# \#gaussian-process

**URL:** https://discourse.mc-stan.org/tag/gaussian-process/103.md

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## [Hilbert-space GP: Rhat inflation and age-specific bias when moving from yearly to monthly birth data](https://discourse.mc-stan.org/t/hilbert-space-gp-rhat-inflation-and-age-specific-bias-when-moving-from-yearly-to-monthly-birth-data/40898)

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**Author:** [@anthony\_462](https://discourse.mc-stan.org/u/anthony_462)\
**Replies:** 5\
**Last updated:** [February 9, 2026, 6:09pm UTC](https://discourse.mc-stan.org/t/hilbert-space-gp-rhat-inflation-and-age-specific-bias-when-moving-from-yearly-to-monthly-birth-data/40898 "2026-02-09T18:09:47Z")

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Aim: I am modelling the number of births y\_{i,m,j} by year i (2000–2024), month m and mother age j (15-50). The goal is to estimate the mean number of births by age without systematic bias. The model should also capture…

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## [Approximate Gaussian process: increase speed and efficiency](https://discourse.mc-stan.org/t/approximate-gaussian-process-increase-speed-and-efficiency/40851)

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**Author:** [@anthony\_462](https://discourse.mc-stan.org/u/anthony_462)\
**Replies:** 5\
**Last updated:** [February 5, 2026, 9:16pm UTC](https://discourse.mc-stan.org/t/approximate-gaussian-process-increase-speed-and-efficiency/40851 "2026-02-05T21:16:28Z")

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Hi all, I am looking for guidance on how to increase the speed and efficiency of a reduced-rank GP in my model. In particular, I am surprised by the number of basis functions I seem to need. Data The data consist of mo…

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## [Performing posterior predictive checks for variational inference models](https://discourse.mc-stan.org/t/performing-posterior-predictive-checks-for-variational-inference-models/40742)

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**Author:** [@jr-leary7](https://discourse.mc-stan.org/u/jr-leary7)\
**Replies:** 4\
**Last updated:** [December 21, 2025, 9:26pm UTC](https://discourse.mc-stan.org/t/performing-posterior-predictive-checks-for-variational-inference-models/40742 "2025-12-21T21:26:18Z")

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Hi all, Apologies in advance for the long post - feel free to jump to the Questions section at the end. Background Over the past year or so I’ve been working on developing a hierarchical approximate Gaussian process (…

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## [Wide credible intervals for fixed effects in brms GP model](https://discourse.mc-stan.org/t/wide-credible-intervals-for-fixed-effects-in-brms-gp-model/40386)

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**Author:** [@Pavel\_Stichauer](https://discourse.mc-stan.org/u/Pavel_Stichauer)\
**Replies:** 5\
**Last updated:** [September 25, 2025, 11:39am UTC](https://discourse.mc-stan.org/t/wide-credible-intervals-for-fixed-effects-in-brms-gp-model/40386 "2025-09-25T11:39:52Z")

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Hi, I am fitting a logistic regression in brms to predict auxiliary selection (binary H/E) from morphosyntactic predictors, verbs, and geography. My baseline model is: AUX\_bin ~ Class + TAM + Cell + (1 | Verb\_Construc…

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## [Setting nug for GP regressions](https://discourse.mc-stan.org/t/setting-nug-for-gp-regressions/40369)

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**Author:** [@jochens](https://discourse.mc-stan.org/u/jochens)\
**Replies:** 2\
**Last updated:** [September 16, 2025, 6:03pm UTC](https://discourse.mc-stan.org/t/setting-nug-for-gp-regressions/40369 "2025-09-16T18:03:34Z")

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I sometimes receive the following error when generating conditional effects after training a GP regression model like brm(y ~ gp(x)) Error: The Gaussian process covariance matrix is not positive definite. This occurs f…

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## [diagSPD for Matérn GP kernels other than 3/2](https://discourse.mc-stan.org/t/diagspd-for-matern-gp-kernels-other-than-3-2/37011)

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**Author:** [@Peter.Stewart](https://discourse.mc-stan.org/u/Peter.Stewart)\
**Replies:** 15\
**Last updated:** [September 12, 2025, 8:14am UTC](https://discourse.mc-stan.org/t/diagspd-for-matern-gp-kernels-other-than-3-2/37011 "2025-09-12T08:14:12Z")

