日本欧洲视频一区_国模极品一区二区三区_国产熟女一区二区三区五月婷_亚洲AV成人精品日韩一区18p

代做3 D printer materials estimation編程

時間:2024-02-21  來源:  作者: 我要糾錯



Project 1: 3D printer materials estimation
Use the template material in the zip file project01.zip in Learn to write your report. Add all your function
definitions on the code.R file and write your report using report.Rmd. You must upload the following three
files as part of this assignment: code.R, report.html, report.Rmd. Specific instructions for these files are
in the README.md file.
The main text in your report should be a coherent presentation of theory and discussion of methods and
results, showing code for code chunks that perform computations and analysis but not code for code chunks
that generate functions, figures, or tables.
Use the echo=TRUE and echo=FALSE to control what code is visible.
The styler package addin is useful for restyling code for better and consistent readability. It works for both
.R and .Rmd files.
The Project01Hints file contains some useful tips, and the CWmarking file contains guidelines. Both are
attached in Learn as PDF files.
Submission should be done through Gradescope.
1 The data
A 3D printer uses rolls of filament that get heated and squeezed through a moving nozzle, gradually building
objects. The objects are first designed in a CAD program (Computer Aided Design) that also estimates how
much material will be required to print the object.
The data file "filament1.rda" contains information about one 3D-printed object per row. The columns are
• Index: an observation index
• Date: printing dates
• Material: the printing material, identified by its colour
• CAD_Weight: the object weight (in grams) that the CAD software calculated
• Actual_Weight: the actual weight of the object (in grams) after printing
Start by loading the data and plotting it. Comment on the variability of the data for different CAD_Weight
and Material.
2 Classical estimation
Consider two linear models, named A and B, for capturing the relationship between CAD_Weight and
Actual_Weight. We denote the CAD_weight for observation i by xi
, and the corresponding Actual_Weight
by yi
. The two models are defined by
• Model A: yi ∼ Normal[β1 + β2xi
, exp(β3 + β4xi)]
• Model B: yi ∼ Normal[β1 + β2xi
, exp(β3) + exp(β4)x
2
i
)]
The printer operator reasons that random fluctuations in the material properties (such as the density) and
room temperature should lead to a relative error instead of an additive error, leading them to model B as an
approximation of that. The basic physics assumption is that the error in the CAD software calculation of
the weight is proportional to the weight itself. Model A on the other hand is slightly more mathematically
convenient, but has no such motivation in physics.
1
Create a function neg_log_like() that takes arguments beta (model parameters), data (a data.frame
containing the required variables), and model (either A or B) and returns the negated log-likelihood for the
specified model.
Create a function filament1_estimate() that uses the R built in function optim() and neg_log_like()
to estimate the two models A and B using the filament1 data. As initial values for (β1, β2, β3, β4) in the
optimization use (-0.1, 1.07, -2, 0.05) for model A and (-0.15, 1.07, -13.5, -6.5) for model B. The inputs of the
function should be: a data.frame with the same variables as the filament1 data set (columns CAD_Weight
and Actual_Weight) and the model choice (either A or B). As the output, your function should return the
best set of parameters found and the estimate of the Hessian at the solution found.
First, use filament1_estimate() to estimate models A and B using the filament1 data:
• fit_A = filament1_estimate(filament1, “A”)
• fit_B = filament1_estimate(filament1, “B”)
Use the approximation method for large n and the outputs from filament1_estimate() to construct an
approximate 90% confidence intervals for β1, β2, β3, and β4 in Models A and B. Print the result as a table
using the knitr::kable function. Compare the confidence intervals for the different parameters and their width.
Comment on the differences to interpret the model estimation results.
3 Bayesian estimation
Now consider a Bayesian model for describing the actual weight (yi) based on the CAD weight (xi) for
observation i:
yi ∼ Normal[β1 + β2xi
, β3 + β4x
2
