To complement the example (and Figure 4), we also show in Figure 5 the Markov Chains generated by our code. Notice that we have plotted the width of our 1 σ, 2 σ and 3 σ confidence regions in the same figure.
695 − 0.107 + 0.123, where the upper and lower values for p correspond to the 1 σ standard deviation. Our final result (shown in Figure 4) is a posterior distribution that matches very well with the results calculated analytically (shown in Figure 1). Then, we introduce the MHA in a Python code. We generate a new candidate p c as p c = p c u + G ( p c u, σ ^ ), where G ( p c u, σ ^ ) is our proposed Gaussian distribution centered at p c u with variance σ ^ = 0.1 p c u is the current value of p, for our first step is p c u = p i. As our first guess for p, we consider p i = 0.1. Īs mentioned before, we consider a likelihood given by the binomial distribution ( 18) and a normal distributed prior ( 11) ( a = b = 1). During the same decade, David Schramm heralded the “Golden Age of Cosmology” at a National Academy of Sciences colloquium. It was not until 1990, when the amount of data increased enough to discriminate and rule out compelling theories, that the BB model awarded was the most accepted. In its childhood, cosmology was a speculative science based only on a few datasets, and it was characterized by a dispute between two cosmological models: the steady state model and the Big Bang (BB) theory. Several observations at that epoch established that the size and dynamics of the cosmos could be explained by Einstein’s General Theory of Relativity. This debate was held between the astronomers Harlow Shapley and Heber Curtis, resulting in a revolution for astronomy at that time by reaching an important conclusion: “The Universe had a larger scale than the Milky Way”. The beginning of the standard cosmology as it is known today emerged after 1920, when the Shapley-Curtis debate was carried out.
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