Consider a Bayesian agent attempting to discover a pattern in the world. Upon observing initial data d0d_{0}, they form a posterior distribution p(h|d0)p(h|d_{0}) and sample a hypothesis h∗h^{*} from this distribution. They then interact with a chatbot, sharing their belief h∗h^{*} in the hopes of obtaining further evidence. An unbiased chatbot would ignore h∗h^{*} and generate subsequent data from the true data-generating process, d1∼p(d|true process)d_{1}\sim p(d|\text{true process}). The Bayesian agent then updates their belief via p(h|d0,d1)∝p(d1|h)p(h|d0)p(h|d_{0},d_{1})\propto p(d_{1}|h)p(h|d_{0}). As this process continues, the Bayesian agent will get closer to the truth. After nn interactions, the beliefs of the agent are p(h|d0,…dn)∝p(h|d0)∏i=1np(di|h)p(h|d_{0},\ldots d_{n})\propto p(h|d_{0})\prod_{i=1}^{n}p(d_{i}|h) for di∼p(d|true process)d_{i}\sim p(d|\text{true process}). Taking the logarithm of the right hand side, this becomes logp(h|d0)+∑i=1nlogp(di|h)\log p(h|d_{0})+\sum_{i=1}^{n}\log p(d_{i}|h). Since the data did_{i} are drawn from p(d|true process)p(d|\text{true process}), ∑i=1nlogp(di|h)\sum_{i=1}^{n}\log p(d_{i}|h) is a Monte Carlo approximation of n∫dp(d|true process)logp(d|h)n\int_{d}p(d|\text{true process})\log p(d|h), which is nn times the negative cross-entropy of p(d|true process)p(d|\text{true process}) and p(d|h)p(d|h). As nn becomes large the sum of log likelihoods will approach this value, meaning that the Bayesian agent will favor the hypothesis that has lowest cross-entropy with the truth. If there is an hh that matches the true process, that minimizes the cross-entropy and p(h|d0,…,dn)p(h|d_{0},\ldots,d_{n}) will converge to 1 for that hypothesis and 0 for all other hypotheses.
（四）转让或者出租与纳税人机构所在地不在同一县（市、区、旗）内的不动产；
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Two months ago, Aston Villa were just three points off top spot in the Premier League. They were on a run of 12 wins in 14 games that included victories against Manchester City and Arsenal. Their run of eight consecutive wins in the league was their best since they won 10 in a row in 1910. You wouldn’t have blamed Villa fans for daring to dream about lifting their first league title since 1981.
，这一点在体育直播中也有详细论述
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