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Hi everyone, I’ve been fitting some Gaussian Process models using the Hilbert space approximation, adapting code from the tutorials by @avehtari here and here. I would like to fit a model which uses a Matérn 1/2 kernel,…

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## [Brms gaussian process se() with log\_normal](https://discourse.mc-stan.org/t/brms-gaussian-process-se-with-log-normal/40173)

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**Author:** [@buf](https://discourse.mc-stan.org/u/buf)\
**Replies:** 0\
**Last updated:** [August 15, 2025, 10:17am UTC](https://discourse.mc-stan.org/t/brms-gaussian-process-se-with-log-normal/40173 "2025-08-15T10:17:57Z")

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Hi there, I try to build a GP model with brms. It is about nitrate concentrations in groundwater that shall be interpolated in space using GP. I have information on measurement errors for each observation. If the nitrat…

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## [Correlation between Gaussian processes](https://discourse.mc-stan.org/t/correlation-between-gaussian-processes/21251)

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**Author:** [@bernibra](https://discourse.mc-stan.org/u/bernibra)\
**Replies:** 8\
**Last updated:** [May 23, 2025, 12:18pm UTC](https://discourse.mc-stan.org/t/correlation-between-gaussian-processes/21251 "2025-05-23T12:18:06Z")

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Hey there, I recently posted for the first time in this forum, and I had such quick and great responses that I can’t help it but ask another question regarding Gaussian processes that has been bugging me for a while (an…

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## [Gaussian process for predictor selection using Stan output](https://discourse.mc-stan.org/t/gaussian-process-for-predictor-selection-using-stan-output/39293)

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**Author:** [@ViktorVdV](https://discourse.mc-stan.org/u/ViktorVdV)\
**Replies:** 5\
**Last updated:** [April 17, 2025, 8:05am UTC](https://discourse.mc-stan.org/t/gaussian-process-for-predictor-selection-using-stan-output/39293 "2025-04-17T08:05:38Z")

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Hi all, I am sorry if this question is too basic or posted under the wrong tags, but here goes: I have modeled forest regrowth trajectories in Stan using an exponential recovery function described by an intrinsic recov…

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## [Formulating a hierarchical multivariate Gaussian process using the Hilbert space approximation](https://discourse.mc-stan.org/t/formulating-a-hierarchical-multivariate-gaussian-process-using-the-hilbert-space-approximation/38562)

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**Author:** [@jr-leary7](https://discourse.mc-stan.org/u/jr-leary7)\
**Replies:** 8\
**Last updated:** [February 7, 2025, 4:44pm UTC](https://discourse.mc-stan.org/t/formulating-a-hierarchical-multivariate-gaussian-process-using-the-hilbert-space-approximation/38562 "2025-02-07T16:44:30Z")

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Hi all, I’m currently working on what I think - based on perusing these forums, the Stan docs, the brms and cmdstanr docs, etc. - is a new-ish type of Gaussian process model. The model combines the Hilbert space approxi…

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## [Estimating fitted values from hierarchical Gaussian process model](https://discourse.mc-stan.org/t/estimating-fitted-values-from-hierarchical-gaussian-process-model/38442)

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**Author:** [@jr-leary7](https://discourse.mc-stan.org/u/jr-leary7)\
**Replies:** 0\
**Last updated:** [January 9, 2025, 9:18pm UTC](https://discourse.mc-stan.org/t/estimating-fitted-values-from-hierarchical-gaussian-process-model/38442 "2025-01-09T21:18:19Z")

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Hi all, I’m currently working with some spatial data (spatial transcriptomics to be exact), which is a rather new area for me. My basic idea is to use a Gaussian process (GP) to estimate the mean and variance of gene ex…

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## [Convergence problems in Hilbert space Gaussian process with ID effect](https://discourse.mc-stan.org/t/convergence-problems-in-hilbert-space-gaussian-process-with-id-effect/37593)

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**Author:** [@Peter.Stewart](https://discourse.mc-stan.org/u/Peter.Stewart)\
**Replies:** 4\
**Last updated:** [January 7, 2025, 12:23pm UTC](https://discourse.mc-stan.org/t/convergence-problems-in-hilbert-space-gaussian-process-with-id-effect/37593 "2025-01-07T12:23:10Z")

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Hi everyone, I have been working on modelling the north-south migration of GPS-tagged animals over time, using a Hilbert space Gaussian process approach. Following my previous post here, I have been incorporating the in…

