Metaphysical Rationalism

Material from this paper appears in Chap. 7 of my book Reason and Being, but there is also stuff here that isn't in the book. In particular, it discusses the claims that, for Spinoza, conceiving implies explaining and that existence is identical to or reducible to conceivability. So, if you're interested in those issues, this paper might be worth a read

Memory and Personal Identity in Spinoza

Locke is often thought to have introduced the topic of personal identity into philosophy when, in the second edition of the Essay, he distinguished the person from both the human being and the soul. Each of these entities differs from the others with respect to their identity conditions, and so they must be ontologically distinct. In particular, Locke claimed, a person cannot survive total memory loss, although a human being or a soul can

A new model to predict weak-lensing peak counts II. Parameter constraint strategies

Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analyses. In this work, we explore and compare various strategies for constraining parameter using our model, focusing on the matter density $\Omega_\mathrm{m}$ and the density fluctuation amplitude $\sigma_8$. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique which makes a weaker assumption compared to the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. We find that neglecting the CDC effect enlarges parameter contours by 22%, and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in an excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.Comment: 15 pages, 11 figures. Accepted versio