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... m i (Y) L(Y | θ)f i (θ)dθ P(Mi|Y) π(i)mi(Y) BIC neglects π(i) and uses asymptotic approximation ...
... m i (Y) L(Y | θ)f i (θ)dθ P(Mi|Y) π(i)mi(Y) BIC neglects π(i) and uses asymptotic approximation ...
bagging
... • Named from the phrase “to pull oneself up by one’s bootstraps”, which is widely believed to come from “the Adventures of Baron Munchausen”. • Popularized in 1980s due to the introduction of computers in statistical practice. • It has a strong mathematical background. • It is well known as a method ...
... • Named from the phrase “to pull oneself up by one’s bootstraps”, which is widely believed to come from “the Adventures of Baron Munchausen”. • Popularized in 1980s due to the introduction of computers in statistical practice. • It has a strong mathematical background. • It is well known as a method ...
Spherical Hamiltonian Monte Carlo for Constrained Target Distributions
... In practice when the analytical solution to Hamilton’s equations is not available, we need to numerically solve these equations by discretizing them, using some small time step . For the sake of accuracy and stability, a numerical method called leapfrog is commonly used to approximate the Hamilton’ ...
... In practice when the analytical solution to Hamilton’s equations is not available, we need to numerically solve these equations by discretizing them, using some small time step . For the sake of accuracy and stability, a numerical method called leapfrog is commonly used to approximate the Hamilton’ ...
Surrogate model of BNS waveforms for measuring the EOS
... • Fixed cost of ~50 ms for computing surrogate (not optimized) • Additional cost for resampling to desired frequencies (interpolation) • Faster than all waveforms in LALSuite (written in C) below ~18 Hz ...
... • Fixed cost of ~50 ms for computing surrogate (not optimized) • Additional cost for resampling to desired frequencies (interpolation) • Faster than all waveforms in LALSuite (written in C) below ~18 Hz ...
The effect of personal taxes and dividends on capital asset prices
... procedures are used to test the implications of this model. Unlike prior tests of the CAPM, the tests here use the variance of the observed betas to arrive at maximum likelihood estimators of the coefficients. Consistent estimators are obtained without loss of efficiency. Also, for ex-dividend month ...
... procedures are used to test the implications of this model. Unlike prior tests of the CAPM, the tests here use the variance of the observed betas to arrive at maximum likelihood estimators of the coefficients. Consistent estimators are obtained without loss of efficiency. Also, for ex-dividend month ...
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... significance of the calendar effect for each published series. REGARIMA combines standard regression analysis, which measures correlation among two or more variables, with ARIMA modeling, which describes and predicts the behavior of data series based on its own past history. For many economic time s ...
... significance of the calendar effect for each published series. REGARIMA combines standard regression analysis, which measures correlation among two or more variables, with ARIMA modeling, which describes and predicts the behavior of data series based on its own past history. For many economic time s ...
Variable Selection and Decision Trees: The DiVaS
... We define a transformation that allows us to use priors from linear models to facilitate covariate selection in decision trees. Using this transform, we modify many common approaches to variable selection in the linear model and bring these methods to bear on the problem of explicit covariate select ...
... We define a transformation that allows us to use priors from linear models to facilitate covariate selection in decision trees. Using this transform, we modify many common approaches to variable selection in the linear model and bring these methods to bear on the problem of explicit covariate select ...
Tilak JF final
... using industrial production index as a related series and compared the quarterly growth rates with the observed ones over the period 1975-1995. Figure 1 plots the results. In the figure the thic k line shows the official records and the line with triangles shows the ones based on the first differenc ...
... using industrial production index as a related series and compared the quarterly growth rates with the observed ones over the period 1975-1995. Figure 1 plots the results. In the figure the thic k line shows the official records and the line with triangles shows the ones based on the first differenc ...
On Label Dependence in Multi
... prediction of several real-valued variables. Historically, multi-label classification has indeed been treated as a specific case of multivariate regression in statistics, for example within the context of vector generalized linear models (VGLMs), as summarized in (Song, 2007, chapter 6) and (Izenman ...
... prediction of several real-valued variables. Historically, multi-label classification has indeed been treated as a specific case of multivariate regression in statistics, for example within the context of vector generalized linear models (VGLMs), as summarized in (Song, 2007, chapter 6) and (Izenman ...
Diagnosis & Exploration of Massively Univariate fMRI Models
... We find that direct application of the CP test is not satisfactory. In simulations with a typical fMRI model (block design experimental predictors and low frequency drift basis) and white noise, we find that the CP test rejects the white noise hypothesis in excess of the nominal level. The problem i ...
... We find that direct application of the CP test is not satisfactory. In simulations with a typical fMRI model (block design experimental predictors and low frequency drift basis) and white noise, we find that the CP test rejects the white noise hypothesis in excess of the nominal level. The problem i ...
投影片 1 - 政大公共(個人)網頁伺服器
... as a random variable: it has a distribution in the population, and drawing a different person yields a different value of (just like X and Y ). For example, for person #34 the treatment effect is not random - it is her true treatment effect - but before she is selected at random from the populatio ...
... as a random variable: it has a distribution in the population, and drawing a different person yields a different value of (just like X and Y ). For example, for person #34 the treatment effect is not random - it is her true treatment effect - but before she is selected at random from the populatio ...
threats to the internal validity of a quasi
... as a random variable: it has a distribution in the population, and drawing a different person yields a different value of (just like X and Y ). For example, for person #34 the treatment effect is not random - it is her true treatment effect - but before she is selected at random from the populatio ...
... as a random variable: it has a distribution in the population, and drawing a different person yields a different value of (just like X and Y ). For example, for person #34 the treatment effect is not random - it is her true treatment effect - but before she is selected at random from the populatio ...
Linear regression
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y. Given a variable y and a number of variables X1, ..., Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ""lack of fit"" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ""least squares"" and ""linear model"" are closely linked, they are not synonymous.