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## [Hypothesis-testing for gaussian process](https://discourse.mc-stan.org/t/hypothesis-testing-for-gaussian-process/37638)

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**Author:** [@Joyyyyyy](https://discourse.mc-stan.org/u/Joyyyyyy)\
**Replies:** 4\
**Last updated:** [December 24, 2024, 9:05pm UTC](https://discourse.mc-stan.org/t/hypothesis-testing-for-gaussian-process/37638 "2024-12-24T21:05:57Z")

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Hi everyone, I’m new to Gaussian Process Regression and Bayesian methods. I’m curious about how to perform hypothesis testing using predictions from a Gaussian Process. For example, the null hypothesis is that \\hat{f}(x^…

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## [Nonnegative Gaussian Process Regression](https://discourse.mc-stan.org/t/nonnegative-gaussian-process-regression/37682)

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**Author:** [@sonicking](https://discourse.mc-stan.org/u/sonicking)\
**Replies:** 5\
**Last updated:** [December 21, 2024, 3:43pm UTC](https://discourse.mc-stan.org/t/nonnegative-gaussian-process-regression/37682 "2024-12-21T15:43:46Z")

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Have anyone tried a Nonnegative Gaussian Process Regression? If you have, do you have any example code you may share? What I mean is that the output is supposed to be non-negative. I found a paper on this method but i…

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## [How does one do predictive inference with the sum of gaussian processes?](https://discourse.mc-stan.org/t/how-does-one-do-predictive-inference-with-the-sum-of-gaussian-processes/37513)

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**Author:** [@sonicking](https://discourse.mc-stan.org/u/sonicking)\
**Replies:** 6\
**Last updated:** [December 11, 2024, 10:39pm UTC](https://discourse.mc-stan.org/t/how-does-one-do-predictive-inference-with-the-sum-of-gaussian-processes/37513 "2024-12-11T22:39:22Z")

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The manual offers a nice example for a single GP: data { int\<lower=1\> N1; array\[N1\] real x1; vector\[N1\] y1; int\<lower=1\> N2; array\[N2\] real x2; } transformed data { real delta = 1e-9; int\<lower=1\> N = N1 +…

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## [Gaussian Process out-of-sample predictive distribution](https://discourse.mc-stan.org/t/gaussian-process-out-of-sample-predictive-distribution/16891)

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**Author:** [@matthew](https://discourse.mc-stan.org/u/matthew)\
**Replies:** 21\
**Last updated:** [December 6, 2024, 12:03am UTC](https://discourse.mc-stan.org/t/gaussian-process-out-of-sample-predictive-distribution/16891 "2024-12-06T00:03:16Z")

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I’m trying to expand upon a model I built previously by using Gaussian Processes. The data that I have is t-distributed that can be grouped hierarchically and modeled with random effects. In addition, the observations o…

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## [Hilbert space Gaussian process for multiple time series](https://discourse.mc-stan.org/t/hilbert-space-gaussian-process-for-multiple-time-series/37015)

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**Author:** [@Peter.Stewart](https://discourse.mc-stan.org/u/Peter.Stewart)\
**Replies:** 10\
**Last updated:** [November 14, 2024, 10:31am UTC](https://discourse.mc-stan.org/t/hilbert-space-gaussian-process-for-multiple-time-series/37015 "2024-11-14T10:31:14Z")

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Hi everyone, I have been using Gaussian processes to model the north-south migration of GPS-tagged animals over time. Due to the number of observations (from several hundred to several thousand obs. per individual, mean…

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## [Spatial Interdependence and Posterior Predictions in a Gaussian Process model](https://discourse.mc-stan.org/t/spatial-interdependence-and-posterior-predictions-in-a-gaussian-process-model/36310)

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**Author:** [@jkalley](https://discourse.mc-stan.org/u/jkalley)\
**Replies:** 5\
**Last updated:** [August 30, 2024, 10:31am UTC](https://discourse.mc-stan.org/t/spatial-interdependence-and-posterior-predictions-in-a-gaussian-process-model/36310 "2024-08-30T10:31:33Z")

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Hi all, I’m working on a Gaussian Process model, using it to estimate interdependence between observations (military alliances). The challenge is that while most GP applications I can find use the interdependence as a c…

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## [Grid based gaussian process speedup](https://discourse.mc-stan.org/t/grid-based-gaussian-process-speedup/27881)

