Above are papers related to the following paper: [Paper_ID] Paper #1154103. 	[Title]  [Abstract] TECHNICAL REPORT NO. 967 August 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #169280. 	[Title] A Flexible Model For Human Circadian Rhythms [Abstract] Many hormones and other physiological processes vary in a circadian pattern. Although a sine/cosine function can be used to model these patterns, this functional form is not appropriate when there is asymmetry between the peak and nadir phases. In this paper we describe a semi-parametric periodic spline function that can be fit to circadian rhythms. The model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated. We also describe tests of fit for components in the model. Data from an experiment to study immunological responses in humans are used to demonstrate the methods. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #263553. 	[Title] A Generalized Approximate Cross Validation for Smoothing Splines with Non-Gaussian Data 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #124224. 	[Title] Behavior Near Zero of the Distribution of GCV Smoothing Parameter Estimates 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117219. 	[Title] Testing the Generalized Linear Model Null Hypothesis versus `Smooth' Alternatives 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #169279. 	[Title] Smoothing Spline Models With Correlated Random Errors 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #431206. 	[Title] Backfitting in Smoothing Spline ANOVA [Abstract] A scheme to compute smoothing spline ANOVA estimates for large data sets with a (near) tensor-product structure is proposed. Such data sets are common in spatial-temporal analysis and image analysis. This scheme combines backfitting algorithm with iterative imputation algorithm in order to save both computational space and time. The convergence of this algorithm and various ways to further speed it up, such as collapsing component functions and successive over-relaxation, are discussed. Issues related to its application in spatial-temporal analysis are discussed too. An application to a global analysis of historical surface temperature data is described. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6910. 	[Title] Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #662416. 	[Title] USING SMOOTHING SPLINE ANOVA TO EXAMINE THE RELATION OF RISK FACTORS TO THE INCIDENCE AND [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6898. 	[Title] Sample Size Calculations for Smoothing Splines Based on Bayesian Confidence Intervals [Abstract] Bayesian confidence intervals of a smoothing spline are often used to distinguish two curves. In this paper, we provide an asymptotic formula for sample size calculations based on Bayesian confidence intervals. Approximations and simulations on special functions indicate that this asymptotic formula is reasonably accurate. Key Words: Bayesian confidence intervals; sample size; smoothing spline. fl Address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110. Tel.: (805)893-4870. Fax: (805)893-2334. E-mail: yuedong@pstat.ucsb.edu. Supported by the National Institute of Health under Grants R01 EY09946, P60 DK20572 and P30 HD18258. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #78994. 	[Title] Adaptive tuning of numerical weather prediction models: Randomized GCV in three and four dimensional data assimilation [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1123188. 	[Title] GRKPACK: FITTING SMOOTHING SPLINE ANOVA MODELS FOR EXPONENTIAL FAMILIES [Abstract] Wahba, Wang, Gu, Klein and Klein (1995) introduced Smoothing Spline ANalysis of VAriance (SS ANOVA) method for data from exponential families. Based on RKPACK, which fits SS ANOVA models to Gaussian data, we introduce GRKPACK: a collection of Fortran subroutines for binary, binomial, Poisson and Gamma data. We also show how to calculate Bayesian confidence intervals for SS ANOVA estimates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152150. 	[Title]  [Abstract] TECHNICAL REPORT NO. 947 June 5, 1995 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12631. 	[Title] Smoothing Spline ANOVA with Component-Wise Bayesian "Confidence Intervals" To Appear, J. Computational and Graphical Statistics [Abstract] We study a multivariate smoothing spline estimate of a function of several variables, based on an ANOVA decomposition as sums of main effect functions (of one variable), two-factor interaction functions (of two variables), etc. We derive the Bayesian "confidence intervals" for the components of this decomposition and demonstrate that, even with multiple smoothing parameters, they can be efficiently computed using the publicly available code RKPACK, which was originally designed just to compute the estimates. We carry out a small Monte Carlo study to see how closely the actual properties of these component-wise confidence intervals match their nominal confidence levels. Lastly, we analyze some lake acidity data as a function of calcium concentration, latitude, and longitude, using both polynomial and thin plate spline main effects in the same model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132083. 	[Title] Spline Smoothing For Bivariate Data With Applications To Association Between Hormones [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12638. 	[Title] Soft Classification, a.k.a. Risk Estimation, via Penalized Log Likelihood and Smoothing Spline Analysis of Variance [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #444191. 	[Title] Automatic Smoothing Spline Projection Pursuit  Automatic Smoothing Spline Projection Pursuit. [Abstract] kj = 1. The standard PPR algorithm of Friedman and Stuet-zle (1981) estimates the smooth functions f j using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M M max , where M and M max are specified by the user. This paper discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients ff j , the amount of smoothing in each direction, and the number of terms M and M max are determined to optimize a single generalized cross-validation measure. Please summarise all the given information.

Paper #1154103 has the title `nan` and the abstract `TECHNICAL REPORT NO. 967 August 1996 
`.
Question: Which category should Paper #1154103 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1154103 has the title `nan` and the abstract `TECHNICAL REPORT NO. 967 August 1996 
`.
Question: Which category should Paper #1154103 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods