understanding of reality. Increasingly, we are asking the right questions.Indeed, since the 1970s there has been rapid development in methods which extend the general linear model, stimulated by the development of Generalized Linear Models (GLMs) (McCullagh and Nelder, 1989). These allow response residuals to be modelled using alternatives to the Gaussian distribution and conditional expectations to be related to covariates via a link function (ƞ(θ)), rather than a direct linear relationship. The general linear model can then be seen as a GLM with an identity link function and a normally distributed response. The principal appeal of the framework is that the adoption of the exponential family as the basis guarantees the likelihood to be log-concave and unimodal so that estimation is straightforward. The adoption of GLMs has greatly extended the realm of linear models and vastly enhanced the scope of linear statistical modelling applications. What remains conspicuously absent is concurrent progress of a similar order in pursuit of nonlinear models, where the properties of the solution surface are more complex.The adoption of Markov Chain Monte Carlo (MCMC) techniques by the statistical community represents a significant new chapter in stochastic modelling. MCMC methods provide a flexible and powerful base from which realistic stochastic models can be built. They are particularly important because models developed in this framework need not have analytical tractability. Provided that the relationships between the component parts are specified, samples can be obtained from the density of the resulting model, allowing estimation and inference from non-standard distributions. This is an enormously empowering development. Most importantly, it promotes the construction of more realistic models. Data no longer need be forced into overly simplistic models just because they are the only soluble forms. Models can now be developed to fit available data.The development of MCMC tools have fundamentally altered the way that statisticians go about their business. But it is not merely statisticians who benefit. Greater accessibility of realistic modelling methods has led to statistical modelling taking a firm hold in primary research across a wide range of applied disciplines. The exchange of purely deterministic models in favour of more realistic stochastic models represents a paradigm shift in the foundation of science.This thesis considers the application of Markov Chain Monte Carlo (MCMC) methods to problems which extend the general linear model in various nonlinear ways. The framework in which these applications are developed is exclusively Bayesian, though the the methods themselves are equally applicable, if perhaps less commonly used, in a likelihood context. Geyer (1995) and Diebolt and Ip (1995), and the references therein, provide details of non-Bayesian applications of MCMC." @default.
- W615631462 created "2016-06-24" @default.
- W615631462 creator A5046910863 @default.
- W615631462 date "2010-01-01" @default.
- W615631462 modified "2023-09-26" @default.
- W615631462 title "Nonlinear applications of Markov Chain Monte Carlo" @default.
- W615631462 cites W112215812 @default.
- W615631462 cites W1249696972 @default.
- W615631462 cites W129305155 @default.
- W615631462 cites W1479881385 @default.
- W615631462 cites W1500794765 @default.
- W615631462 cites W1509562192 @default.
- W615631462 cites W1513618424 @default.
- W615631462 cites W1517555081 @default.
- W615631462 cites W1526098631 @default.
- W615631462 cites W1528905581 @default.
- W615631462 cites W1530249877 @default.
- W615631462 cites W1533179050 @default.
- W615631462 cites W1556631438 @default.
- W615631462 cites W1572076522 @default.
- W615631462 cites W1578044518 @default.
- W615631462 cites W1579579143 @default.
- W615631462 cites W1582801283 @default.
- W615631462 cites W1602551265 @default.
- W615631462 cites W1810615071 @default.
- W615631462 cites W1965284210 @default.
- W615631462 cites W1965761421 @default.
- W615631462 cites W1966249644 @default.
- W615631462 cites W1967049326 @default.
- W615631462 cites W1967485420 @default.
- W615631462 cites W1968172088 @default.
- W615631462 cites W1978351537 @default.
- W615631462 cites W1981457167 @default.
- W615631462 cites W1985093013 @default.
- W615631462 cites W1985211806 @default.
- W615631462 cites W1987617600 @default.
- W615631462 cites W1988520084 @default.
- W615631462 cites W1989385733 @default.
- W615631462 cites W1990777389 @default.
- W615631462 cites W1990939301 @default.
- W615631462 cites W1991594255 @default.
- W615631462 cites W199310666 @default.
- W615631462 cites W1996977322 @default.
- W615631462 cites W2007846998 @default.
- W615631462 cites W2015749074 @default.
- W615631462 cites W2018291069 @default.
- W615631462 cites W2020999234 @default.
- W615631462 cites W2021413916 @default.
- W615631462 cites W2024081693 @default.
- W615631462 cites W2025610145 @default.
- W615631462 cites W2030748132 @default.
- W615631462 cites W2032113267 @default.
- W615631462 cites W2038429130 @default.
- W615631462 cites W2042221696 @default.
- W615631462 cites W2048971218 @default.
- W615631462 cites W2050373719 @default.
- W615631462 cites W2053565514 @default.
- W615631462 cites W2056760934 @default.
- W615631462 cites W2060818806 @default.
- W615631462 cites W2061171222 @default.
- W615631462 cites W2064129461 @default.
- W615631462 cites W2065274576 @default.
- W615631462 cites W2067750291 @default.
- W615631462 cites W2070612147 @default.
- W615631462 cites W2070779353 @default.
- W615631462 cites W2072216292 @default.
- W615631462 cites W2072643767 @default.
- W615631462 cites W2083875149 @default.
- W615631462 cites W2084803500 @default.
- W615631462 cites W2087070363 @default.
- W615631462 cites W2088151068 @default.
- W615631462 cites W2091886411 @default.
- W615631462 cites W2093223772 @default.
- W615631462 cites W2093713098 @default.
- W615631462 cites W2094436494 @default.
- W615631462 cites W2097581696 @default.
- W615631462 cites W2102650396 @default.
- W615631462 cites W2102862543 @default.
- W615631462 cites W2103041471 @default.
- W615631462 cites W2106139345 @default.
- W615631462 cites W2108207895 @default.
- W615631462 cites W2133501628 @default.
- W615631462 cites W2134012062 @default.
- W615631462 cites W2135973421 @default.
- W615631462 cites W2136796925 @default.
- W615631462 cites W2138309709 @default.
- W615631462 cites W2142449924 @default.
- W615631462 cites W2148534890 @default.
- W615631462 cites W2152977846 @default.
- W615631462 cites W2156273867 @default.
- W615631462 cites W2162193517 @default.
- W615631462 cites W2163738067 @default.
- W615631462 cites W2166600059 @default.
- W615631462 cites W2167731203 @default.
- W615631462 cites W2170143582 @default.
- W615631462 cites W2312713519 @default.
- W615631462 cites W2313383114 @default.
- W615631462 cites W2318812168 @default.
- W615631462 cites W2466198720 @default.
- W615631462 cites W2764485636 @default.