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**Author:** [@ScottAlder](https://discourse.mc-stan.org/u/ScottAlder)\
**Replies:** 10\
**Last updated:** [July 1, 2024, 11:38pm UTC](https://discourse.mc-stan.org/t/grid-based-gaussian-process-speedup/27881 "2024-07-01T23:38:08Z")

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Hello, I have data sampled on a 2D regular rectangular grid, and would like to use Gaussian process methods for modelling. My data can potentially be very large, so I’d like to use some kind of speedup or approximation…

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## [Generating quantities from Gaussian processes](https://discourse.mc-stan.org/t/generating-quantities-from-gaussian-processes/34412)

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**Author:** [@sonicking](https://discourse.mc-stan.org/u/sonicking)\
**Replies:** 2\
**Last updated:** [March 28, 2024, 2:27am UTC](https://discourse.mc-stan.org/t/generating-quantities-from-gaussian-processes/34412 "2024-03-28T02:27:21Z")

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Hello, the Gaussian Processes chapter in the manual has this example: data { int\<lower=1\> N; array\[N\] real x; vector\[N\] y; } transformed data { vector\[N\] mu = rep\_vector(0, N); } parameters { real\<lower=0\> rho…

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## [Adding multiple multilevel terms and control for areal/genetic bias - everything everywhere all at once?](https://discourse.mc-stan.org/t/adding-multiple-multilevel-terms-and-control-for-areal-genetic-bias-everything-everywhere-all-at-once/34403)

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**Author:** [@Tarotis](https://discourse.mc-stan.org/u/Tarotis)\
**Replies:** 4\
**Last updated:** [March 25, 2024, 4:09pm UTC](https://discourse.mc-stan.org/t/adding-multiple-multilevel-terms-and-control-for-areal-genetic-bias-everything-everywhere-all-at-once/34403 "2024-03-25T16:09:10Z")

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Hi all, I am currently running into problems with my model and the specification of multiple multilevel terms for a very heterogeneous dataset. My main data points are the duration of around 900,000 segments from 51 dif…

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## [Scalable Gaussian process inference](https://discourse.mc-stan.org/t/scalable-gaussian-process-inference/30151)

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**Author:** [@tillahoffmann](https://discourse.mc-stan.org/u/tillahoffmann)\
**Replies:** 27\
**Last updated:** [March 25, 2024, 2:32pm UTC](https://discourse.mc-stan.org/t/scalable-gaussian-process-inference/30151 "2024-03-25T14:32:20Z")

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We (JP Onnela and I) have been working on a library to scale up Gaussian process inference in Stan using two methods: Sparse approximations using directed acyclic graphs to encode which dependencies to retain. The meth…

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## [GP Docs - Predictive Inference for Gaussian Processes Proposals](https://discourse.mc-stan.org/t/gp-docs-predictive-inference-for-gaussian-processes-proposals/16971)

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**Author:** [@anon79882417](https://discourse.mc-stan.org/u/anon79882417)\
**Replies:** 6\
**Last updated:** [February 5, 2024, 12:03pm UTC](https://discourse.mc-stan.org/t/gp-docs-predictive-inference-for-gaussian-processes-proposals/16971 "2024-02-05T12:03:26Z")

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Hey - Users aren’t able to use our documentation easily to implement posterior predictives for GPs, and they’re leaning on other resources. Here are some proposals as to how I’d like to re-write the section “Predictive …

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## [Modelling a timeseries as a 2D field including AR1 noise and smooth seasonal cycle and trend (new to bayes and stan)](https://discourse.mc-stan.org/t/modelling-a-timeseries-as-a-2d-field-including-ar1-noise-and-smooth-seasonal-cycle-and-trend-new-to-bayes-and-stan/32313)

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**Author:** [@ezra\_eisbrenner](https://discourse.mc-stan.org/u/ezra_eisbrenner)\
**Replies:** 2\
**Last updated:** [August 2, 2023, 9:22am UTC](https://discourse.mc-stan.org/t/modelling-a-timeseries-as-a-2d-field-including-ar1-noise-and-smooth-seasonal-cycle-and-trend-new-to-bayes-and-stan/32313 "2023-08-02T09:22:27Z")

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Before I start, hi there Stan community! I’m both new to Bayesian statistics and to Stan, so feel free to comment on anything you think is worth commenting on :) The goal I like to model sea surface temperatures (SST) i…