i
)].
To ensure positivity of the variance, the parameterisation θ = [θ1, θ2, θ3, θ4] = [β1, β2, log(β3), log(β4)] is
introduced, and the printer operator assigns independent prior distributions as follows:
θ1 ∼ Normal(0, γ1),
θ2 ∼ Normal(1, γ2),
θ3 ∼ LogExp(γ3),
θ4 ∼ LogExp(γ4),
where LogExp(a) denotes the logarithm of an exponentially distributed random variable with rate parameter
a, as seen in Tutorial 4. The γ = (γ1, γ2, γ3, γ4) values are positive parameters.
3.1 Prior density
With the help of dnorm and the dlogexp function (see the code.R file for documentation), define and
document (in code.R) a function log_prior_density with arguments theta and params, where theta is the
θ parameter vector, and params is the vector of γ parameters. Your function should evaluate the logarithm
of the joint prior density p(θ) for the four θi parameters.
3.2 Observation likelihood
With the help of dnorm, define and document a function log_like, taking arguments theta, x, and y, that
evaluates the observation log-likelihood p(y|θ) for the model defined above.
3.3 Posterior density
Define and document a function log_posterior_density with arguments theta, x, y, and params, which
evaluates the logarithm of the posterior density p(θ|y), apart from some unevaluated normalisation constant.
2
3.4 Posterior mode
Define a function posterior_mode with arguments theta_start, x, y, and params, that uses optim together
with the log_posterior_density and filament data to find the mode µ of the log-posterior-density and
evaluates the Hessian at the mode as well as the inverse of the negated Hessian, S. This function should
return a list with elements mode (the posterior mode location), hessian (the Hessian of the log-density at
the mode), and S (the inverse of the negated Hessian at the mode). See the documentation for optim for how
to do maximisation instead of minimisation.
3.5 Gaussian approximation
Let all γi = 1, i = 1, 2, 3, 4, and use posterior_mode to evaluate the inverse of the negated Hessian at the
mode, in order to obtain a multivariate Normal approximation Normal(µ,S) to the posterior distribution for
θ. Use start values θ = 0.
3.6 Importance sampling function
The aim is to construct a 90% Bayesian credible interval for each βj using importance sampling, similarly to
the method used in lab 4. There, a one dimensional Gaussian approximation of the posterior of a parameter
was used. Here, we will instead use a multivariate Normal approximation as the importance sampling
distribution. The functions rmvnorm and dmvnorm in the mvtnorm package can be used to sample and evaluate
densities.
Define and document a function do_importance taking arguments N (the number of samples to generate),
mu (the mean vector for the importance distribution), and S (the covariance matrix), and other additional
parameters that are needed by the function code.
The function should output a data.frame with five columns, beta1, beta2, beta3, beta4, log_weights,
containing the βi samples and normalised log-importance-weights, so that sum(exp(log_weights)) is 1. Use
the log_sum_exp function (see the code.R file for documentation) to compute the needed normalisation
information.
3.7 Importance sampling
Use your defined functions to compute an importance sample of size N = 10000. With the help of
the stat_ewcdf function defined in code.R, plot the empirical weighted CDFs together with the unweighted CDFs for each parameter and discuss the results. To achieve a simpler ggplot code, you may find
pivot_longer(???, starts_with("beta")) and facet_wrap(vars(name)) useful.
Construct 90% credible intervals for each of the four model parameters based on the importance sample.
In addition to wquantile and pivot_longer, the methods group_by and summarise are helpful. You may
wish to define a function make_CI taking arguments x, weights, and prob (to control the intended coverage
probability), generating a 1-row, 2-column data.frame to help structure the code.
Discuss the results both from the sampling method point of view and the 3D printer application point of
view (this may also involve, e.g., plotting prediction intervals based on point estimates of the parameters,
and plotting the importance log-weights to explain how they depend on the sampled β-values).
請加QQ:99515681  郵箱:99515681@qq.com   WX:codehelp 

標簽:

