of MH and SMC is known as the particle Metropolis-Hastings (PMH) algorithm [@AndrieuDoucetHolenstein2010]. The MH acceptance probability depends on the intractable likelihood, which in PMH is estimated using SMC (see Section \[sec:overview\]). Despite the apparent approximation, this results in an algorithm that targets the correct posterior distribution [@AndrieuDoucetHolenstein2010]. The original PMH algorithm makes use of a marginal proposal for $\theta$, i.e. only the current parameter is used when proposing a new parameter. The theoretical properties of the marginal PMH algorithm have been analysed in @AndrieuVihola2012 [@PittSilvaGiordaniKohn2012; @DoucetPittKohn2012] and it has been applied for a number of interesting applications in, e.g., economics, social network analysis and ecology [@FluryShephard2011; @Everitt2012; @GolightlyWilkinson2011].

In this paper, we show that information such as the gradient and the Hessian about the posterior can be included in the construction of the PMH proposal. This idea is first suggested by @DoucetJacobJohansen2011 in the discussions following @GirolamiCalderhead2011. In two previous proceedings, we have applied and extended this idea with gradient information [@DahlinLindstenSchon2013a] and also using Hessian information [@DahlinLindstenSchon2014a]. The present article builds upon and extends this preliminary work. A PMH method using gradient information similar to @DahlinLindstenSchon2013a has recently been proposed by @NemethFearnhead2014.

In the context of MH sampling, 