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## [Bayesian kernel machine regression in Stan](https://discourse.mc-stan.org/t/bayesian-kernel-machine-regression-in-stan/28700)

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**Author:** [@Theresa\_U](https://discourse.mc-stan.org/u/Theresa_U)\
**Replies:** 22\
**Last updated:** [July 19, 2023, 6:58pm UTC](https://discourse.mc-stan.org/t/bayesian-kernel-machine-regression-in-stan/28700 "2023-07-19T18:58:02Z")

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Hi, I am trying to model multipollutant effects of cancer incidences on a county basis with a Poisson regression model that also accounts for spatial correlation. I was planning to do this with a Bayesian kernel machine…

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## [Are exponential GP kernels easier to fit than exp\_quad?](https://discourse.mc-stan.org/t/are-exponential-gp-kernels-easier-to-fit-than-exp-quad/31840)

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**Author:** [@potash](https://discourse.mc-stan.org/u/potash)\
**Replies:** 1\
**Last updated:** [July 3, 2023, 8:18pm UTC](https://discourse.mc-stan.org/t/are-exponential-gp-kernels-easier-to-fit-than-exp-quad/31840 "2023-07-03T20:18:33Z")

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I am finding that while exp\_quad kernel GP models require careful prior specification (see e.g. @betanalpha’s GP tutorial) of the length scale \\rho, my exponential kernel GP models seem to fit fine with very basic constr…

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## [Evaluating a brms model with a Gaussian Process](https://discourse.mc-stan.org/t/evaluating-a-brms-model-with-a-gaussian-process/31721)

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**Author:** [@jgoldberg](https://discourse.mc-stan.org/u/jgoldberg)\
**Replies:** 5\
**Last updated:** [June 14, 2023, 9:21pm UTC](https://discourse.mc-stan.org/t/evaluating-a-brms-model-with-a-gaussian-process/31721 "2023-06-14T21:21:28Z")

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Hi everyone, I’ve spent a good amount of time over the past several months reading and thinking about Gaussian processes. I’m now starting to implement them in some work them I’m doing, modeling time-series of various v…

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## [Lower bound in parameter vector causes GP to have nan values](https://discourse.mc-stan.org/t/lower-bound-in-parameter-vector-causes-gp-to-have-nan-values/30326)

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**Author:** [@AndreasB](https://discourse.mc-stan.org/u/AndreasB)\
**Replies:** 0\
**Last updated:** [February 9, 2023, 3:47pm UTC](https://discourse.mc-stan.org/t/lower-bound-in-parameter-vector-causes-gp-to-have-nan-values/30326 "2023-02-09T15:47:08Z")

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I try to explore the likelihood surface of a Gaussian Process with regard to its parameters. All of this is done with pystan. If I run the following python/Stan code I sometimes get the following error: Informational…

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## [Gaussian processes in Stan: all the transitions of one chain hit maximum treedepth, but none in the other chains](https://discourse.mc-stan.org/t/gaussian-processes-in-stan-all-the-transitions-of-one-chain-hit-maximum-treedepth-but-none-in-the-other-chains/30005)

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**Author:** [@anthony\_462](https://discourse.mc-stan.org/u/anthony_462)\
**Replies:** 3\
**Last updated:** [January 17, 2023, 5:19pm UTC](https://discourse.mc-stan.org/t/gaussian-processes-in-stan-all-the-transitions-of-one-chain-hit-maximum-treedepth-but-none-in-the-other-chains/30005 "2023-01-17T17:19:41Z")

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Hi all, The aim of my Stan model is to capture trends in count data over time. It could for example be the number of weekly deaths in a given population. To do so, I used Gaussian processes (GPs) that capture three diff…

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## [Validating hierarchical GP with SBC](https://discourse.mc-stan.org/t/validating-hierarchical-gp-with-sbc/29858)

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**Author:** [@Lisar](https://discourse.mc-stan.org/u/Lisar)\
**Replies:** 3\
**Last updated:** [January 3, 2023, 5:11pm UTC](https://discourse.mc-stan.org/t/validating-hierarchical-gp-with-sbc/29858 "2023-01-03T17:11:04Z")

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Hi all, I’m trying to validate hierarchical Gaussian process regressions using the SBC package. My real-world dataset is vegetation data, which was collected at many locations within many plots, and I’m interested in est…

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