掃一掃在手機打開當前頁
  • 上一篇:代寫game of Bingo cards
  • 下一篇:代寫PLAN60722 – Urban Design Project
  • 無相關信息
    昆明生活資訊

    昆明圖文信息
    蝴蝶泉(4A)-大理旅游
    蝴蝶泉(4A)-大理旅游
    油炸竹蟲
    油炸竹蟲
    酸筍煮魚(雞)
    酸筍煮魚(雞)
    竹筒飯
    竹筒飯
    香茅草烤魚
    香茅草烤魚
    檸檬烤魚
    檸檬烤魚
    昆明西山國家級風景名勝區
    昆明西山國家級風景名勝區
    昆明旅游索道攻略
    昆明旅游索道攻略
  • NBA直播 短信驗證碼平臺 幣安官網下載 歐冠直播 WPS下載

    關于我們 | 打賞支持 | 廣告服務 | 聯系我們 | 網站地圖 | 免責聲明 | 幫助中心 | 友情鏈接 |

    Copyright © 2025 kmw.cc Inc. All Rights Reserved. 昆明網 版權所有
    ICP備06013414號-3 公安備 42010502001045

    日本欧洲视频一区_国模极品一区二区三区_国产熟女一区二区三区五月婷_亚洲AV成人精品日韩一区18p

              黄色成人片子| 欧美日韩国产综合视频在线观看中文 | 国产色综合久久| 亚洲国产精品成人综合| 久久高清福利视频| 国产精品丝袜白浆摸在线| 夜夜嗨网站十八久久| 欧美jizzhd精品欧美巨大免费| 欧美日韩三级视频| 亚洲激精日韩激精欧美精品| 亚洲一区日韩在线| 欧美人与性动交α欧美精品济南到 | 国产精品免费小视频| 亚洲一区二区黄| 国产精品美女久久久久久久| 欧美成人亚洲成人| 国产精自产拍久久久久久| 国产精品你懂的| 欧美一区深夜视频| 精品91在线| 欧美日韩国产一区| 欧美一级视频一区二区| 亚洲电影激情视频网站| 欧美精品一区二区高清在线观看| 日韩午夜在线| 国产视频一区三区| 欧美电影在线观看| 亚洲在线1234| 99在线精品观看| 国产一级揄自揄精品视频| 欧美精品日韩www.p站| 亚洲砖区区免费| 亚洲国产一二三| 欧美视频四区| 亚洲一区二区三区在线看| 精品不卡一区| 国产午夜一区二区三区| 欧美日韩亚洲一区二区三区| 久久久久久国产精品mv| 亚洲第一天堂无码专区| 国产综合色一区二区三区| 国产精品麻豆va在线播放 | 欧美精品性视频| 欧美一激情一区二区三区| 夜夜嗨av色综合久久久综合网| 精品9999| 在线成人www免费观看视频| 国产午夜精品理论片a级大结局 | 香蕉免费一区二区三区在线观看 | 亚洲视频在线观看网站| 亚洲电影在线播放| 黄色一区三区| 在线观看亚洲精品| 亚洲国产精品嫩草影院| 国产在线拍揄自揄视频不卡99| 欧美色大人视频| 欧美激情麻豆| 国产精品青草久久久久福利99| 免费亚洲视频| 国产精品色午夜在线观看| 欧美日韩成人一区二区| 欧美日韩成人综合| 欧美午夜美女看片| 国产一二三精品| 亚洲国产cao| 一区二区久久久久| 欧美一级网站| 欧美日韩妖精视频| 国产深夜精品| 国产欧美日韩| 亚洲精品国产精品国自产在线| 夜夜爽www精品| 老司机久久99久久精品播放免费 | 国产精品高潮视频| 亚洲欧洲一区二区三区久久| 