Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture

Stone, Charles J.; Hansen, Mark; Kooperberg, Charles; Truong, Young K.

doi:10.1214/aos/1031594728

Cited by 373 publications

(234 citation statements)

References 59 publications

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“…3 plots histograms 5 for the prior (i.e., dotted line) and the posterior (i.e., thick solid line). In addition, the thin solid lines represent logspline nonparametric density estimates (Stone, Hansen, Kooperberg, & Truong, 1997). The mode of the logspline density estimate for the posterior of h is 0.89, whereas the 95% confidence interval is (0.59, 0.98), matching the analytical result shown in Fig.…”

Section: Bayesian Parameter Estimationsupporting

confidence: 73%

“…Fig. 3 shows the logspline estimates (Stone et al, 1997) for the prior and the posterior densities as obtained from MCMC output. The estimated height of the prior and posterior distributions at h ¼ :5 equal 1.00 and 0.107, respectively.…”

Section: The Savage-dickey Density Ratiomentioning

confidence: 99%

“…(14). For the posterior distribution, the thin solid line indicates a logspline nonparametric density estimate (Stone et al, 1997), the procedure that we will use throughout this article to estimate distributions.…”

Section: Unrestricted Analysismentioning

confidence: 99%

“…For its computation, the Savage-Dickey method requires an estimate of the height of a uni-dimensional posterior distribution at a single point. In this article, we have used the logspline nonparametric density estimator proposed by Stone et al (1997). This estimator is implemented in in the R package polspline, and concrete examples of its use are provided in the online R code associated with this article.…”

Section: Limitations Of the Savage-dickey Density Ratiomentioning

confidence: 99%

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Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

610

619

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a b s t r a c tIn the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility.

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Section: Bayesian Parameter Estimationsupporting

confidence: 73%

Section: The Savage-dickey Density Ratiomentioning

confidence: 99%

Section: Unrestricted Analysismentioning

confidence: 99%

Section: Limitations Of the Savage-dickey Density Ratiomentioning

confidence: 99%

See 2 more Smart Citations

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

610

619

View full text Add to dashboard Cite

show abstract

“…References include Stone (1980), Stone (1982), Stone, Hansen, Kooperberg, and Truong (1997), Zhou, Shen, and Wolfe (1998), Huang (1998), Zhou and Wolfe (2000), and Huang (2001). If p is the order of the spline, let the number of knots increase as n 1/(2p+1) ; that is, as n 1/7 for quadratic splines and as n 1/9 for cubic splines.…”

Section: Convergence Ratesmentioning

confidence: 99%

Change-point estimation using shape-restricted regression splines

Liao

Meyer

2017

Journal of Statistical Planning and Inference

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CHANGE-POINT ESTIMATION USING SHAPE-RESTRICTED REGRESSION SPLINESChange-Point estimation is in need in fields like climate change, signal processing, economics, dose-response analysis etc, but it has not yet been fully discussed. We consider estimating a regression function f m and a change-point m, where m is a mode, an inflection point, or a jump point. Linear inequality constraints are used with spline regression functions to estimate m and f m simultaneously using profile methods. For a given m, the maximum-likelihood estimate of f m is found using constrained regression methods, then the set of possible change-points is searched to find them that maximizes the likelihood. Finally, we consider the change-point estimation with generalized linear models. Such work can be applied to dose-response analysis, when the effect of a drug increases as the dose increases to a saturation point, after which the effect starts decreasing.iii Tanz . iv DEDICATION To the cutest, Francis, Nilus and

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Spline Smoothing

Turlach¹

2005

Encyclopedia of Biostatistics

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Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture

Cited by 373 publications

References 59 publications

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Change-point estimation using shape-restricted regression splines

Spline Smoothing

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