Statistics-lab™可以为您提供uio.no STK4021 Bayesian Analysis贝叶斯分析课程的代写代考和辅导服务！
STK4021 Bayesian Analysis课程简介
- Bayesian inference: This refers to the process of updating prior beliefs or probabilities based on new data or evidence. In Bayesian inference, probabilities are treated as subjective degrees of belief rather than objective frequencies.
- Advanced Monte Carlo methods: Monte Carlo methods are a class of computational algorithms that use random sampling to obtain numerical solutions to complex problems. Advanced Monte Carlo methods, such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC), are commonly used in Bayesian inference to simulate from complex posterior distributions.
- Asymptotic theories: Asymptotic theories provide a framework for understanding the behavior of statistical procedures as the sample size approaches infinity. In Bayesian inference, asymptotic theories can be used to derive the properties of Bayesian estimators and hypothesis tests.
- Adaptive methods: Adaptive methods refer to techniques that adjust the model or algorithm based on the data at hand. In Bayesian inference, adaptive methods can be used to select the appropriate prior distribution, adjust the tuning parameters of MCMC algorithms, or perform model selection.
- Bayesian nonparametrics: Bayesian nonparametric models are a class of models that can accommodate complex data structures without specifying a fixed parametric form. Bayesian nonparametric models are flexible and can handle a wide range of data types, such as count data, categorical data, and functional data.
PREREQUISITES
Here is a tentative course outline with weight in parentheses:
- Methods (1/2): nonparametric Bayes such as Gaussian process, Dirichlet process, Chinese restaurant process, Mixture models, Introduction to asymptotic theory, and variable selection
- Computation (1/3): advanced MCMC such as sequential Monte Carlo, variational methods, convergence assessment, approximation method, and statistical efficiency.
- Application (1/6): selected areas such as machine learning, structural biology, biomedical research (such as brain connectome, neuroimaging), etc.
STK4021 Bayesian Analysis HELP（EXAM HELP， ONLINE TUTOR）
Step 1: When we know that the defendant has been charged and brought to trial, both the probability of “Verdict” = “Guilty” and the probability of “guilty” $=$ “Yes” increase, as shown in Figure 16.20 (this also reflects the empirical knowledge that most defendants brought to trial for a serious crimes are eventually found guilty – the UK figure in 2011 was $81 \%$ ).
Step 2: We hear that the jury Verdict = “Innocent” (Figure 16.21). Note that the probability of not guilty jumps to $92.59 \%$.
Step 3: Now we discover that the defendant has a previous conviction for a similar crime, so enter “Yes” in that node, as in Figure 16.22. The probability of “not guilty” does not decreaserather, it increases slightly to $94.97 \%$. There is also a small decrease in the probability of the hard evidence. Essentially, the fact that the defendant was charged in the first place is explained away more by the previous conviction than the evidence. It can be shown that the fallacy “holds” for a wide range of sensitivity.
Suppose we know the following:
Fact 1 : item $\mathrm{X}$ was found at the crime scene that is almost certainly linked to the crime. Fact 2 : item $\mathrm{X}$ could belong to the defendant.
Fact 3: despite many public requests (including, e.g., one on the BBC Crimewatch UK program) for information for an innocent owner of item $\mathrm{X}$ to come forward and clear themselves, nobody has done so.
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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