久久亚洲春色中文字幕| 国产视频一区二区三区在线观看| 中文久久乱码一区二区| 欧美国产视频日韩| 亚洲国产精品第一区二区| 久久国产免费| 伊人精品视频| 欧美极品欧美精品欧美视频| 在线视频成人| 欧美成年人网| 99综合精品| 国产欧美精品在线| 久久午夜羞羞影院免费观看| 黄色亚洲免费| 欧美国产一区视频在线观看| 亚洲精品综合久久中文字幕| 久久国产精品网站| 影音先锋亚洲电影| 欧美三日本三级少妇三2023| 亚洲午夜免费视频| 伊人蜜桃色噜噜激情综合| 欧美成人a视频| 亚洲欧美视频在线观看视频| 国产一区二区av| 欧美激情成人在线视频| 夜久久久久久| 伊人久久大香线| 欧美日韩另类综合| 久久久久久久尹人综合网亚洲| 91久久黄色| 国产精品亚洲视频| 欧美经典一区二区| 久久精品99| 亚洲天堂黄色| 一区二区三欧美| 亚洲国产乱码最新视频 | 国产视频欧美视频| 欧美日本一区| 男女精品视频| 伊人成人开心激情综合网| 国产精品成人免费| 欧美久久久久久久| 久久精品视频在线看| 一区在线视频| 国产一区二区中文| 国产欧美日韩综合一区在线播放| 欧美大片免费观看在线观看网站推荐| 久久精品国产69国产精品亚洲| 亚洲一区二区三区高清| 一区二区三区|亚洲午夜| 亚洲美女在线观看| 亚洲精品国产精品国产自| 亚洲黄色免费电影| 亚洲精品视频在线| 一本色道久久88精品综合| 国产精品99久久久久久久久久久久 | 一二三区精品福利视频| 亚洲一区二区三区色| 午夜视频久久久久久| 久久噜噜亚洲综合| 老司机凹凸av亚洲导航| 欧美理论大片| 国产原创一区二区| 亚洲电影免费观看高清| 一区二区免费在线观看| 午夜欧美视频| 欧美精品videossex性护士| 欧美日韩在线三级| 国产一区二区三区日韩| 日韩视频免费观看高清完整版| 亚洲一区二区视频| 欧美韩日一区| 国产日韩专区在线| 伊人成人在线视频| 亚洲一区二区三区三| 久久露脸国产精品| 国产精品免费视频xxxx| 亚洲电影免费在线 | 久久国内精品自在自线400部| 欧美成年人网站| 伊人成人开心激情综合网| 亚洲综合日韩在线| 欧美日韩午夜视频在线观看| 亚洲激情视频在线| 久久婷婷av| 伊人蜜桃色噜噜激情综合| 久久成年人视频| 国产主播一区二区三区| 欧美在线综合| 黄色日韩网站视频| 久久久久久久波多野高潮日日| 国产精品剧情在线亚洲| 在线一区二区三区做爰视频网站| 欧美视频在线免费看| 亚洲欧美日韩一区在线观看| 国产日本欧美一区二区| 久久精品欧美日韩| 伊人精品在线| 欧美日韩国产成人高清视频| 一区二区三区国产精华| 国产日产精品一区二区三区四区的观看方式| 一区二区三区欧美成人| 国产精品一区二区视频| 久热精品视频在线免费观看| 日韩一区二区免费看| 国内成+人亚洲+欧美+综合在线| 久久精品在线观看| 亚洲美女一区| 在线成人亚洲| 国产精品欧美久久| 欧美另类videos死尸| 欧美在线视频a| 亚洲桃色在线一区| 在线精品视频一区二区| 国产精品理论片| 欧美成人午夜剧场免费观看| 亚洲欧美日韩在线观看a三区 | 国产日韩欧美不卡在线| 欧美日韩国产二区| 欧美福利视频| 可以免费看不卡的av网站| 亚洲自拍偷拍福利| 亚洲午夜国产一区99re久久| 亚洲精品网站在线播放gif| 狠狠入ady亚洲精品经典电影|