Billy Nisbett

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on the atlas — 6

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One example of this is in survival analysis, where time-to-event data is modeled using probability densities that are designed to accommodate censored data. An exponential survival function, where c=0 denotes failure (or non-survival), is defined by: f(c,t)={exp⁡(−λt),if c=1λexp⁡(−λt),if c=0 Such a function can be implemented as a PyMC3 distribution by writing a function that specifies the log-probability, then passing that function as an argument to the DensityDist function, which creates an instance of a PyMC3 distribution with the custom function as its log-probability. For the exponential …
Probability Distributions in PyMC3 — PyMC3 3.11.5 documentation
with pm.Model() as mdl_fish: # define priors, weakly informative Normal b0 = pm.Normal("Intercept", mu=0, sigma=10) b1 = pm.Normal("alcohol", mu=0, sigma=10) b2 = pm.Normal("nomeds", mu=0, sigma=10) b3 = pm.Normal("alcohol:nomeds", mu=0, sigma=10) # define linear model and exp link function theta = b0 + b1 * mx_ex["alcohol"] + b2 * mx_ex["nomeds"] + b3 * mx_ex["alcohol:nomeds"] ## Define Poisson likelihood y = pm.Poisson("y", mu=np.exp(theta), observed=mx_en["nsneeze"].values)
GLM: Poisson Regression — PyMC3 3.11.5 documentation
A less limited view of power sees it as an expression of the risk curve for a 0-1 loss function. A Bayesian analysis integrates that risk over the prior probability. However, good Bayesian analyses consider the sensitivity of their results to the choice of prior distribution. That would seem to place us right back into the domain of power analysis. Although it might not go by that name and would be computed differently, the purpose would be the same: namely, determining how large a sample to obtain in order to be reasonably sure of meeting the study objectives.
Is power analysis necessary in Bayesian Statistics? - Cross Validated
I disagree with Srikant's answer on one fundamental point. Srikant stated this: "Inference Problem: Your inference problem is: What values of θ are reasonable given the observed data x?" In fact this is the BAYESIAN INFERENCE PROBLEM. In Bayesian statistics we seek to calculate P(θ| x) i.e the probability of the parameter value given the observed data (sample). The CREDIBLE INTERVAL is an interval of θ that has a 95% chance (or other) of containing the true value of θ given the several assumptions underlying the problem. The FREQUENTIST INFERENCE PROBLEM is this: Are the observed data x reason…
bayesian - What's the difference between a confidence interval and a credible interval? - Cross Validated
Credible intervals capture our current uncertainty in the location of the parameter values and thus can be interpreted as probabilistic statement about the parameter. In contrast, confidence intervals capture the uncertainty about the interval we have obtained (i.e., whether it contains the true value or not). Thus, they cannot be interpreted as a probabilistic statement about the true parameter values.
bayesian - What's the difference between a confidence interval and a credible interval? - Cross Validated